The current status of charm

T H E C U R R E N T STATUS O F C H A R M R. J. C A S H M O R E

Nuclear Physics Laboratory, Oxford University, KebIe Road, Oxford OX1 3RH, U.K.

CONTENTS L ~NTRODUCTION 1.1. The need for charm 1.2. The resolution of the problems "Thecharm quark 1.3. The charm quark in hadrons 1.4. Production of charm quarks 1.5. The observation of charm and its subsequent study 2. MESONSCONTAININGCHARMQUARKS 2.1. The spectrum of mesons 2.2. Charm = 0 mesons--Hidden charm 2.3. Charm = _+i mesons--Open charm 3. BARYONSCONTAININGCHARMQUARKS 3.1. The spectrum of baryons 3.2. The observations of charm baryon states 3.3. Summary and comments 4. MODELS OF MESONSCONTAININGCHARMQUARKS:MASSES,TRANSITIONSAND PRODUCTION MECHANISMS 4.1. The C = 0 cgmesons--The charmonium model 4.2. The confrontation of the charmonium model with the data 4.3. The C = +_1 mesons--Models and data 4.4. Above the charm threshold 4.5. The strong and electromagnetic properties of the charm quark 5. THE WEAK [NTERAC~['IONSOF THE CHARM QUARK

5.1. The V-A nature of the current 5.2. The weak current and its quark structure 5.3. The strength of the interaction 5.4. Summary 6. HADRONIC,PHOTO-AND ELECTROPRODUCTIONOF CHARM 6.1. Hadronic production of~'s 6.2. Hadronic productio~ of charm 6.3. Photoproduction of ~ and charm 6.4. Muon and electroproduction of the ~kand charm 6,5. Summary 7. CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

225 226 227 229 231 233 235 236 239 251 260 260 263 268 269 269 273 279 282 285 285 286 287 294 295. 295 295 298 298 3oo 302 302 3o2 303

1. I N T R O D U C T I © N I n t h e c u r r e n t v i e w o f p a r t i c l e p h y s i c s t h e f u n d a m e n t a l c o n s t i t u e n t s o f m a t t e r are t h e q u a r k s (1) a n d l e p t o n s . T h e l e p t o n s (e, #, z) c a n b e o b s e r v e d b u t t h e q u a r k s r e m a i n c o n f i n e d w i t h i n t h e h a d r o n s . T h e e v i d e n c e for t h e e x i s t e n c e o f t h e s e s p i n ½ p a r t i c I e s , d e r i v e d f r o m 225

226

R.J. Cashmore

the spectroscopy of known particle states and the deep inelastic scattering of electrons and neutrinos from nucleons is overwhelming. However, it was the observation of hadrons containing a new quark, the charm quark c, which finally confirmed this view. The enormous number of hadronic states can be simply explained by postulating the existence of five flavours of q u a r k - - u ( Q = 2/3), d(Q = - 1/3), s(Q = - 1/3), c(Q = 2/3), b(Q = - 1 / 3 ) from which they are constituted. Mesons are quark antiquark (qq) systems and baryons three quark (qqq) systems/2~ However, this scheme is not without its complications and a further degree of freedom, colour, {3) is necessary in order to arrange the correct wavefunctions for baryons and account for the large cross-section for the production of hadrons in e+e - annihilation3 #~ Each quark then appears in three varieties, often called red, yellow and blue. The non observation of free quarks is then summarized in the d o g m a of colour confinement--no state explicitly carrying colour (e.g. the quark) can be observed. These leprous and quarks experience the weak and electromagnetic interactions, which are united in current gauge theory approaches and mediated by the exchange of vector b o s o n s - - t h e 7, W +- and Z °. However, the strong, cotour force is experienced only by the quarks and is mediated by the exchange of zolour vector gluons. The electroweak interaction is described within an SU(2)x U(1) gauge group {s} and the strong interaction within an S U(3) (6~ gauge group. All particles lie in representations of these groups. This review deals with the charm quark. [ts observation and its properties were of fundamental importance in the creation of this framework.

12t. The ~eed for c h a r ~ The specific need for charm was mainly due to the apparent suppression of strangeness changing weak neutral currents embodied in the results (7} F ( K [ --, ~ % , - ) F ( K [ --+ all)

10- 8

F(K +- ~ r r - + e + e - )

= {2.6 _+0.5) x 10- v

F(K +- --+ all)

(1.1.1)

F(K ± -~ r~-+v~) < 0.6 x 10 -6 F(K -+ --+ all)

MK~--I-V2tK~} =

0.7 X 1O - 1 4 .

These strangeness changing weak neutral currents might have been expected, since the existence of the charge-changing weak current d~ = q?v½(1-Ts}r+q

= qL°/~T+_qL

(t.t.2}

implies, within unified theories, ~5) the existence of the current J~o = q p / T o q L

(~.~.3)

To = [g+, TA.

(1.:.4)

with equal strength Gv, so that

The Current Status of Charm d K°

227

Wu

v

W÷ Fig. 1. Second order charged current transition leading to K ° ~ / ~ + / ~ .

Here T_+ change the electric charge of participating quarks by _+ 1 unit and To leaves the charge unchanged, qL (=½(1-75)q) is the left handed component of the quark field. The charged current is known to have the Cabibbo form (8~ (with 0 ~ 0.25) J"+ = @~½(1 - 75) (dcos 0r + s sin 0c) + ...

(1.1.5)

which would lead to a neutral current d"o = £?"½(i-T5)dsinOccosOo+ ...

(1.t.6)

resulting in AS = 1 neutral interactions of order GF. However, the suppression implied by the observed rates (1.1[.1) is much greater than that expected from (L1.6), the transitions being even weaker than those calculated from the 2nd order charged current transitions of the type of Fig. 1. There is a further technical problem within gauge theories associated with the existence of the triangle anomalies of Fig. 2 which spoil the renormalizability of the gauge theory. (9) This problem can be avoided within the S U(2) x U(1[)gauge theory by requiring that

2Q: =

0

(~.1[.7)

where the sum is taken over all elementary fermions, the leptons and the quarks. Before the observation of the charm quark this equality was net satisfied leptons" Q~ + Q~ = - 2 quarks:

~

(i. 1[.8)

Q,+Qd+Q,=O.

colour

Thus a clever way had to be found to avoid alI of these difficulties. o2° The resolution of the proNe~ns--The charm e~ark The method proposed to solve these dlfficuIties, the GIM mechanism, (1°) was the introduction of a new quark--the charm quark. This new spin ½ quark would carry a new quantum number, charm (C), have charge 2/3 and a left handed weak coupling to the orthogonat Cabibbo combination ( - d s i n O ~ + c c o s O c ) of strength Go. Thus the weak

A

f

Fig. 2. The Anomalous Triangle diagram of gauge theories. V and A represent vector and axial currents and f a n elementary fermion.

228

R.J. Casbmore

charged current would be written d~r = ~ 7 ~ ½ ( 1 - 7 5 ) ( d c o s O c + s s i n O c ) + 6 7 ~ ½ ( 1 - T s ) ( - d s i n O c + s c o s O c )

(1.2.i)

= @~½(1-75)d'+eTn½(1-ys)s'

(t.2.2)

= ~c? ~ d'L + 8c7~s'c

(1.2.3)

where we have introduced the notation d' = dcosO~+ssinO~ s' = - d sin 0c + s cos 0~

(1.2.4)

i.e. the Cabibbo rotated quark states. Equation (1.2.2) then demonstrates that the quark multiplets in terms of S U(2) × U(1) representatSons are , , d')L S'

CR' sR'

(1.2

5)

and the weak charged currents cause transitions within the multiplets of left handed quarks white ~.lg~t handed quarks are impotent. Furthermore in the Cabibbo entranced weak transitions (i.e. c -~ s) the selection rule AC = AS = AQ is apparent in analogy with "&e famiIiar AQ = AS rule for weak decays of strange particles [as summarized in the first term of eqn. (1.2.1)3. The transitions to strange quarks are favoured over transitions to down quarks by a factor ~ cot 2 0c (~ 16). The postulate of the charm quark solves the problems summarized in Section 1.1 in the foliowing ways. (i) N o flavour changing neutral currem The commutator (1.1.4) would now imply a neutral current of the type Jo~ = &,~'~(1 -~,~)d' + ~'7~½(1 - 7~)s'

(~.2.6)

which, suppressing the 7 matrices, becomes Jo" : d' d' +,~'s' = dd+ss

(12.7)

(1.2.8)

by using expression (1.2.4). Thus there are no flavour changing neutral currents, i.e. no d to s quark transitions. (ii) Suppression of second order charged current transitions The diagram of Fig. 1 is no longer the only contribution to K~-~/t+/~ -. A further diagram, including the charm quark, has to be added, so that the amplitude is given by the addition of the processes in Fig. 3. Diagrams (a) and (b) toad to amplitudes Aia)~ sin 0 cos 0 (~ ~i~,,) A(b):~--sinOcosO ~ )

(1.2.9) (i.2.10)

d

The Current Status of Charm d

W-

W ÷

229 W-

~

W ÷

(b)

(a)

Kig. 3. Contributions to K ° ~ # ÷ # - decay from intermediate up and charm quarks.

so that the total amplitude is Atot0~ sin O cos

t ~ z ;~4u

~ZF~c) .

(~.2.] [)

A cancellation can occur in this amplitude, suppressir~g this second order charged current transition. Clearly, if m~ = m. the cancellation would be complete while if m~ ~ oo the previous analysis would hold. Thus this transition; together with the other results (].].i), set a iinlit on the charm quark mass ~*t~ of

M~ ~< 1.5 GeV. (iii) Triangle anomalies The relation (1.1.7) is dearly satisfied by including the charm quark with the u, d, s quarks and the e, # leptons leptons: Qe + Q, = - 2 quarks:

~

Q,+Qe+Qc+Qs= 2

(t.2.t2)

colour

i.e. Zf Qz = O. However, the discovery of the z ]epton (12) has once again invalidated this equaIity and Nrther quarks (b, t) are expected to redress this difficulty, the b quark having already been observed (i 3) Thus the properties of this new quark am very specific: (1) new quantum number, charm, in hadronic states; (2) charge 2/3; (3) spin ½; (4) ( V - A ) weak currents; (5) the strength of its weak interaction is Go; (6} it undergoes charged current weak transitions to the Cabibbo quark composition

(-dsinO~+scosO~); (7} there are no flavour changing, i.e. (c --, u, s --, d) weak neutral current transitions. Experiments of the last 5 years have investigated each of these properties and it is now possiNe to check them in detail. .3. T h e c h a r m quark ~m barrens

In present models the quarks are confined within hadrons, so that in order to identify the new charm quark new hadrons must be observed which contain this quark, i.e. new mesons and baryons should exist. ~1.~

230

R.J. Cashmore

Mesons. Two classes of new mesons are expected:

(i) c( states, tn this case the mesons do not carry the new charm quantum number and are known as hidden charm states. (ii) cq and (q states. ]In these mesons q = u, d, s - - o n e of the old q u a r k s - - a n d C = +_ 1 is carried by the meson. These are open charm states. Baryons. For baryons, composed of 3 quarks, C = + 1, + 2, + 3 states are possible depending on the number of charm quarks included, i.e. all states carry the charm quantum number.

Some of the low lying states can have the remarkaNe properties discussed below: (i) Narrow high mass states If the mass of the lowest cC states is such that Mce < 2M~q

(i.3.1)

then the Zweig rule {1) allowed transition of Fig. 4 is forbidden. An alternative mechanism must be introduced to atlow this state to decay strongly. This mechanism is the annihilation

Fig. 4. The decay o f a cdmeson allowed by the Zweig rule.

of the c( system into gluons (15~ (as in Fig. 5), which is expected to be suppressed compared with the Zweig allowed decays leading to a narrow width. (ii) Long lived high mass mesons The lowest lying e~ (dq) states, cannot decay either hadronically or electromagnetically, since these interactions conserve the new quantum number. This implies that the decay must occur via the weak interaction, so that these states have long lives. Because of the structure of the weak current [eqn. (1.2.1)], the decay of the charm quark witl lead preferentially to a strange quark, resulting in a high proportion of the decays containing a strange meson, e.g. (1.3,2)

D+(cd) -+ K-rc+'a + c

q q Fig. 5. The decay of a d" = i cd meson via intermediate gluon systems.

The Current Status of Charm

23 i

Furthermore, the observation of a narrow state in K - n +n + systems implies charm, since it is impossible to construct a conventional (qq) meson carrying Q = + 1 and S = - 1 with the u, d and s quarks alone° Knowing the strength and form of the interaction it is possible to estimate the lifetime of the new quark (~4,~m and hence that of the hadrons containing it. These arguments lead to a charm particle lifetime z(charm) ~ few x 10-13 sec

(1o3.6)

(iii) Long lived high mass baryons Similar arguments to those in (ii) lead to the existence of long lived narrow baryon states with lifetimes ~ t0-13 sec. 11.4o Pre~ctfiee ef eElarm quarks F r o m the explicit weak and electromagnetic properties of the charm quark, reasonable predictions can be made for production mechanisms by these interactions. (~*) However, estimates of their production via strong interactions are difficult (14) in the absence of specific models, but their observation might be expected in highly inelastic interactions. (i) Weak production C h a r m production can be expected and estimated in v reactions via the mechanism of Fig. 6, which apparently leads to AQ = - A S transitions, when only the final s quark is

Fig. 6. Charm quark production in v reactions.

observed (e.g. in a K meson). This would then violate the AQ = AS rule of the light quark sector (see Section 1.2). The Cabibbo favoured transition from the strange quark only occurs from sea quarks in the target nucleon and hence the production will be suppressed. (~7)

(ii) Electromagnetic production Since the charm quark has charge its coupling to the electromagnetic current is specified, being proportional to Qc = 2/3, and its production can be expected in both photoproduction and e + e - annihilation. In the latter case the reaction occurs via the mechanism of Fig. 7 where the charm quarks may be either bound within a c( meson or part of a continuum final state, e.g. (cq)+ (q(), providing Ecr~ > 2mc4. Indeed, far above the charm

232

R. J. Cashmore

Fig. 7. Charm quark production in e+e - annihilation.

meson threshold the value of R, the ratio of the e+e hadroMc annihilation cross-section to the ~+/~- cross-section, can be expected to increase by AR = 3 x (2/3) = = 4/3

(1.4.~)

where the factor of 3 is due to colour. (iii) Hadronic production A variety of mechanisms are possible: (a) (b) (c) (d)

q~ annihiiation to a photon with subsequent coupling to cd; q~ direct (Zweig disallowed) coupiing to cC; cd scattering, the charm quarks originating from the hadron seas:; g# scattering to cC, the gluons lying in the hadron sea.

Although charm production is expected in these inelastic reactions predictions are difficult'l 4) and imprecise.

BO-2¢2 Events~

b~

70 N

6O 5O

g 4O 8 E Z

3O 2O 1olrl_

2.5

n o

2,75 3.0 3.25 3.5 me.o- (GeV/c 2)

Fig. 8. The J/'~ discovery in pp interactions, observed in the e+e - decay n~ode.

The Current Status of C h a r m

233

]1o5. The ehservat~o~ of charm a~d its s~bsequeat s t ~ y ]n October t974 two spectacular observations were a~nounced: (a) A state of mass ~3.1 GeV, called the J, was observed in the e+e - final state in coIlisions (~8~ (Fig. 8) pp ~

pp

(1.50i)

e+e - + ...

(b) A n a r r o w resonance at 3.090 GeV, n a m e d the ¢, in the reaction ~19) e+e

~ hadrons

(1.5.2)

leading to an increase in cross-section of the order of 100 (Fig. 9). 10000 -~ e+ e=-~ hadrons

% e

/

1000

o o

o

C

{

{ {{

I00

+

1

3.088

3.096

n

I

3.10/~

gc.m. (SeV)

Fig. 9. The discovery of the ~ in the total hadronic annihilation cross-section in e+e - reactions in the vicinity of 3.1 GeV. In both cases the widths were consistent with the experimental resolution. A little later another n a r r o w state, the ~,', was observed ~2°) in e+e - annihilation at a mass of 3.585 GeV. Since previous observations of / ~ - / ~ production (21) and AS = - A Q (22) events in v,'~ reactions were consistent with the charm hypothesis, these states were widely believed to be the c e m e s o n s of 1.3 although other interpretations were possible. (23) However, further information was quickly accumulated, particularly from e + e - annihilation, confirming the presence of this new quark, the charm quark: (i) 7-ray transitions from the ¢ ' to other states in between the ~ and ~' were observed~24); (ii) a threshold identified in the e+e - total cross-section at energies greater than 3.8 GeV which also possessed resonant tike structure ¢=s) (Fig. 10); and then finally

R. J. C a s h m o r e

234 I

I

i

I

I

U

t-~!

8-

6 R

t 2

0 --n 0

I

I

i

I

~

I

2

3

~

5

g

?

Ec.m. ( GcV)

8

Fig. 10. The ratio, R, of the e+e hadronic annihilation cross-section to the H+# - cross-section. The threshold in the region of 4 GeV corresponds to charm meson production.

BOO I

,

,

,

~

re*-K~

,

~ 6001% %

o

.N,r"

,

Ol E,

I

I

=

a

u

K+~'T'~ ± n ;

300

oE

~J 200 •~

I 0C

1.6

n i i

mnvariant

l~B

21.0

2.2

N a s s {GeV/c 2 )

K + n + mass spectram. (b) K - n+ +- mass Fig. 11. The first observations of the D meson. (a) The unwelghted ' spectrum weighted by the probability of one of the tracks being a K. (c) The K n + n - n + mass spectrum again weighted by the probability that one of the tracks is a K.

The Current Status of Charm

235

100 K-~~ T ~ ; (Exotic) Ec.m. = 4-03 GeV

80 >

:E

tt+t4t+t++ t o

6C

.£

.el

os

(D

4c

t;

z= 2o

01~-6

r

1.8 2,0 Invariant Mass (OeV / c 2 )

2.2

Fig. !2. The D meson in the exotic channels K-+~=Tz;. No peak is seen in the corresponding r~on exotic channels K ±7c±7z--"

(iii) a narrow meson, the D meson, was discovered (26l at a mass of 1.875 GeV decaying into Krr arid KTr~zfinal states (Figs. 11 and !2). Since those earty days information has continued to accumulate to such an extent that the charm quark might now almost be said to have passed into the realm of'otd quarks'. With the mass of information now accumulated the G I M hypothesis can be confronted in detail and the charm quark systems even used as a laboratory for t~ae study of strong, electromagnetic and weak interaction. (27- 29) tn this review Sections 2 and 3 deal with the observation of mesons and baryons containing charm quarks, and the associated spectroscopies and decays. Xn Section 4 models of the strong and electromagnetic characteristics of the charm are compared with the data while Section 5 deals with the weak interactior.s. Sectiort 6 summarizes the status of hadronic production of the ~ family which in general throws more light on hadronic structure than on charm itself. Finally, Section 7 summarizes the status and open questions of charm. Many of the points dealt with in these sections find a parallel in the discussion of the more recently discovered and even heavier, b, quarks. (2s~ Indeed tee initial observation of charm in e +e- annihilation was confused by the production of the new heavy lepton ~(~2) which was the precursor of new quarks. Perhaps many of the questions left unresolved in the study of charm quarks may find answers in the detailed study of the i', 7', 7" and 7"' systems and the associated open bottom particles.

2. M E S O N S C O N T A I N I N G C H A R M Q U A R K S The study of mesons containing charmed quarks has, to date, been the major source of information on the charm quark. Before discussing the experimental evidence for these states and their decays the expectations are summarized in the following section.

236

R.J. Cashmore 2.1. The spectrum of mesons

Mesons are constructed from a q~ system. (2'3°)

Colour Confinement requires the qq system to be a singlet state in the S U(3) c d o u r - - i . e , if the three colours are represented by R, Y and B then the colour wavefunction would correspond to 1

co our - ./3

+

+ss}

- - t h e singlet in the combination 3x3=1+8.

(2ol.2)

C

U

S

Fig. 13. The 4 representation of S U(4) in which the u, d, s and c quarks lie.

S U(4), S U(3)

and quark structure

Four quarks of similar mass and strong interactions independent of their flavour might lie in the 4 representation of S U(4) shown in Fig. 13. Mesons, constructed as above, then also lie in representations of S U(4} given by 4x2~ = 1+15.

(2.1.3)

These 16 states are shown in Fig. 14, together with their quark content and the SU(3) composition of the multiplet. There are 3 states with identical quantum numbers, Z = g = C = 0. The composition of these states is 1:q51 =

l~(u~2+dd+sg+c~) ,/4

15: ~b~s = ~1~ ( u ~ + d d - 2 a g )

(2.i.4)

,/6 q~ s -

1

( u a + d d + sO- 3cO).

However, the S U(4) is extremely badly broken. The charm quark mass is much greater than the u, d, s masses ~11} so that the S U(4) symmetry is only vestigial and it is clearer to

The Current Status of Charm c

237

F÷(c~)

ffd) D ~

~

D~ (2u)

F-(~s)

Fig. 14. The quark content of the 16 plet of S U(4).

discuss the states in terms of their SU(3) or even just quark contents. The expected = Y = C = 0 states then become ~¢~

4)1 = ~ (u~+dd) 42 ~---SS

(2A.5)

with 4)s being much heavier than the other two and lying in an SU(3) singlet. Mesons containing one charm quark are much heavier than their counterparts containing only light quarks, although lighter than the cd states. These mesons, which contain the charm quark, lie in the 3 and 3 representations of S U(3). Thus it is natural to consider the cd system ~31~ (the charmonium system) and the cq system quite separately, although the spectrum of states will be similar.

Angular momentum, parity and charge conjugation jPc ~f a non relativistic model of these heavier quark systems is appropriate then the yPc values can be constructed as follows S = 9, 1--the spin state of the qc] system J --- L + S--where L is the orbital angular m o m e n t u m P = ( - 1 ) L+I C = ( - 1) L+s The resulting states are summarized in Table 1.

238

R. J. Cashmore T a b ! e 1. d P c a n d s p e c t r o s c o p i c n o t a t i o n of systems Spectroscopic notation

jec

0

1S o

0- +

1

3S 1

1- -

0

1P 1 3p 0

1+ 0++

L

S

0 ]

1

0

2

1

31° 1

1 ++

3p2

2 ++

1D a 3D t 3D 2 3D a

2 123

qq

+ -

etc.

tn potential models there is a further degree of excitation possible in the radial part of the wave function. Thus these angular momentum states can be repeated as radial excitations and are denoted by n, 2s+ 1Lj where n gives the degree of radial excitation. We expect the states of Fig. 14 to be repeated with these different angular momentum properties. Thus the D meson is expected to have excited states usually labelled D*, D** etc. and similarly for the F meson.

Mass values of different states The ordering of the above levels depends on the type of potential assumed. ~n Fig. 15 the order of levels is shown for SHO potential and the Coulomb potential. Dynamical degeneracies exist, e.g. in the SHO the 2s and id states are degenerate in mass, whi]e in the Coulomb potential the 2s and 2p are degenerate. Thus the ordering of the levels can revea] the potential involved. Finally, the mass splittings in a given level, e.g. in the P states, depend on the exact character of the residual interactions, the spin-orbit, spin-spin and tensor interactions.

ct.

(a)

(b)

V= 7-

t,s

2s

3p

2d

12__

2f

If 2s

1s S

V = br 2

W (GeV) 2p

W (GeV)

ld

15 P

D

S

P

B

F

Fig. 15. O r d e r i n g of levels for different p o t e n t i a l s . (a) C o u l o m b . (b) Simple H a r m o n i c O s c i l l a t o r ( S H O ) .

The Current Status of Charm

239

Easily accessible states

~n e+e - armihilation through a singIe photon the most easily accessible state must have the quantum numbers of the photon, d e c = 1 -, i.e. the 3S~ state. Furthermore, this state has the necessary property that qb(0), the wavefunction at the origin, is non zero enabling the point production of the c8 pair. Thus resonances similar in character to the p, co and q6 vector mesons are expected. Since these resonances are a~so produced from photon beams the c( vector state is expected there also. Other c6 mesons (~4'3i) are obtained in the radiative decays of the c8 vector states and, providing the mass of a c8 state is large enough, cq and 6q may be observed in its decay. 2°2° Charm = 0 mesens--H~dde~ charm ~n this section the status of information on c ( states is summarized. This then forms the basis for the discussion of the physics of the charmonium system in Section 4. 2.2.1. The 0 and 0' mesons The discovery of the 0 and 0' states represented the major initial experimental evidence for charm. The 0 was identified as the ground state, 13S1, of the c( system and the 0' as its first radial excitation, 23S1. meson

Since the first observations the major properties of the 0 meson and its decay modes have been obtained. (32) The principle properties are summarized in Table 2 from which many of the quantum numbers of the 0 can be derived. (27l Table 2. The ~ meson Mass 3097 _+2 MeV, width 67 _+ 12keV J Pc = 1- Decay channels

Branching fraction

ee

7 ±l

~z+zc (~+~)~o 2(~r+~ - ) 2(~r+~z- )~ ° 3(~ +~z- ) 3(rc+~-))z ° 4(~+~r )~z° K/(* p/~ A.~

yE(E ~ KiK~)

0.01 +0.005 ].1 +0.2 0.4 +0.1 3.7 _+0.5 0.4 +0.2 2.9 _+0.3 0.9 _+0.3 0.61 +0.08 0.21 _+0.02 0.16 _+0.08 0.12 _+0.02 0.51 +0.18 0.15 _+0.03 0.28 __0.14

Decay mechanism

Partial width keV

7~

7r/' }f

leptonic (e+e + # + / ~ - ) hadronic (!?) direct to hadrons

9.4 _+1.4 12 _+2 46 + 12

240

R.J. Cashmore

jec = 1--

This is obtained by studying the interference between the # + p - pairs from the resonance and the directly produced (1~/) # + # - pairs. This interference requires j v c = 1 - and is destructive below resonance and constructive above.

G ~ -1 Table 2 demonstrates that final states containing odd numbers of pions are favoured. The even pion final states are consistent with decay via a single photon as indicated in Fig. 16. Since strong interactions conserve G-parity this implies that the G parity of the ~ is - 1.

* ~

hodrons

Fig. 16. ~ decayvia a singlephoton. t=0 Knowing the G-parity is negative implies I = 0 since = c(-

1) I.

This is further substantiated by considering the ~p decays where the branching fractions to the various charge states zc+p -, zc°p°, rc-p + are consistent with t = 0. S U(3) singlet For an S U(3) singlet the 7cp and KK* decays should be equal as should the N N and AA decays. ARer accounting for differences in phase space these decays are indeed consistent with an S U(3) singlet assignment. The remaining entries summarize some of the photon transitions of the ~ to explicit states as well as the leptonic, single V and direct hadronic decay widths. The later decay clearly indicates that the ~ is a hadron. However, a multitude of final states contribute, the branching fraction for any one not exceeding 4 ~o. There are other decays of interest in discussions of the charmonium system and its QCD interpretation. (i) 0 ~ vX, V~cThere does not appear to be any radiative decay to states in the region of 2.83 GeV which had been claimed in earlier experiments. (33) However, there is evidence (a4"as) for the decay to a state of mass 2980 MeV, which is presumably the ~c (see Section 2.2.3). (ii) 0 --' 7~, V~', '/f, 7E. These states are produced quite strongly in the electromagnetic decay of the ~(33- 36) The very low rate of ~/~0 probably indicates a mechanism in which the v-ray is emitted from the charm quark so that the hadronic system still has I = 0. Thus these decays can be used as indicators of the cg or perhaps glue component of the final mesons. Some problems surround the decay to the E(1410). This state does not appear to have the same decays as

The Current Status of Charm

241

is observed in h a & o n production and there is no definitive evidence for the spin parity. However, this presents an exciting possibility since k might be associated with long sought gtuebMt states expected in the light meson sector.

(iii) ~ -+ 7 +

.

.

.

.

In this case the direct ~-ray is not monochromatic and it is difficult to resolve from the background due to the n°s in ~ decay. Two experiments (37'3s) do, however, measure such ?-ray signals (at ~ 4 ~£ level for x 7 > 0.6), but differ in the xT(E;,/Eb) distributions that are observed. Hence it is difficult to draw reliable conclusions.

~' meson The principb properties of the ~' are summarized (2v) in Table 3. Table 3. The ~,' meson Mass 3686 _+3 MeV, width 228 Decay channel ee y# 0n+n ~hn°rc° Or/ 2(n+n -) 2(~+n-)n ° 7Z(3415) 7Z(3510)

7z{3555)

7 _+2 0.35 _+0.15

bptonic (e+e - +,u+g ) hadronic (17) Onn

~,~ YZ hadronic direct

=

0.9 _+0.1 0.8 _+0.2 33 _+3 17 _+2 4.2 _+0.7 0.08 _+0.02 0.4 _+0.2 7 _+2 7 _+2

,/G(2980) Decay mechanism

,]PC

_+ 5 6 k e V J P c = 1 - -

Branching fraction

Partial width keV 3.9 _+1 4.2 _+ 1 ] 14 _+29

9.6 _+2.8 48 _+ ]4 48 _+i9

]--

This is again obtained from interference in the # + # - final state.

G-parity The decay finn demonstrates G 0, = - 1. ~r=0 In the decay 4,nn the ratio of n+Tr - compared to n°n ° is consistent with the pions being in an ? = 0 state. Pspin conservation then impIies that I # = 0 and this is consistent with the values o f G and C.

242

R. ~. Cashmore

S U(3) singlet The evidence for this is scanty and relies on very low branching fraction cha#.nels, e.g. ~' - , p/~ and - - - +, which are consistent with an S U(3) single assignment. The major difference in the ~' decays lies in the existence of cascade decays to the ~(39~ and the intermediate states ZJ 24,341 These form the major part of the ~' decays. Indeed, after subtracting these cascade decays the ~nal direct hadron decay is similar to that of the both in size and in the variety of finaI states obtained. These results are derived entirely from studies of the ~ and ~' in e+e annihilation. Observations of the ~ and ~' have aiso been made in hadronic coUisions over the fult range of proton accelerator energies. {t s,40> Lktle information, except for the original d~scovery,(~8~ has been obtained that is of direct value in the discussion of charm properties. Early photoproduction experiments (4~) on heavy targets were, however, valuable in establishing that the O'tot ( / ~ N ) ~ 1 mb demonstrating that the ~ was ~ndeed a hadron. 2.2.2. Further vector mesons In Fig. t7 the variation of R(~had/c~#~) is shown just above the ~' demonstrating the existence of a further structure, the ~", which is yet another resonanceJ 42'43) At the higher energies (4) shown in Fig. t8 the rise in R expected from being above the DD thresho]d is finally seen together with rich structure associated presumably with other resonant states or new thresholds, e.g. DD*, F F or FF*. There are some experimental discrepancies, both in exact structure and the absolute value of N, but there appear to be at least the states Usted in Table 4. Since all of these states couple to the pEoton, j c = 1- -. The spectroscopic

observed R

I

4

~P' ,

I

°j

i

I

(~b) Z

correcfed

'

3.6/+0

3220 3.800 3.880 Ecru.GeV)

Fig. 17. The valueof R just above the ~' mesonindicatingthe presenceof the ~"(3772).

The Current Status of Charm

243

e+e--~.-hodrens

I

T a) SLAC- LBL

3 R

b) DASP I

I

I

I

I

I

E-I

I

I

I

I

I

I

:

I

J

i

~-

,J rl,l,,, L,'lll'l'Elflll"J l l l tJ'",,i,l,l, rlltlI[l[ilFil lIIIIIl tl Ij

iI

ill I ]]1II @lJJl c ) DELCO

(nO Fodi corr.) I

:

:

:

I

i

I

I

J I

I

i

i

i

J

3 d) PLUTO 1

I 3.5

i

i

i

I

I

l

t

I

I

q

L

I

4.5

4.0

I

I

I

,

5.0

E~, (GeV)

Fig. 18. The vMue of R in the threshold region areund 4GeV.

Tab]e 4. Resonances observed in the hadronic cross-section Name

Mass

~' ~" ~"

3097 3686 3768 4028 4160 4414

_+2 _+3 _+4 ±5 ±201 _+7

Frot (MeV)

Fee (keV)

67 _+12keV 228 _+56keV 25 ± 3 52 _+10 20MeV 43 ± 10

4.7 _+0.7 2 _+0.5 0.255 _+0.060 0.75 ±0.1 0.77 _+0.2 0.429 _+0.130

Spectroscopic assignment n 2s+ 1L s 13SI 23S1 13D1 33St 23D1 4aS1

244

W. 9. Cashmore

assignments are then made on the basis of experimen%aPevidence and theoretical prejudice, e.g. the lower leptonic widthC42,“3) of the $” is suggestive that the wave&m&m at the origin q5(0) is nmch smalPer than for the (I’, which is consistent with $” being a D state whereas the .$’ is an S state. The assignments of the 4.03 and izigher mass structures are specdative particularly as these states may well be mixtures of both S and D wave angular momentum StatfiX

lS------

Pig. 19. Open channels

in the region of 4 C&V.

1%is ah importantto remark that no classical resonance proofexists, i.e. the phase variation of a Breit-Wigner amphtude %hrough - 180”. This means %ha%%he s%ructures observed might be purely kinematic enhancement effects pahticulady as many new chamek are opening in this region, e.g. DD”, D*D*, F;F, FF”, F*F* as shown in Fig. 19. Some degree of scepticism is advisable although it would be foolish to ignore these states on the grounds that there is no conclusive demonstration that they are resonances. Finally, these sesoaraHlces/enhancements all have large widths, > 30 MeV, which indicate that they decay hadronically via Zweig akwed processes and thus charm mesons may be expected to be copiously produced in their decay. Indeed the +” decays entirely into DD states (being below DD* threshold) and thus provides a D factory in which to study the D meson. At 4.03 GeV, where the D and D* mesons were originally discovered, the final state is dominated by DD* and D*F. One might expect the other states then to be associated with other specifk final states, e.g. FP anad P*F*.

The Current Status of Charm

245

Clearly this rich structure should be valuable in providing the form of the cd potential but caution is necessary given the existence of these new thresholds. 2.2.3. Other cC states Given the existence of the q/, ~' and ~" it is natural to expect other c( states corresponding to those listed in Table 1. Providing the mass M of the new state is such that M > M v - 2 M = , where M v is the mass of the decaying ,/Pc = ! - - ~ state, then only those states which can be obtained by radiative decays from the ~ and ~' will be easily accessible. This electromagnetic transition is allowed by the Zweig rule. (1} These states must have opposite charge conjugation from the ~ and 0', i.e. 1So, 3Po,~,2, aD2 states. The 3p states are expected to lie between the ~ and ¢' and the 1S0 states below their corresponding vector states. Thus the transition scheme of Fig. 20 is expected where the new states might either decay radiatively to the ~ or by direct hadronic coupling (just as the ,~ and ~').

qj~

h[tdrons

1So

3SI

3p0,1,2

Fig. 20. Transitions between the expected c( states.

Excellent evidence exists for the 3p states and there are now good indications of the 1 1S0 state. However, no transition to a 1D2 state is observed as might be expected since the mass of this state will probably be close to the 0", which is also a D state, and hence above the 0'-

3p states: Z(3410}, Z(35t0), Z(3550) These states are all observed in the radiative decay of the ~' ~ ' - - ' 7Z.

This leads to a monochromatic ?, ray and the transitions are predominantly E1 in character. The states subsequently decay either hadronically or via a y-ray arriving at the 0- This second 7-ray will not be monochromatic since its energy is Doppler broadened due to the motion of the source. In Fig. 21 are displayed the beautiful results from the Crystal Ball experiment at SLAC. (34) Three monochromatic 7-rays are observed in the region

R. J. Cashmore

246 7000

X(3510) --q)y

6000 I~

-j xm

X ( 35551

5000

#t

c,000

;

i

X(5555) X(3510)

X13~10)

g o %_)

3000

2ooo! -,% loool 5o

,

~

a

,

I

100

I

t

~

200 EGAM (MEV)

I

500

i

,

, I0'00

Fig. 21. The ,/-ray spectrum observed in decays from the ~' in the crystal ball experiment (Ref. 34). Transitions to the Z and t/c states are apparent.

E./< 500 MeV, accompanied by 2 other Doppler broadened y-rays. These y-rays correspond to the transitions

~ ' ~ yz(3550)

I

,y~,

if' ~ 7Z(3410). tn the case where two sequential ,/-rays occur, the final state Z' ~ YYff can be observed; the ~ decaying to e+e - or #+/~- for a dean signal A scatter ptot can be made of Elow vs Ehigh, where Elow and Ehig b a r e the tow and high energy y-rays, and the Doppler broadened y identified as shown in Fig. 22. (3*) A mass plot can then be made of the high effective mass fly combination--since this corresponds to the Z state--as shown in Fig. 23 where the Z(3510) and Z(3550) are dramatically visible. Note however the absence or at best very tiny signal corresponding to the Z(3410). This state must clearly decay predominantly to hadronic final states. The hadronic decays of these states have been observed (24) by selecting ~' decays containing a y-ray ~' --, y + hadrons the results being shown in Fig. 24. Again three states are observed with the ;((3410) and Z(3550) being particularly prominent. Information on the intermediate P states is summarized in Table 5. The charge conjugation is determined by the radiative decay. The spin parity assignments are less well

The Current Status of C h a r m

MEMO''

I

'

.

.

.

.

.

]

. . . .

I

500 ~. . . .

247 I

. . . .

. . . .

q Subfracfed .:..'

m

L~O0

350

:

;~:.:

-

I~

- -

+

'... :

.

30C

.....

250

I

I

I

I

0

i

I

I

50

I

I

100

I

I

I

I

I

l

I

150 Low Ey

I

I I I I I

200

250

3()0 MeV

Fig. 22. The scatter plot of EThigh VS E7iow i n @' ~ ~/7}' after subtracting the ~' --+ ~br/contribution.

verified although alI evidence points to these values. That the Z(34t0) and Z(3550) are natura~ parity states is indicated by their decays to z~ and K/< whereas no such decay is seen for the Z(3510), suggesting J P = 1 +. These assignments are consistent with the angular distributions of the 7% in the if' ~ 7Z transitions, the subsequent 7. --' 7@ decays and the final --, e + e - decay. The other points of interest lie in the magnitudes of the branching fractions. In the decays 7. ~ 7@, the 7.(3410) has a remarkably sinai] branching fraction implying either a suppressed decay or a large total width. Unfortunate]y no direct measurements of the 7. widths are available, the experimental resolution masking any true width. Just as in the ff and ~'

(3510)

X

25

II

~20 >~ ~Z

X (3555)

~15

I

~>10 3410

3450

11

I

I I

I '

335

''

iIIi.tll I

3.¼0

h'

I l l l Ill

3.45

I I

3591

Ii

iI Ill ,,i, i , , i , .

~55

350

High ¢,¥

3.60

mass

Fig. 23. The high m a s s ~7 system in ~' ~ ~'77.

3.65 GeV

R . J. C a s h m o r e

248

SLAC- LBL J

~L=~y, hadrons ]

i

i

i

'4

4

25 20 15

I0 7-n+n-K + Kb 0 ~> 6 c

3(~+rt-)

- ~

0

i L or n+ K~-÷ K-

f

i

2.8

3.0

3.2

3.t~ 3.6

3.8

Mass {GeV/c21 Fig. 24. The invariant mass of various hadronic systems in the decays ~' --+ 7 + hadrons. Peaks corresponding to the Z states are apparent.

hadronic

d e c a y s t h e v a r i e t y o f f i n a l s t a t e s is l a r g e s o 1 h a t n o o n e s t a t e d o m i n a t e s

s t a t i s t i c a l m o d e [ is p r o b a b l y

appropriate.

will l e a d t o s o m e u n d e r s t a n d i n g

Finally, the mass differences between

of the residual interactions

and some these states

in cg models.

Table 5. Z state properties

z(3550)

Mass = 3551 _+3 Declay channel (f) o/~ n+n-/K+K Other than ;,~

dPc = .2 + + (3p2) B(O' -+ 7Z) B(Z ~ f ) 0.0!3 _+0.0025 (0.02 +-0.01)10 2

B(~// --+ 7Z) = 0.07 +--0.02 B(Z -+J') 0.19 _+0.07 (0.28 _+0.14)10 -2 0.81 _+0.07

z(3510)

Mass 3510 _+4 Decay channel (.f) 7g' n+rt-/K+K Other than 7~

j P c = 1 + + (3p1) B(g,' --+ ;'Z) B(Z -+J) 0.021 _+0.0042 <0.015 x 10 -2

B(~' -~ VZ) = 0.07 _+0.02 B(2 -+f ) 0.30 _+0.i0 <0.21 x 10 .2 0.70 _+0.I0

Mass 3410 _+6 Decay channel ( f )

j e c = 0 + + (3po) B(~' ~ ~Z) B(Z --, f )

B(ff' ---,7Z) = 0.07 _+0.02 B(Z -~ f ) <0.7 x 10 -2 9.02 _+0.097 > 0.993

Z(3410)

70

< 0 . 0 5 × 10 - 2

rc+n / K + K Other than V~

(0.14 +-0.03)× 10 2

The Current Status of Charm

249

aP x state

No observation of this state has been made which might be expected to lie near the 3p states, h could be observed in the M1 transition 3po,1, 2 ~ 1P 1

but the probable low energy of the 7 could result in a transition rate too low to be observed and/or a 7-ray difficult to resolve from experimental backgrounds. 1S o states: the ~c (1 1So) and the ~; (2 ~S0)

These states can be expected via M1 radiative decays of the 0 and 0' 0 -" 7~c

7~'~. Previous sightings of such possible states at 2830, (3a) 3455 ~44) and 3591 (45) have now been ruled out by the crystal ball experiment. (34) This is a welcome relief since the masses and M1 transition rates were in conflict with all known models. It is much more likely that the qc and ~/; lie close to the ~ and 0' in mass so that the M1 transitions will have low rates leading to very low branching fractions for

and 7-rays which are again hard to observe. The remaining possibility Iies in observing the transition

8000~ 7000

:,f

=

i

'

I

i

L

r

r

[

,

E

5000

~.000

o-

3 0 0 0 ~ [-

300I

90 100

BO

70

F

Z

2O0 0 -200 -400 ~

n 70

d BO

subfmcted 90 100

y energy (MeV)

t@' 600

700

600

700

-100f 500

3/ energy (MeV)

Fig. 25. The v-ray spectrum in ~' and ¢, decay in the vicinity of transitions to the qc(2980) state.

250

R.J. Cashmore

even though this wil! be suppressed due to the orthogoaal nature of the radial wavefunctions of the @' and ~ (in any potential model for these states). In Fig. 21 an enhancement in the "/-ray spectrum is seen at E . / ~ 640 MeV, this region being expanded in Fig. 25. Also shown in Fig. 25 is the 7-ray spectrum in @ decay, for m o m e n t a around 100 MeV. A b u m p is clearly seen in both cases, corresponding to the state ~, of mass 2.98 _+0.015 GeV. Fits to the 7 spectrum yield a width of 2a+~6MeV.~_lt The branching fractions are B(O' ~ "/i7~) = (0.2-0.5) x 10 -2 which are not unreasonabie in any charmonium model. (34'3s) This G state at 2980 can be further studied in exclusive final states observed in ~' decay. Both the crystal ball experiment and the M a r k ti experiment quote results which are summarized in Table 6. No definitive measurement of the spin parity exists but the 7-ray angular distribution in the @' decay is consistent with an M1 transition to a 0 - state. Table 6. t/¢ properties Mass 2 9 8 0 ± 1 5 M e V Width 20+- I~ MeV Decay channel K~KZ)z + KR~ /~P 2=+2~z t/n+= -

Branch fraction ( %)* 4.3 + 1.7 12.9 +_5.1 0 •2+o.2 -o.1 1.3+-°: 9 3±1.5

,,~

<0.5 00% CL)

* These figures assume B@' - , 7t/c) = 0.35 ~.

2.2.4. Summary and comments A rich spectrum clearly exists in the cC system possibly 6 vector (t - - ) states and at least 4 other C = + 1 (charge conjugation) states. These states are summarized in the level scheme of Fig. 26. This spectrum has already played an important role in the study of the c( potential and the residual interactions, while the decays provide interesting tests of the cC wavefuncdon and gIuon counting rules of QCD. These topics are discussed at length in Section 4.

~'(3684)

//

~

~

,

~

x (3550 I

/ "q(2980) /

-5-

iJ/@(3098) e+e, u+la -

Hadrons Hadr0ns jPC

0~-

1--

0 ++

1 ++

2 ++

Fig. 26. Level scheme of cc systems.

The Current Status of Charm

251

As rich as this spectrum is it will be overshadowed by the 7, 7' and 7" system where the same questions are relevant and the spectrum is even more complete since the 3"' is also narrow in contrast to the ~". N o n e the less a final understanding of these heavy quark systems will need a model of both cC and bb states/2 s) 2°3° C~arm = + ~ rnesens--Ope~ e]mrra It was the observation of the mesons carrying charm as an explicit quantum number that finally confirmed the G~M charm hypothesis. (26/The quark content of these mesons was given in Section 2.] D + =cd

D °=cff

F + =cg

and they are expected to occur not only in the ground state (~So) but also in excited states, the D* arid F* (3Sx) as well as :he remaining states of Table 1. However, these other states will be more difficult to observe since they are not as copiously produced as the vector meson states (@',...) and must be sought amongst the decay products of sach states in e+e annihilation. To date only the D and D* mesons are unambiguously identified. (46) The F and F* despite some indicative resuks, (4v~ remain elusive and only with further detailed work will they become apparent. The D's as well as confirming charm have been the re.ajor laboratory for studying the weak interactions of the charm quark (although valuable information is Table 7. The D mesons d e = 0 DO

D+

Mass 1863,3 +0.9 Decay

1868.3 +0.9

Branching fraction ~

Hadronic exclusive 2.6 -+0.5 2.2 -+1.1 3.9 -+0.9 9.7 -+3.0 5,0 _+2.0 0.09 +0.04 0.31 -+0.09

K rc + KO~ 0

K-rc~-/r + ~ /~+)T

K+K

Total

23.8 -+ 3.3

Inclusive K K+ Ko no K

Branching fraction %~ 1.9 -+0.5 5.1 +1.0 12,9 -+8.4 8,4 +3.5

K n+n + K°n-:: °

K°n~:r+:r /<'OK+ K -rr+:z+ rr+::

0.5 -+0.27 <4.1 (90 ~ CL)

Total

28.8 -+ 8.6

Inclusive 45,4 -+7.0 7.9 +_2.9 34.6 +11

Semi leptonic Inclusive e +

Decay Hadronic exclusive /{0~-

59 _+ 12 27 -+12 14 _+17 2.46 _+0.14

(Ref. 43) (Ref. 4)

(5.5 _+3.7) < 5%

(Ref. 43) (Ref. 4) emMsion

2 . 4 x 1 0 13 < 3 . 5 x 10 13 +0.53 x 10 13 1.0_o.

K K+ K° noK

14.5 +4,1 6.0 +4.0 47.6 ! ! 8 . 0

e+

I8 + 6 52 + 2 0 30 -+21 2.16 _+0.16 !6.8 +6.4 24.0 ! 4 . 0

Excbasive e+Kv/e+vx

Lifetime (secs)

(45 + 24) % 7 . 2 x 1 0 13 8+5×10 13 ~ 0,~ q + 14.1 0 . h x l 0 13 ~

252

R. J. Cashmore

r 30-

ZO-

IO-

O20-

Fig. 27. The angular

distributions

cf DB meson production

at the $”

60

0 20

100 80 60 b0

20 0

Mass

iMeV/lcZl

Fig. 28. The D meson in a variety of final states. The data was taken at the $“.

The Current

Status

ofCharm

253

4 0 1803

1823

1843

1863

1883

Mass (MeVlc2)

101

I

’

1803

1823

1843

1863

1883

1843

1863

1883

G-8 $6

zz NI*

-I

g2 LO

1803

1823

Mass PleV/c21 Fig.28 (continued)

R. J. Cashmere

254 2511 /

125

I

I

I

I

I

I

I

I

I

I

I

(al

re- TI;+

(b)

K;

n; +-

100 ~c

75

--

50

"E

25

>

0

25

(c)

K-K*

20

0 1623

1%3 1863 1983 Mass (MeV/cz)

2103

Fig. 29. T h e C a b i b b o u n f a v o u r e d d e c a y s of the D o m e s o n to ~z+~ - a n d K + K - c o m p a r e d w i t h the KT)z z decay. P e a k s at m a s s e s o t h e r t h a n the D m a s s are d u e to m i s i d e n t i f i c a t i o n of a particle in the Krc final state.

obtained from v induced reactions). In this section the strangeness zero states, the D and D*, are discussed first, followed by the evidence for the strange mesons, the F and F*. 2.3.1. The strangeness 0 states Historically, the first observations of the D and the D* were made at EcM of 4.03 GeV. Narrow structures were observed in K~ and K~zTcmass spectra at 1.865 GeV (see Figs. 11 and 12) including structures in ~exotic' quantum number channels. Such quantum numbers are impossible for a conventional q~ state constructed from u, d and s quarks alone, e.g. K - ~ + ~ + would correspond to a meson ofQ = + i, S = - 1. The D* was then identified in the missing mass spectrum recoiling against the D meson states. The 4.03 region has remained the major source of information on the D* but has been superseded by the ~" as a D source. All of the major recent results on D's have originated from the ¢" D factory. (4'43'4s~ 1So state: D meson The presently known properties of the i) mesons are summarized in Table 7. ( 4 ' 4 8 ' 4 9 ) Most of these measurements are made at the ¢" mass. The spin value is obtained by studying the angular distribution for Z)13 production at the g)" as shown in Fig. 27 which is consistent with J = 0. (~) Observation of the decay to K~ and a study of the Dalitz plot in the K~Tz decay imply opposite parity and hence that the decay is weak in nature. (5°) Prejudice then suggests that the spin-parity is 0 - in keeping with all other known lowest lying meson states. All measured angular distributions are consistent with this assignment. The major information on charm lies in the different decays of these states, which are obtained from mass spectra of the type shown in Fig. 28. (43'4s~ There, nine explicit

The Current Status of Charm

255

hadronic decays of the D + and D O are shown. In Fig. 29 the evidence for the rr+~z and K + K - decays of the D O is shown343) These are important as they correspond to Cabibbo suppressed decays of the charm quark and will thus be useful in discussions of the Cabibbo form of the weak current. It should be noted that the identified hadronic decays still only correspond to a comparatively small fraction of the total decay rate. Recent measurements of the semi leptonic decays have provided another of the interesting results of Table 7. (4,43) (These results must supersede earlier measurements since at the g/' the charge of the D mesons can be accurately tagged.) The branching ratio B(D + -+ e +) appears dramatically larger than the branching ratio B(D°--* e+). This either implies a different totat width for the two states or different values for the semi leptonic decays. As the latter is less likely the suggestion is that the D O has a much smaller lifetime than the D + (cf. K ° and K+}. Observations of the lepton m o m e n t u m spectrum, (4) as in Fig. 30, reveal information on the hadrons involved in the semi leptonic decay. The major components of ti~e hadronic system are apparentiy the K and K*, the rr being much smaller. tn T a N e 7 the inclusive branching fractions to K - , K +, K ° are included. ~n the decays of D °, D + the G t M mechanism would imply that the c quark leads to S = - 1 mesons, i.e. K and R ° and these should dominate the decay. Although this is the case there is a surprisingly high proportion of decays without K's, particularly in the case of the D + (especially after account of double counting is made). The precise measurements of the D o and D + mass come from data taken at the ~,,{4a) This decays into D°D ° and D+D final states with a Q value of ~ 4 0 M e V . Thus the m o m e n t u m of the D mesons, Pz) is small so that an accurate value for the mass is obtained from

YG =

G

=

since E b is very well known and inaccuracies in PD unimportant. DELCO

/' z~O

,

I~

---- K*(890)ev

.

I

{a)

-

\.

20

, I 40-

0[ l

0

'

,

[Nixfure of

- - i ~ e v , K~v,

.,Fa~l T E

~K*(890)ev.

' L,_' -eI

i

i

~

l

I

n

I

I

I

I

A

O5 1.0 Electron momentum (GeV/c)

Fig. 30. The 1upton m o m e n t u m spectrum in D decay. The curve corresponds to the fitted contributions of trey, K e y and K * e v . PPNO 7

-

o

R. J. Cashmore

256

Table 8. The D* mesons d P = 1 D *0

D *+

2008.6 _+ 1.0

Mass 2006.0 4- 1.5 Decay D% °

Branching fraction 66 + 15

D°7

34 -4-6

Decay D% + D+~o D';,

Branching fraction 64 i l l 28 + 9 8_+7

Finaily the lifetimes are quoted assuming a value for the width for the semi leptonic decay of the D's. This is discussed in detail in Section 5. The only other source of information on charm particle lifetimes comes from measurements of charm particle flight paths in emulsions {sl,52) the total number of such decays being ~ 20 with in many cases ambiguity in the identification. However, from this data crude estimates of the D -+ ar.d D o lifetimes can be made leading to z(D °) ~ 10 -13sec z(D +) ~ 10x 10-13sec which are included ira the table and are consistent with the values derived from the O semi leptonic branching fractions.

D" 0° 20

D°D DD (a]

I0

>

0 20

Z

o

g > 0

It)

15

K~ TCt ~± D÷

10

0

0

gO0 800 Po MeV/c

Fig. 3l. The D mo men tum spectrum at 4.03 GeV. Contributions from the various processes are indicated: e+e - ~ D*/)*;D *÷ -, D%+(A),D *°--* D°~°(B),D *°-~ D°7(C),e+e ~ D * D + D * D ; D D *o ~ D%°(E), D°(F), D *° _, D°7(G), e+e ~ D°/iS°(H).

*+ -,

D°~+(D),

The Current Status of Charm

257

3S~ state: D* meson

The present state of the D*'s is summarized in Table 8. The results are mainly derived from measurements at Ecru : 4.03 GeV where momenta spectra for the D meson of the type shown in Fig. 3I are obtained. (s3) These spectra are complicated due to the production of D~0, DD* and D*/~* final states with a variety of decays. Branching fractions are obtained together with the respective production rates. However, a more direct measurement is desirable and preliminary results are available from the Crystal Ball experiment. After correcting for phase space effects the production ratios of the various final states are D°D °:D°z] * ° + D ° D *° - D*°D *° = 0.2 _+ ] :4.0 _+0.8:128 _+40

the D*lh* system being favoured. However, 4.028 GeV is only just above D*/)* ~hreshold and hence the phase space factors are of enormous importance so that these ratios should be treated with care. The mass difference between the D* and D states ;orbids some strong decays, e.g. D *° -+ D+~ . A situation thus arises in which the electromagnetic decays can compete and result in the large radiative transitions 'Jsted in Table 8.{53'54) Finally the spin, parity assignments, JP = 1 are consistent with both the experimental evidence and prejudice. Other States

The P states and higher are presumably produced in the region 4-5 GeV. However, their production rates are probab]y low (unless some accident causes their enhancement) and their decay channels many, resulting in great difficu]W in their observation. Surm'nary

"['he t) and D* meson systems are comparatively well understood and summarized in Fig. 32. 2.3.2. Strangeness = -+ 1 states The evidence for the existence of the t<` meson states is rather fragmentary. They might be expected in the 4.0-5.0 GeV region e* e annihilation and, using the D system as a guide,

°I

2010l j-- 20051-. > u

Z

<( Z

bl I l

". / ~

¸ IZ+°3±°91

187(

1865 D0

I860 Fig. 32. 7"heD and D* meson systems.

258

R.J. C a s h m o r e

to occur in reactions of the type e+e - -+ F F *

and

FF*

~So s t a t e : F m e s o n a n d 3S~ s t a t e : F * m e s o n

Since the quark content of this meson is cg, the weak decay will lead preferentially to two strange quarks, sg, in the final state. (14) Thus states containing K K , ~/, r/' or ~b are expected (the r1 and ~' have large sgcomponents), i.e. F--+ K K + . . . -+ ~ + . -~ 'I' + . --+ ~ + . ..

Furthermore, even if the Q value is sufficiently large, isospin conservation forbids the strong decay F* ~ F~ so that the only possible decay mechanism for the F* is via a radiative transition, i.e. F* -+ FT. Observa'dons of an increased ~ yield have been made at Ecru = 4.42 GeV (one of the structures in the annihilation cross-section) by the D A S P group (4v) and furthermore these ~/'s appear to be correlated with a low energy y-ray suggesting an F F * origin. Events of the type e+e - --+ ~:= + ~ + y ~ + x are thus selected and a fit is made to the reaction sequence e+ e - _+ F ~ F *~: _+ (zc±~1)(F+ve)

requiring that the ~z+~ mass equal the recoil mass (x). Events satisfying this hypothesis are shown in Fig. 33. The 4.42 GeV data show a peak at M ~ = M F = 2.04 +_0.02 GeV. The 7-ray energy in these events corresponds to an F* mass M e , = 2.15 + 0 . 0 5 G e V and the value for the production rate at 4.42 GeV is e v B ( F ~ rrr/) = 0.41 +0.18 nb.

Preliminary results from the crystal ball experiment (ss> do not appear to show this increased 77production at 4.42 and studies by other e+e - experiments have not yet revealed the F, (43) although the limits on production at 4.42 GeV are not totally incompatible with the D A S P result

~B(F --+ rc-+~/) < 0.26 nb ~rB(F ~ K ± K °) < 0.22rib.

The Current Status of Charm

259

e+e ~ F F ° ~ F y F

1 Ec m =/+./+2@eV

~o

e

2.0 >

~1.5

t

IK

°

o ©

1.0

signal F 6

>

/+ t,,i

g, ,,>,

1.0 Nfit

1.5 [ GeV]

2.0

Fig. 33. The scatter plot of M(rln) vs M e recoil in the kinemafically fitted reaction e*e

~ F ± F TM -~ ~±~lF~?,.

A possible enha~cement (56~ in the K/(~n system at 2.04 GeV has not been confirmed by a more recent high statistics experiment. (43~ Clearly, the F situation in e+e - annihilation is confused and it would be desirable to have a clear result on inclusive ~/production in the charm threshold region. Other evidence for an F is obtained from a photoproduction experiment (57~ where this meson is again observed in the decay channel F -* ~n in conjunction with a low energy Y as shown in Fig. 34. (Observations are aiso made in ~/3n and ~/5n final states without requiring the presence of a 7-ray.) Once again these effects are of marginal statistical significance and would not be noted were it not for the fact that they are at the mass observed in the DASP experiment.

60 50 IE

~0

o

,,, 30 '~ 2c

I'.6

i

i

1.8

2

__

212

2'.4

ETA °PI Fig. 34. Evidence for the F in photoproductiorL A peak is observed in ~n when a high Pr ?-ray is required in the reaction.

260

R.J. Cashmore

The hast evidence for the F comes from emulsion experiments where possible sightings ( ~ 3) have been reported with masses of ~ 2050 MeV. These experiments also indicate a lifetime of 2 •2 -1.1 + 2.8 × i 0 - 1 3 s e c Ciearly the confirmation of the F and F* states remains the outstanding problem in the fieid of charm mesons. At the moment the evidence is far from compelling but probably points to the F at a mass of 2,04 +_0.02 GeV. The situation could be confused if the expected Cabibbo enhanced decays do not dominate (see Section 5) so that the clear signature for the F is lost. 2.3.3. Summary and comments The observation of the D and D* provide overwhelming evidence for the existence of a new quantum number, charm. However, the F and F*, just as essential, remain somewhat elusive and must be confirmed in fut'are experiments. To identify the other excited states of these mesons, e.g. P states, will p r o b a N y be hard due to the low production cross-sections and diversity of decay channels. The many properties of the D mesons provide evidence for the G I M mechanism and allow studies of the weak interaction of the charm quark• However, this is postponed until Section 5 where it is treated in detai!.

3. BARYONS C O N T A I N I N G C H A R M Q U A R K S The observations of charmed baryons have been few and thus they have not contributed, in any large sense, to the understanding of charm. However, it is important that they do exist for the charm quark to be regarded on an equal footing with the other quarks. The expectations are summarized first, followed by a discussion of the observations. 3.1o The spee~r=n~ of baryons Baryons are constructed as qqq states. (2t Coleur To obtain non coloured states the baryons must lie in the singlet resulting from the S U(3)c combination 3x3x3=

1+8+8+10

(3.1.])

and this is an:isymmetric in the quark labds. In order to obtain an overall antisymmetric wavefunction under interchange of any two quarks this implies that the remaining part of the wavefunction must be totaily symmetric in the q'.aark indices. S U(4), S U(3) and quark structure If the quarks lie in a _4 representation of SU(4) then the baryons lie in the following representations 4x4x4

= i+20+20+20'

(3.1.2)

The Current Status of Charm

CY•I3

x~

x~+ :--2

2 .

.

.

.

261

.

~ c y /s,*r ,' /

Z -I° \ /

~:Z + C : O I 0 I

Fig. 35. The baryons lying in the 20 representation of SU(4). This contains the SU(3) octet of non charm states (see Table 9).

the quark structures and S U(3) content of which are shown in Figs. 35 and 36. A number of remarks are necessary: (i) the 20 representations have mixed symmetry in the quark indices and a s'aitab]e combination is necessary to ensure the correct overal] symmetry properties; (ii) the 20' is totally symmetric in quark labels and hence contains states iike the well known A + + and I2- ;

,C

~Y

Fig. 36. The baryons lying in the 20' representation of SU(4). This contains the SU(3) decaplet of non charm states (see Table 10).

R. J. Cashmore

262

Table 9. The charmed 1/2 + b a r y o n states Notation

Q u a r k content*

SU(3)

U, Ia)

S

C

Mass (GeV t

Co A" A°

cEu, d] c[s, u] c[s, d]

3 3 3

(0, 0) (1/2,1/2) (1/2, - i/2)

0 - 1 - 1

1 1 1

2.26 2.47 2.47

C[ + C~ C~ S+

cuu c{u,d} cdd c{s,u}

6 6 6 6

(1, 1) (1,0) (1, - 1) (1/2,1/'2)

0 0 0 - 1

1 1 1 !

2.42 2.42 2.42 2.56

x°

c{s, d}

6

(1/2, - 1/2i

- 1

1

2.56

To

css

6

(0, 0)

- 2

l

2.73

X ~+ + X 2 X]

ccu ccd ccs

3 3 3

(1/2, i/'2) (I/2, - 1/2) (0, 0)

0 0 - 1

2 2 2

3.61 3.6t 3.79

* [a, bl, {a, b} denote antisymmetric and symmetric combinations of the flavour index.

(iii) as the s y m m e t r y is badly b r o k e n it is sensible to discuss quite separately the states of different charm; (iv) all of the charm quark states contain explicitly the charm q u a n t u m number.

Angular momentum and parity J P If the low lying baryons have zero orbital angular m o m e n t u m in the 3 quark system then the parity must be positive and the total angular m o m e n t u m is entirely due to the intrinsic spins of the quarks, i.e. J = 1/2 or 3/'2. The low lying states are listed in Tables 9 and 10. (24's8~ Higher angular m o m e n t u m states can be obtained from orbital excitations as in the light quark models of the non charm baryons.

Mass values of different states The Tables 9 and 10 include some predictions for the masses of these states since these will not be discussed in detail later. (58;

Table 10. C h a r m e d 3/2 + b a r y o n states Notation

Q u a r k content

S U(3)

(l, 13)

S

C

Mass (GeV)

C *+ + C* + C~ ° S* +

cuu cud cdd cus

6 6 6 6

(1,1) (1, 0) (1, - 1) (1/2, 1/2)

0 0 0 - 1

1 1 1 1

2.49 2.49 2.49 2.6!

S *° T *°

cds css

6 6

(1/2, - 1/2) (0, 0)

- 1 - 2

1 l

2.61 2.77

X *+ + X~ + X* +

ccu ccd ccs

3 3 3

(1/2, 1/2) (1/2, - 1/2) (0, 0)

0 0 - 1

2 2 2

3.67 3.67 3.85

0 +"

ccc

i

(0,0)

0

3

4.89

The Current Status of Charm

263

Decay schemes Following the charm hypotheses the lightest baryons are expected to decay weakly resulting in strange particles in the final state, e.g. C~ ~ A ° + (nrc) +

(3.1.3)

Co~ ~ K N + (mz)

(3.1.4)

C{ ~ A° +e+v+(nrc) °

(3.1.5)

Or

where the AC = AQ = AS rule (see Section 1.2) is obeyed in the semi leptonic decays. These final states are also obtained in the decays of S = - 1 hyperon resonances, e.g. E + (1385) --, A%z+. However, the weak decays lead to small widths in contrast ,to the large decay widths of the hyperons which are due to the strong interaction. Higher mass baryons might decay hadronically to states such as Core, DN which conserve charm, providing that sufficient energy exists for the decay to occur.

3.2o The observations of charm 5arye~ states The different observations of the charmed baryons are discussed separately in this section.

v Reactions Historically the first observation of charm (22) was probably made in a bubble chamber experiment reported in 1975 in the reaction

v + p ~ ] ~ A°n+n+n+n -.

(3.2.1)

This reaction was remarkable since it corresponded to a A~2 = - A S transition not expected in the weak models without a charm quark. However, with the introduction of Charm a natural explanation was possible vp ~ ~ - c ~ +, c ; + + c ? ~ +, c~ -~ A°~+~+~ the masses of the charm baryons being

m(C~ + ) = 2426 _ 12 MeV m(C~) = 2260 + 12 MeV. Of course the existence of the C + + is not assured as the reaction could have been vp-~/~ C~-z +. Subsequent measurements in v bubble chamber experiments have identified the following possible states. (i) C + --+ K~°--+--~59~'~,,~ ,~ .

where C~ is produced in the reaction vn -~ g - C J

and M(K°sprC+~ ) = 2254 _+10 MeV.

W.9. Cashmore

264 (ii)

c,++

p80n+wQ.

where a rather weak signal is enhanced by considering onPy hon+ systems whid3 could be obtained by a 71cascade from a state of nl2ss 2426 MeV. If a similar procedure is applied to the firnal states K,Op, Aon +7c+K, K,Ojm+ n- some enhancement is seen around 2260 MeV but the evidence is not statistically compelling in each channei. From the Aorc + channel

M(C, j = 2257 i IO (iii ) G + ~-~~+(61): This event was observed in an emulsion stack, the decay occurring primary production vertex. From this event M(C,‘) ad the proper predictions.

354 microns

= 2284 f 16 MeV

time of flight is (7.3 +0.1)f0-13

set, consistent

with charm

These experimen&al resuh all point to ihe existence of the state i& = 2260 + 10 MeV. A further possibie state Cl + might occur at a mass Photvprtiuctivn

from a

liffetime

CG with

a mass

of

IMeV.

-

2420

reactions

The mass spectra (62’ofthe fin.% states Anfzpxand An-n+~, obteined in high energy photon collisions, are shown in Fig. 37. A prominent peak is observed at a mass of 2260 * 10 MeV which is interpreted as C,+. The wiGPh is consistent with the experimen:d resolu~im asd this, together with tine absence of a sign& in the AX +z +C spectrum, argues against its interpretation as an excited hyperm. The only problem is the absence of a peak ifi the Az+n+Y spectrum correspondhg to C,+ production. woiald be expected to be similar if the production process is

The numbers

of C,+ and C,+

MQSS distribution For K iI+Tc-Tc30 20 g 10 w 0 _y?40 k w) 30 20 IO 0

l-5

2.0

2.5

3.0

3.5

4.

Mass (GeV) Fig. 37. Photoproduction

oftbe anti-charm

baryon

in the final states ji”?c+7[+z-

and ~“z’~~z

T h e C u r r e n t Statv.s o f C h a r m 500

(a)

265

K p r~-

z~O0

300 200 >~ z

100

0 ~500 ~- /+00 E

:~ 300

200 100 0 2.0 2.2 2.3 2.5

IS

3.0

Mass GeV/c2

gig. 38. The K plr and K p:r ~ mass spectra from ISR collision (Ref. 63).

A~Tc~

Masses

a) A m + ~ + T t -

30-

. N = 2~ 255

i i

10~ ¢.131 > O/

0

I

I

H A rc+rc-~-

z

20

M= 2 . 2 5 5

0

rr ~

1.7

A

1

I

2.0

2.3

2.6

MGsS

--!!H

~, G e V l 2 ~'

Fig. 39. TheA)z+Tc+~ andA~+~ ~ mass spectra from ISR collisions (Ref. 63).

266

R.J. Cashmore

while a process 7P ~ D C g X

w o u l d lead to m o r e C~. O b s e r v a t i o n of this state, the C~ w o u l d i m p r o v e the plausibility of the Co~ . Hadronic production

C h a r m e d b a r y o n s have n o w been o b s e r v e d in three [SR experiments, (63 65) in v a r y i n g k i n e m a t i c a l regions b u t all a s s o c i a t e d with diffractive processes. E x a m p l e s of the results are i n d i c a t e d in Figs. 38 an.d 39 t a k e n from one of these experiments. W h i l e in all cases the signal is strong in the K - p T z + channel, K * p a n d KA, being a p p r e c i a b l e c o m p o n e n t s , (6s~ the evidence for A~z decay is weak/63'64) The three experiments are s u m m a r i z e d in T a b l e 11. The observatio:~, when the K * p a n d K A decays are selected, is s o m e w h a t surprising considering the results from e + e - a n n i h i ! a t i o n indicate very small b r a n c h i n g fractio~s in these cha~nels. This w o u l d i m p l y e n o r m o u s p r o d u c t i o n cross-sections (~> i rob) a n d it is then difficult to believe t h a t these b a r y o n s w o u l d have gone u n d e t e c t e d for so long.

Table 11. Charm baryon production in hadronic collisions Experiment

Ref.

Channel

Mass

Region

o" B(pb)

pp

63

2260

pp

64

0.3 < x < 0.8 0.8 < x < 0.975 0.75 < x < 0.9

pp

65

K pTr+ Arr+~+)zK p~+ A°rc~~z+)z /~,Op

0.7 --+ 1.8 0.3 ~ 0.7 4.6 _+0.6 5.6 _+2.0 3.0 ~ 6.0 3.0 ~ 6.0

K - u r + K A- +

2290 2280 2260 2260

Finally, in a n o t h e r version (65) of one of these experiments when the mass s p e c t r u m of K -pTr + (particles unidentified) is p l o t t e d an e n h a n c e m e n t at ~ 2260 M e V is observed, when an electron, e , is also present. The e - is s u p p o s e d to originate from the a s s o c i a t e d / ) or 0 state. P r o d u c t i o n in e + e - a n n i h i l a t i o n

The t o t a l cross-section rise a r o u n d 4.0 G e V (Fig. 10) indicates protific c h a r m p r o d u c t i o n a n d hence c o u l d be a source of c h a r m baryons. Evidence (4'43) t h a t this is indeed the case is given in Fig. 40 where the values of R(p + i5) = 2o(6)/o,~

R(A + A) = (~(A) + ~(A))/a,~ are p l o t t e d for this region. T h e b a r y o n yield follows the t o t a l cross-section t r e n d with the p r o t o n yield being greater t h a n t h a t of the A's. T h e sizes of the steps, 0.3i + 0 . 0 6 a n d 0.10 _+ 0.03 for p + p - a n d A + A respectively indicate t h a t the A / p fraction in c h a r m b a r y o n decays (C~) is (41 ± 15) ~o after r e m o v i n g p r o t o n s from the A decay. Conclusive evidence (4'43) comes from the o b s e r v a t i o n of the b a r y o n s in the final states, in Fig. 4t are shown the p K ~ mass distributions, an e n h a n c e m e n t being clearly visible at

The Current Statas of Charrr_ 0.8

267

l

0.6

A + rc~.

0.4

0.2

l

0.100 _

1

0.075

<

00,0f 0,025

o Mark I (Picco[o, ef aL) O! 3

I

i

I

4

i

I

5

i

I

6

~

I

7

8

E....(GeV) Fig. 40. The increases in (a) Rp,p = 2~r(6),/~.~ and (b) R x a = (a(A) + cr(A)),,'cr u in e - e

b

I

annihilation.

I

60

(o)

pK-T~+ K+~-

30-

' (el

7

~ >

I

J

40 &--u

t

Z o

,,>,

°

I

601 (b)

22

23

2.~-

I

pX+~

+~K+~ ÷ + +pK

'"

40

20 0

I

2.0

2.2 Mass

2.4

M(pK~F*

2.6

2.8

(GeVlc 2)

Fig. 41. The i n v a r i a n t mass spectra in pK~ final states d e m o n s t r a t i n g the existence of the c h a r m b a r y o n C o.

R.J. Cashw_ore

268

2286 + 6 I'£eV in the pK- rr- and/bK + = - states bu~ not the others. This would be consistent with the decay of a C~ baryop, although the mass is different from ;hat derived from the experL~nents described earlier. By assuming that MI charm baryon production eventuMly cascades down to C~, that the C~ decays to a proton wkh a branching ratio of 0.6 _+0.1 (r_eutrons being the other baryon), and that the step in proton production is entirely due to charm baryons, it is possible to calculate a Co~ production cross-section of 0.8 _+0.2rib. Co~sequentiy the absolute branching fraction can be cMculated B(C o - , p K

' ~ t = (2.0 _+0.8)70.

FinMly by studying this ~nal state and others ::he following brancMng fractior_s are obtained

K*°p/K

K-A++/K rr+p

~r+p = (12 _+7)Yo

K°p/K-rc+p = A~+/K

~+p < 0.75 (95 Yo CL)

I~ particu!ar the slate,

K*p and

= 17 _+7Yo

(0.8 _+0.4)

Arr+rr+=

/K

rr+p < 0.8 (95 ~ CL)

KA systems appear to be a small proportion of the Kp~z ~nal

3.3. $,~mmary and ¢emmen~s The obse:'vations of the previous sections are summarized in Table i2. That a baryon of the quantum uumbers of the C O exists is quite clear bur the various mass measurements are in conflict. Presumably there are not two states involved and these difficulties will be accounted for by systema~dc changes in the measurements. It is also clear that C$ decays to .g2N(+X} are favoured over decays containing a A, although the evidence is not overwhehning. As with other charm particles there appear to be a variety of decay channels each, presumably, with a small branching fraction (see Cg --, K p~*).

Table 12. Observations of charm baryons Experiment

Ref.

Decay channel

Mass

v9 %p v~d %Neon Emulsion

22 22 59 60 61

A~+=-=+~r A~+rc*~ K°rc*rc-p K°p, ATzK-pro +

2426+ 12 2260 _+20 2254 _+ 12 2257 + 12 2286 ± 16

Photoproduction 2N

62

~.Tz+~r ~

2260 _+20

Hadronic production PP

63

K-rc+p

2260 + I4

PP

64

K-p~ +

2280 _+7

v production

ATe + 7~ + 7~

PP e+e e+e

65

K ~z+p

2260 _+ ?

43, 66

p K ~+,ffK=~ /£0p

2285 _+6

annihilation -

The Current Status of Charm

269

The evidence for other baryon states is very poor. Perhaps another state, the C[ +, exists at a mass of ~ 2.42 GeV but only further experiments will reso]ve this situat'om Clearly the spectrum of charm baryons is in a much more p i m k i v e state than that of charm mesons. Correspondingly the quality of the information on the charm: quark is much poorer and hence baryons have had little impact in the discussion.

4. M O D E L S O F M E S O N S CONTAIN}~NG C H A R M Q U A R K S : MASSES, TRANSITIONS AND PRODUCTION MECHANISMS in this section the simple models of c6 and cq mesons are s-~mmaized and the transitions between states and the production mechanisms are then confronted with the data of the previous sections. The bound or ~nearly bound' states are discussed initially and then the production properties of charm above threshold in e+e annihilation are reviewe& Thus attention is focused on the strong and electromagnetic interactions, while the weak interactions of the charm quark are explicitly reserved until Section 5. One exception is made in that hadronic production mechanisms are discussed in Section 6, since these boa: less on the specific properties of the charm quark, and more on the nature of t?_e ha&cons participating in the reactions. 4olo The C = 0 c6mese~a--TSe ehar~eoi~m medei

4.1.1. Masses The observation that the mass differences between cc states were small when compared with their masses (e.g. m~) suggested that a non relativistic potential model might be applicable to these quark states. {31) This was a rather novel departure since in the spect::um associated with the u, d and s quarks mass differences were comparab!e to the masses of the states~ To proceed it is necessary first to choose the potentiaI and a variety of ~osslbiiities exist in the literature. (3.'6v) The most popular is that motivated by Q C D (3 t)

Vo(,')

K =

-

,"

--

r +

a2

g

*

~,4.~.!)

where the first term represents the short range asymptotically free interaction and the second the long range confining force. K is expected to be related to the running coupling constant of Q C D 4 2). K(Q ~) : ~%(@

@.,_.2)

The remaining parameter in determining the masses is the charm quark mass, m~, believed to be approximately 1.5GeV (me/2). Equation (4.1.1) is best regarded as a pureiy phenomeno!ogical potential although it does have a slightly better pedigree. Other potentials have similar free parameters and the extent to which the quark mass (which is common to them all) varies gives some feeling for its probable value. Solving a non relativistic Schr6dinger equation or its equivalent will lead to the mass va]ues for the various states. The presence of the confining term in (4.2.1) will remove the degeneracies between the 2s, 2p states; 3s, 3p, 3d states etc. normally associated with the Coulomb potential, tn fact the lp states are expected to !in between the is and 2s ]evels as

270

R.J. Cashmore

indicated in Fig. 15 (which also contains examples of level schemes associated with other potentials). Finally in order to predict the mass values of each individual state spin interactions have to be introduced. Once again the prescription is not unique and a variety of possibilities exist in the literature. (6s-7°/ However, all approaches result in spin dependent potentiais analogor~s to the Breit-Fermi interaction in which the following terms are present: (i) Spin-orbit term: L - S : (ii) Spin-spin term: S~ $ 2 ; (iii) tensor term: 3(S 1 -~) (S 2 -J:) - S1 ' $2. The first of these results in a splitting of the 3P0,~, 2 levels and the second in the mass separation of the 3S~ and ~So states. 4.1.2~ Tra~sitions Solving for the mass values also leads to the quark wavefunctions of the various states so that predictions can be made for both the electromagnetic transitions between these levels and the hadronic decays. Whereas the former rely p'.arely on the electromagnetic properties of the quarks (charge, 2e/3 and magnetic moment 2/3.eh/2Mcc ) a further ingredient is required for the hadronic decays. This new ingredient is the gluon counting rules motivated by asymptotically free Q C D J 15~ The bound states, lying below D/) threshoid, are forbidden to decay directly to the light quarks by the Zweig rule. The final state is reached in this model through an intermediate state containing the minimum number of gh;~ons consistent witt: the quantum numbers of the decaying state. Intermediate states containing more than the minimum number of gluons are expected to be suppressed by powers of the coupling constant z(Q2), assumed to be in the range ~0.2. The decays of the .~ are summarized in Fig. 42. C

(a)

E~ecfromagnefic

C

(b)

Hadponic

gig. 42. Decays of the tp.

With these rules the electromagn, etic and hadronic decays of the states of Table 1 and Fig. 15 can be eval~aated. These results are summarized (2s'71) in the following Tables 13, 14 and 15. In these expressions ~,~(0} represents the radial wavefunction at the origin of the cg state, ~;~/(0) its derivative, z~ is the running coupling constant of Q C D and M,,~ the mass of the decaying state. ~n the electromagnetic transitions between states, E~y and M~I are integrals associated with the electric dipole (El) and magnetic dipole (M1) transitions. In the case of n'3S~ +~ n3So, M~f will be ~ 1 if n' = n, since the radial wavefunctions are similar, and much smaller if n' ~ n due to the approximate orthogonality of the radial wavefunctions. In the S ~ P and P ~ D transitions multipoles other than E1 are in general possible, leading in principle to more complicated results. In the hadronic decays

The Current Status of Charm

271

TaMe 13. Electromagnetic decays State and decay S-states F(n3Sl-,e+e

) -

4~; =lGo(O)L;~/~ 2 m ~ l tz ,~- - ~ / t .../|

4 m ~ ''2

M,,o

F(n3S1 '---> 7 -+.hadrnns) - F(n3S1 --+ e + e - ) R (e+e - --+ hadrons) R ~(e+e - ~ # + # ) F(n3SI -4 7 + hadrons) =

off resonarme

32 , 2 2 ~2[~"°(0)12 9 ~= - 9 ) % g g --~/}5o°

F(nlSo--+yT) = 12Q4cx2 ]~,,o(0)[2 P-states F(n3P0 -+ 77) = 432Q 4:~z IG~(°)I2

r(n~Pa --' 7V')= 576 Q+~=IG~,~40)IZ5

M,,

the n 3 p 1 and nlPa formulae are conspicuously different. This is due to the 2 gluon decay of a 1 + being forbidden (at least for massless gluons) and the decay has to proceed as indicated in Fig. 43. This results in an extra power of a s as weil as the logarithmic factor. A notable absence from TaNe 13 is the 3D1 --, e ' e - decay which is forbidden in non relativistic models since t),2(0 ) = 0. Thus this state could only be excited by an admixture of a 3S, state. From a comparison of the hadronic and leptonic widths of the has1 state an evaluation of ~s is clearly possible 5

2

F(n3S1 ~ hadr°ns)/F(n3S1 --+ e+e ) = 18~ (~ - 9 ) ~

Table t4. Electromagnetic transitions between states Q , ( S ++ P) = Fr(3D1 +-* 3po) = l-.e(3D 1 ++ 3P1) =

4/2Jf+15

~

2 3

4/2JI+1\

,

* 3

4/2df+151

F),(3DI <-+ 3P2) = 4 [ 2 J f + l \ F;(3S1 .~ ISo) -- T16( 2 S f +

Eif = Mif = PPNP

7 - R

.~ 1

2 3 ~

2 3

1)~/ ~Q 2 aiM.;[ 2co3 \Zinc~

[ r2 drlOi(r)t/Q (r)r

fo

~ r2

drjo (½cor)~ i(r)~s f

(r)

~3

(4.1.3)

272

R. J. Cashmore Table 15. Hadronic decays S-states F(n3S1 -+ hadrons) = 8417r(Tz2 - 9 ) e 3

I~,,,o(0)l2 M,2,o

F(nlSo ---,hadrons) = 8 ~2 I~',,o(0)12 3

M,,a

P-states F(n3po - . hadrons) = 96c~ 1ff;'1(0)]2

M4~

128 ~10;,~(0)1-'. [ 4mq2 F(n3p1 -~ hadrons) = 3re ~s Mn 1 ~4 111~4mq - ~_mnl

5 )

F(n3p2 -+ hadrons) = 128 ~:''^!O,~aJ~)l2 5 " M,,

F(ntPl~hadrons)= 320~l~'~,,~)21n ( 4m2q 9n M,1 \ 4mq - m.~ j

where the wavefunction dependence factors out. Knowing this result, predictions can then be made for F(n3S1 --, hadrons)/F(nlSo --, hadr0ns) = 5 (nz_ 9) 277r G Fin3Po + hadrons):F(n3pl ---, hadrons): F(n3p2 -~ hadrons)

=I"

4c~, ( 4m: ) 4 9~ln 2--- i " - - . \4m c - M n l 15

There remain two important transitions, i.e. ~'--, ~zrC, ~/, for which no specific predictions can be made within the charmonium model, since the momentum of any gluons would be too ]ow (and couplings large) for gluon counting to be reliable. 4.1.3. QCD corrections Clearly, in performing all of these caiculations first order perturbation theory is assumed. However, recent calculations (72'73) have indicated that the higher order corrections may be

3p 2

3p r

0

Fig. 43. Decays of (a) the 3P2 and 1Po via gg," (b) the 3p~ and 1P 1 via gqq.

The Current Status of Charm

273

Table 16. Estimates of QCD corrections to cg decays Quantity

Correction

F(3S, ~e+e -)

F(e*e )=Fo(e+e-)(1- 37r ]

R

16~)

(ISo --+hadrons) (~So~ ?'?')

f22.14

0~s

substantial and where estimates for these exist they are summarized in Table 16. The variations are due to different calcu~ationd schemes and indicate the reliability of these estimates at present. However, if G ~ 0.2 --+ 0.3 then ~ 100 % corrections can be expected suggesting great caution in both the appiication of these form~:lae and the credibility of precise numerical successes. More theoretical effort is clearly needed not only to improve the caIculations but also to extend them to a greater number of states. 4.1.4. Open channels Knowing the large number of charm particles which exist and the proximity of their tl~resholds (e.g. DD, DD* etc.) to the expected charmonium states, it is rather naive to expect a simple cC approach to be totally successful. Attempts have been made to include these open channels (3~ leading to changes in mass values and wavefunctions for the states due to mixing between cc states and the open channds. Indeed spectacular predictions have been made for the existence of the 0"(3772) and the variation of R in the threshold regions. (3 ~ 4.2. The eeefrema~io~ ef ~he eharme~i~rn model with Che da~a tn this section the charmonium model is confronted with the data summarized in Section 2. 4.2.1. Parameters ~n order to obtain the major parameters of the Q C D motivated potential model, me, K and a, input data has to be used. This is "usually the ~b ,~' mass difference, the centre of gravity of the 3p states and the leptonic width of the 0. The parameters that resuit from fitting those do not in general reproduce all the observed data. tn particular the Et transition rates, 0' --+ 7 + 3p, are too large and no sensible choice of parameters Mlows both ~9 -+ e+e and these rates to be accounted for simultaneously. The question of Q C D corrections clouds the issue, although it rnay wel~ reduce the discrepancy, tn the work of Eichten et al. (31~ a poor fit to the t) -+ e+e - decay is accepted in order to retain low quark velocities and hence to preserve an approximately non relativistic model and so stay within the spirit of the charmonium idea. (The Q C D correction (Ta~ naively applied with their parameters leads however to good agreement but this is probabiy fortuitous). The parameters that resuit are M c = 1.84GeV

K = 0.52

a = 2.34GeV

I

(4.2.1)

Early approaches using the same Q C D model but different input yielded the parameters M~ = t.65 GeV

K = 0.30

a = 2.07 G e V -

R. J. Cashmore

274 1.0

Lineclr+ coolom ;/

0.8 0.6

0.4 02 > L~ c

o -0.2

)

I 0 l~

-0.6 -0.8 -0.10

/ //

0.'2 Oil& 016 018 I.'0 112 1 r(fm)

Fig. 44. The QCD inspired cgpotential (Ref. 31) compared with the logarithmic potential (Ref. 67).

while yet other forms of potential (logarithmic etc.) give M c = 1.1 GeV and 1.98GeV. ~67) Thus the variation is great and hence tittle attention should be paid to the specific values of parameters, e.g. mc, that resutt. These are best regarded as purely phenomenological quantities. The results quoted are those of Ref. 31 and the potential is shown in Fig. 44, where it is compared with a logarithmic potential which has bcew fitted to the q family. 4.2.2. Mass spectrum Gross structure. The parameters, eq~a. (4.2.1), lead to the gross structure of Table 17, where the experimentally observed states of Section 2 are identified with charmonium states. ]In this table are also included the effects of the coupled channel calculations. (3t) In Table 18 the corresponding levels assuming a logarithmic potential (6v) are listed, but these results do not include any coupled channel consequences. It is difficult to distinguish one potential from another, although the e+e - widths of the higher ~, states, the 4,(4160) and ~(4414),

Table 17. c6bound states Naive

Coupled Channel

State

Mass (GeV)

Fee (keV)*

(rz) 1/z

Mass

F~

Candidate

13S1 13P~ 13P~ 13p0 23S1 13D 1 33S1 23D1 43S1 53S~

3.095

4.8

0.47

4.8

3.522

--

0.74

3.684 3.81 4.11 4.19 4.46 4.79

2.1

0.96 1.0 1.3 1.35 1.7 2.0

3.095 3.523 3.517 3.5t9 3.684 3.755 4.225 4.230 4.625

6`(3095) Z(3555) 7`(3510) 7.(3415) 6`(3684) 6`(3772) 6'(4028) 6`(4160) 6`(44!4)

1.5 -1.1 0.8

h~cludes a QCD correction factor of l -

3~z ]"

2.3

The Current Status of Charm

275

Table 18. c ( b o u n d states with logarithmic potential State

Mass

F~

Candidate

F ~ Obs

1S 2P 2S 3D 3P 4F 3S 4D 4S 5S

3.097* 3.530 3.686* 3.87 3.91 4.07 4.07 4.08 4.23 4.41

4.80

~(3.097) Z ~b(3.686) ~(3.772)

4.8

1.73

2.1

0.98

~,(4.028)

0.75

0.71 0.51

~,(4.160) 0(4.41)

0.77 0.44

may eventually distinguish the models. ~n the QCD motivated potential (3:; model the ~(4160) is largely a D state, having a small Fe+ e- due to mixing with S-states, while in the other model {6v) it is predominantly an S-state. The ~'(3772) can be regarded as a triumph for the c6 model, although the closeness of the coupled channel prediction is probably fortuitous. In TaNe 17 the radii of the mesons are included to emphasize the point that .the quarks spend most of their time in regions dominated by the confining potential rather than by the Q C D part of the potential. Since little is known of this potential forms can be chosen and this leads to the variety of phenomenological models. Furthermore, although well motivated, the QCD part of the potential plays little role in defining the mass spectrum and hence this cannot be adduced to prefer this potential over all others.

Fine structure. The fine structure due to the L_. S, S i

• ~_2 and tensor terms varies from model to model, as indicated in Table 19. The major problem to be accounted for is the character of the splittings in the 3p states. For a purely L . S interaction

M ( a p 2 ) - M(3P1) M(3P1)-M(3po)

2 1

whereas in practice it is found that M(3P2)-]ff(3P1) ~ 0.42. M(3p1)- M(3P0) Only one of the models (7°~ succeeds in approximately achieving this result and at the same time reproducing the ~-~c mass difference. (This assumes that the state at 2980 MeV is identified with the t/c. Previously the large ~ X(2830) mass difference had been an even more embarrassing problem but with the demise of the X(2830) this has fortunately Table 19. Fine structure ofc6states Author

Expt Schnitzer ~6s) Purnplin ~69) Henriques ~v°) Celmaster<6V)

M(3P2)-M(3p1) 44 _+6 87 152 40 92

M(3P1)-M(3po) M(13SI)-M(13So) ,'vI(23S1)-M(21So) 95 _+5 63 1 !7 80 100

100 _+15 70 119 95 !50

58 92 -80

276

R.J. Cashmore

disappeared.) It should also be noted that where quoted the M(23S,)-M(21So) mass difference is smalI placing the ~/'~dose to ~he @' as well as the r/~ close to the ~. 4.2.3. Transitions

decays. The leptonic w~dth of the ~ is consistent with the predictions providing either a relativistic motion is assnmed for the quarks (logarithmic potential) or the Q C D corrections are invoked within a non relativistic situation (Coulomb and linear potential). Thus some degree of unease must be attached in both cases. The direct hadronic coupling provides an estimate of ~ using the formula of Section 4.I. tn particular, eqn. (4.1.3) leads to ~ ~ 0.I9.

Direct decays. Having obtained this result for % it is now possible to calculate ~he widths listed in Table 20. (28~ The most notable results of this table are the comparatively large widths for the ~h., ~I~., Z0 and Z2 states whereas the Z~ state is much closer to the ~ and ~' (as expected from Section 4.1 ). The other notable result is the predicted decay ~ -+ 7 + hadrons (assumed to be via 7gg) which is comparable to the experimental results, although some doubt is cast on this comparison by the conflicting x~. distributions (37'38~ and the tack of clear evidence that the ? has its origin in this Q C D type process. T a b l e 20. D i r e c t decays in c h a r m o n i u m

Decay

Width (keV)

Branchingratio (%)

t/~ --, h a d r o n s ~h, -~ )'7' -, ~+hadrons Zo - ' h a d r o n s Z0 --+ 77 )fl -~ h a d r o n s Z2 -~ h a d r o n s Z2 --+ 77 ~/; -+ h a d r o n s ~/; -> "*'7 0 ' --+ h a d r o n s ~' - , e ' e ~b' --+ 7 + h a d r o n s 1P 1 -~ h a d r o n s

5!00 7.1 6.1 1800 2.5 105 480 0.7 3300 4.5 3i 3.4 3.9 87.5

100 0.14 8.0 90 0.13 21 48 0.07 97 0.13 14 1.5 1.7

To calculate the totai ~/; width a partial width for

has to be assumed and this is taken to be r { ~ ; --, ~cTrrc) = r ( ~ , ' --, ~,Trr0.

Also for the Z states account has to be taken of the 7-ray partial widths, which are discussed in the following section, before branching fractions can be quoted.

Electric dipole transitions. Using the formulae of Section 4.1, the E1 transitions @' --+ X and Z ~ ~b can be calculated and are summarized in Table 21. Clearly, in order to make

The Current Status of Charm

277

Table 2t. E1 transitions

Decay

Naive

if' --+ 72o 7Z1 7Z2 Zo --+ 7~' Zt ~ "/~ Z2 ---'7~

50.0 45.3 28.9 141 289 398

Zo -~ 70 Z~ --' 7~' Z2 ~ ~'~

0.07 0.55 0.45

F (keV) Coupled channel

Expt (keV)

43.2 34.4 23.7 130 257 350

16 + 9 16 -+9 16 + 9

Branching fractions 0.07 0.71 0.42

<0.7 x 10 -2 0.3 i 0 . 1 0.!9 -+0.07

predictions for the X--' ~0 branching fractions (which are experimentally measured) the totat width of the Z state is needed. This is taken as F t o t ( Z ) = ~ ( Z --+ ~/0) + ~ ( X ---* h a d r o n s ) +

F(Z ~ 7~)

where the last two widths are quoted in Table 20. [n all cases the predicted electromagnetic widths of the 0' are apparently far too large, by factors of ~ 2 - 3 , and the discrepancy is probably even greater in the Z decays. However, it is encouraging to note t h a t {27)

F @' ~TZo) _ F ( 0 ' - ' T Z ~ ) _ F ( 0 '--.7Z2) _ 0.6:0.7:1.0 3

3

where ratios of 1 would be expected from pure E1 transitions. Finally, if the electromagnetic decays 7. ~ 70 are assumed to be known, iota1 widths can be calculated for the Z states as indicated in Table 22. However, in view of the results above this would seem to be a poor assumption and so in parentheses appear resuks assuming different electromagnetic widths consistent with suppressions required in the 0' ~ 7Z decays Table 22. Total hadronic widths of z states*

Zo Z1 Z2

F(Z ~ 7~9) (keV)

Ftot (keV)

Fdlrect (keV)

130 (48) 257 (121) 350 (236)

> 18871 ( > 6857) 856 (403) 1842 (i242)

> 18571 ( > 6857) ~ 600 (282) ~ 1500 (1006)

* Values in parentheses correspond to suppressed 7 widths.

as observed above. The main issue here is the ratio F(7~2 ~ hadrons)/F(z0--' hadrons) which is 'reliably' predicted by Q C D (7n to be 0.27 (4/15), whereas the experimental value is <0.081 (<0.15). Thus a conflict might be present aithough, in view of the inadequacy of the description of the E1 transitions, this is a rather premature conclusion.

Magnetic dipole transitions. F r o m Section 4.1 numerical values for the unhindered M I transitions are given by (2s'31) 16 [ ec \2 F@,' -~ 7~(c)/k3 = r(@ ~ 7%)/k 3 = 3 <2~n~) ~ = 1275

keV

(GeV)

R. J. Cashmore

278

Table 23. M1 transitions in charmonium 2"ransition

FMI (keV)

O' ~ ?r/~ ~' ~ ?G 0' ~ 7q; r/; -~ ~

0.88 1.23 0.15 L97

BR

0.40 x l0 2 1.81 x 10 -2 7.0 x 10-'* 10 3

whereas there is a suppression factor introduced for transitions q'~ ~ 70 and ~b'~ 7~Assuming that the mass difference M(0) - M(G) ~ 100 MeV and M(~k') - M(~;) ~ 50 MeV results are quoted in Table 23. It can be immediately seen that the cascade decays

0'-* 7~; and

wilt be hard to observe. However, the observed ~ ' ~ VG and ~ ~ 7 ~ transitions are qualitatively compatible with these predictions. ~34) Finally, i~ is amusing to note that the 1P ! state could be obtained from the 3p states by an M1 transition providing its mass has a suitable value.

0' decays, tn the preceding sections m a n y of the decays of the 0' have been calculated. These are compared with the experimental results in Table 24. The agreement is good except in the case of the radiative decays as noted earlier. This might indicate that the problem lies more in the ~ states than elsewhere. Unfortunately, as remarked earlier, no predictions exist for 0' ~ ~rTr and 0' ~ ?q, both of which violate the Zweig rule but are too low in hadron energy to be susceptible to Q C D arguments. Table 24. ~' decays

Decay

Predicted wid'~h (keV)

Expt (keV)

q / ~ e+e - +~+/~0' -~ '/Z ~' -* hadrons direct

6.8 101 31

3.9 + 1 48 _+!4 48 _+ 19

~" decays. Using the coupled channel approach, this state was predicted (a~ before its observation to be at a mass of ~ 3770 MeV with a total width of ~ 30 MeV (above Dt) threshold). These values are in remarkable agreement with the current observations. Refinements have changed the predictions littte. This state acquires its leptonic coupling predominantly from a 2as1 admixture 10"(3772) > = cos0

[13DI >

+sin0123Sa >

and this width is predicted (28'3~ to be ~ 70 eV (0 ~ 10°). This is substantially smaller than the experimental value of 255 _+60 eV (see Table 4) corresponding to ~ 2 0 ° and perhaps indicates the need for more complicated potentials which would induce such mixing. None the less, this was a great triumph for the coupled channel charmonium m o d e l

The Current Status of Charm

279

Pseudoscalar states. The observation (34~ of the state at 2980 MeV means that the pseudoscalar system is now qualitatively consistent with the charmonium model. Clearly these states are difficult to observe, but the first hadronic branching fractions are now appearing ~34'35) and even estimates of the total width, ~ 2 0 _+ ~6 MeV. This value, wi~h its large errors, is only L5 standard deviations from the Q C D prediction of an ~/~ width of 5 MeV. Light quark states. The decays of the ~ to 7~/ and 7r/' can be used to estimate the mixing between the ~/, ~/' and G. (36~If the G is written as ;7c = c£+~r/+~'r/' then these decay rates imply e ~ i0 -2 e' ~ 2.2 x i 0 - 2 The high decay rate ~o t h e f m e s o n can be similarly interpreted (36~ (it is much greater than the V M D model would suggest from the observed o)f ° decay) as being due to substantial cd admixtur e in the f 0 wavefunction. The decay of o/E(1410) is surprising and might indicate a ~.arge gluon component in the E(1410) wavefunction. Indeed the de = 1 +D and E mesons have very narrow widths which is not easy to understand in the light quark meson sector. However, more evidence (je, decay modes) is required to indicate that the same E meson is actually being produced (3sl in the ~ decays and in hadron reactions, before gluebatls have to be invoked. 4.2.4. Summary In general the Charmonium Model provides an adequate qualitative description of ttle cd mesons bu'L there are q~antitative problems, e.g. mass differences, E1 ~ransition rates, hadronic decay widths. Complicating the modei by the introduction of coupled open channels leads to some improvement but not sufficient to believe the sotu~ion has been found. A possible resolution of the difficulties may reside in the Q C D corrections which appear to be largeF 2'73) However, these calculations are in their infancy and it wilt be necessary to study the corrections to higher orders ( > 2rid) and for m a n y decays before definitive conclusions can be drawn. After a few years of effort it now appears that the ~ system is not quite the °hydrogen atom' of strong interaction physics. Perhaps the 7 system wilt come a little closer to this ro~e.

4°3° TEae C = + ~ meseo--Medels ~

da~a

These mesons are systems of the type cq(dq) and a similar approach can be applied to that used in the case of charmonium. (28'31) However, due to the light mass of the ~old' q~aark (u, d, s) the problem immediately becomes relativistic and the application of such a model should be regarded with some scepticism. 4.3.1. Masses The mass of the iowest D O state is approximately given by

MD ~ Mc + M ,

280

R.J. C a s h m o r e

with mc ~ m0/2 = 1.55 GeV a n d M , , M d = 0.33 GeV. (These choices of q u a r k mass emphasize the flexibility a n d no i m p o r t a n c e should be attached to :heir specific values.) The D* state then appears ~ 150 MeV higher in mass. ~fthe cq system is likened to the sq system (another rash a s s u m p t i o n ) then the following relation is expected (31) nl s

M I D * ) - MCD) _~ - - {.+(K *) - M ( K ) } m c

which is a p p r o x i m a t e l y satisfied (with ms ~ 0.46 GeV). The F a n d F* states can then be calculated from the formulae (2s'31)

MtF*) = M ( D * ) + M @ ) - M t K * ) =

2.135

M(F) = M ( F * ) - [ M ( D * ) - M(D)] = 1.994. These results are c o m p a r e d with the data in Table 25 a n d there is reaso~lable agreement, although the identifications a n d m e a s u r e m e n t s are !ess t h a n certain (see Section 2.3.2). Estimates of the electromagnetic mass differences (7~ in the D, D* m e s o n states can atso be m a d e assuming that they are due to the u p - d o w n q u a r k mass difference plus some single p h o t o n exchange c o n t r i b u t i o n . This c o m p a r i s o n is also included in Table 25. F i n a l l y the masses of the P states of the cc] (q = u, d) system (which c o n t a i n s two d P = 1 + states) can be estimated (3~) from these potential models resulting in

MD(O + ) = 2.354 GeV MD{1 + } = 2.364GeV

MD(1 +) = 2.503 GeV MD(2 +) = 2.511 GeV with c o r r e s p o n d i n g l y larger values for the F m e s o n states.

Table 25. C = ± 1 meson masses and mass differences Masses

State Do D*° F F*

Predicted (GeV)

1.994 2.I35

Observed(GeV} 1.863 2.006 2.03 + 0.06 2.14 _+0.06

Mass differences States D+ - D O

D*+-D *°

Predicted (MeV) 7.0 6.5

4.3.2. Transition amplitudes The principle t r a n s i t i o n amplitudes are D* --, D? F* -~ F 7 D* ~ DTr

Observed(MeV) 5.0 +0.8 2.6 +_!.8

The C u r r e n t Status of C h a r m

28t

ar~,d simple f o r m u l a e can be given for these decays. The y-ray t r a n s i t i o n s are b o t h M1 in c h a r a c t e r a n d giver~, by (28'31) 4 [ ec r ( D * ( c 4 ) -> DCc(I)+ 7) = ~ ~ ~2m~ +

.3

\z171 c

eq ,~z p3 2mq/

z~,~s/

where eq, e s, e c are the q u a r k charges a n d m s, m s, m c their masses (ms = 0.335 GeV, m~ = 0.45 G e V a~d m~ = 1.84 G e V ) a n d p the p h o t o n m o m e n t u m . The h a d r o n i c decay of the D* is given by {2s'3.) p3 2 /- 12 F(D* ~ Drc) - 72rcM~, C ] x / ? d D , E D E ~ A w h e r e ~D,Tz = (p 2 +MD,~) 2 1;2 . , p is the decay r n o m e n t u m , C is an isospin Clebsch G o r d a n

coefficient a n d A an a m p l i t u d e derived from K* - , Krc decay by a s s u m i n g t h a t a similar m o d e l app~.ies with the c h a r m q u a r k replaced by a strange quark. A = 47.8 G e V -3/2. Using the m e a s u r e d D, D*, F and F* masses c a l c u l a t e d widths a n d b r a n c h i n g ratios are s u m m a r i z e d in Tab'~e 26 a n d c o m p a r e d with the data. Table 26. D* and F* decays Mode

Predicted width (keV) Predicted BR

D*° -, D°'/ D*° --+D% ° D* = --+D+7 D*+ ~D=~ ° D*+ -~ D% + F *+ --' F7

35.2 43.4 2.4 22.2 53.4 0.32

0.47 0.53 0.031 0.285 0.685 1.0

Exp BR 0.34 ±0.10 0.66 ±0.10

The d r a m a t i c difference in the D *° a n d D* +7 decays is due to the difference in the m a t r i x elements for different q u a r k charges. The differences in m o m e n t a lead to any remairSng changes in the widths (~p3). Since the D* is close to the Drc t h r e s h o l d this h a d r o n i c width is m e a s u r e d in keV r a t h e r t h a n the usual MeV, while isospin invariance forbids the d e c a y F * - + F ~ a n d energy c o n s e r v a t i o n the decay F*--+ Frt~. T h u s the accident of mass differences leads to the r e m a r k a b l e situation that e l e c t r o m a g n e t i c t r a n s i t i o n s are principle, a n d in some cases the entire, decays of these vector mesons. A l t h o u g h few c o m p a r i s o n s can be m a d e at present, a n d the d a t a tentative, there do n o t a p p e a r to be any d r a m a t i c discrepancies. 4~3.3. S u m m a r y T h e d u b i o u s a p p l i c a t i o n of n o n relativistic m o d e l s to the co7 system leads to m a n y successful results. This success is p e r h a p s surprising b u t n o n e the less continues to indicate a qualitative u n d e r s t a n d i n g of systems c o n t a i n i n g this h e a v y quark.

282

R.J. Cashmore 4.4° Above the eharra Chreshe~4

There are two clear energy regions which require separate discussion--the resonance region and the high energy region. 4.4.t. Resonance region The charm threshold is clearly passed in the region of 4 G e V and discussion of the spectrum solely in terms of c( states is inappropriate. The introduction of a coupled channel approach (31) within the charmonium scheme, which leads to some improvements for the bound states, is essential for a description of this region. ~n Section 4.2 a number of these structures were identified with specific states of the mode1. The prescription (3~) for introducing the open channels is very specific: (i) only charmonium states coupling to the photon are included; and (ii) only quasi two body production (DD, DD*, D'D* etc.) from these states is considered. Hence the predictions are also very specific, the ~"(3772) being a great success of this model. The individual channel cross-sections, e.g. DD, are given by the probability of decay of a cC state to this channei which is related to the form factor for that cd state, i.e. if the overlap of a (cq) + (Cq) system with the c( state is large then this decay wilI be important. Examples of such form factors, (3 ~) as a function of the D meson m o m e n t u m are given in Fig. 45, the zeros corresponding to the nodes in the cd wavefunction. Thus, if the m o m e n t u m of a DD meson system corresponds to one of these zeros the production rate wil] be smalL

n=2

D_

S o p{Gev)

Fig. 45. The cC Decay Amplitude to cv7 (D) and gu (D), as a function of the D momentum.

The results of including D£}, Dt)* and DD*, D*/)* channels in calculating AR are shown in Fig. 46 and bear a striking (although not exact) resemblance to the effects observed in the experimental data of Fig. 18. In particular the sharp rise around 4.0 GeV is associated with the close proximity of the 33S1 cC state and the D*-D* threshold, while the lack of production of D£) is understood in terms of the presence of a zero in the ' 0 ' --' DD wavefunction at this momentum. Thus there is a natural understanding of the rather remarkable DD, DO* and D ' D * production rates in this region and this can be interpreted as another success for the coupled channel model. Introduction of F mesons makes little change to this semiquantitative feature. Of course other explanations for these structures in terms of D'15" molecules, (Ts)

The C u r r e n t Status of C h a r m

4

283

------- AR DB D-~o

<:E l Z2031

IA

~

~

+

-

°

3.7 3.8 39 40 4.1 42

4.3 4./+ /*5

W(GeV)

Fig. 46. Predicted contributions of DD ; DD* + D'D, D'D* to the value of R in the region of charm threshold.

excitation of v i b r a t i o n a l degrees of freedom in string models (76) exist. However, they are rather ad hoc in n a t u r e a n d do n o t address other features of the c h a r m system as does this coupled c h a n n e l approach.

4.4.2. Above the resonance region Well above c h a r m q u a r k threshold the change in R=

o-(e+e - - , h a d r o n s )

a(e'e

~1~+#

)

is expected to be given by (77) R =

3

1+

z

R

+ (1.98-0.12N~

Ii} ~

2i

A {0.7 0.5 o.3 .....

0

~ 2

'

i 4

+

i _,

44

1 6

'1 8

(GeV) Fig. 47. QCD predictions for the variation of R above She charm threshoM. Curves correspond to differentvalues of A (0.3, 0.5, 0.7 GeV).

284

R.J. Cashmore

for a spin ½ quark, where the QCD corrections have been included and % is given in terms of A 2 by :~s - (33 - 2Nz) In Q2/A2 The first order corrections to R are large ( ~ 10 %), the second order corrections smaller ( ~ 2 70) and the asymptotic value of R is approached from above. In Fig. 47 the predictions are shown (for different values of A) together with the experimental data. The increase in R above threshold is consistent with the production of a charge + 2/3, spin ½ quark. However, the agreement is only qualitative beyond the resonance region and there is an indication that the predictions may be too low at high energies. At these high energies it is possible to observe D production and the inclusive spectrum is shown c'9) in Fig. 48, where it is compared with that of rr's and K's. There is an indication that the spectrum is higher at large z, which is consistent with predictions that the charm quark fragmentation function should indeed be harder. (s°~

4.4.3. Smnmao, Within the resonance region there are still discrepancies between experiments which dearly need resolution before finai conclusions can be drawn about this rich area of the

_ ~ Do+ B ° !

100

[] D% U-.~ 6"0< Ecru < 7.8 G~ ore% ~-] 6 ~2K s .~ .1
%%

10

A

oo

O

o

O0

o :=-i

~1~ N

---

0.1

+

°°to e)

)

!

0.01

0o001 0

0.2

0.4

0.6

0.8

1.0

Fig, 48. T h e inclusive D s p e c t r u m in h i g h e n e r g y (Ec, , = 7 . 4 G e V ) e + e - collisions c o m p a r e d w i t h c o r r e s p o n d i n g ~z a n d K spectra. T h e r e is a n i n d i c a t i o n of a h a r d e r c o m p o n e n t .

The Current Status of Charm

285

charmonium system'. At high energies charm observation is in its infancy, although the possibly high value of R may indicate the need for more sophisticated descriptions of the charge 2/3, spin ½charm quark production (or perhaps a revision of the data). 4.5. The strong aed electromagnetic properties ef the charm q~ark The evidence of these last tEree sections leaves no doubt that a r_ew q:dark has been observed carrying a new quantum number, charm, and possessing charge + 2/3 and spin ½. The spectroscopy, masses and transitions are ali consistent with this identi£cation. The quantitative results are not perfect, but then '.:he system is not entirely the non relativistic one that was initially hoped. Nonetheless this new heavy quark has provided the stimulus for many studies Of QCD, and together with yet heavier quarks may provide a valuab]e guide to the strong (colour) interactions. Thus the first 3 properties of the charm q~:ark listed in Section 1.2 have been substantiated.

5. THE WEAK INTERACTIONS OF THE CHARM QUARK The original motivation for introducing the charm quark was to deal with problems in weak decays and the resolution of these difficulties dictates the exact form of the weak interactions of the charm quark (see Section 1.2). The weak current involving the charm quark is given by jx+ = E,/;½(1- 75) ( - d sin Oo+ s cos 0c)

lo)

Semi lepfonic decoys v,

v¢ W+

-

cos Oc

{ b)

~ sin

0c

Hadronic decoys U

U

-cOSOc cOSOc

~sinOc cosOc

g

-cosO c

sin0:

W ÷

g

-sin0 c sin0:

Fig. 49. The weak decays of the charm quark.

(5.1)

286

R. ,L Cashmore

leading to an effective Hamil:onian for :he weak decays of the charm quark of the form Pt =

i

~GF[&/(I--T5)

,/2

(-dsinO~+scosOc)]

× i(dcOSOc+eSinO~)Y.,(1-;"s) u+

r=e.~2&a(1-->,,)vej+~ermi~ianconj'ngate. (5.2)

This current (5.1) leads to the selection ruie that 5C = AQ = _+ 1 ( = AS, for the Cabibbo enhanced--cos 0--decays) and the various decays are summarized in Fig. 49. Decays to z leptons should be included in this Hamiltonian but since the z mass is probably greater than :hat of the charm quark it makes no contribution. Thus the principle features which must be tested are: (i) (V A) nature of:he current; (ii) quark structure of the weak current, in particular the Cabibbo mixing and the absence of neutral current transitions; (iii) strength, GF, of the interaction. tn the following sections the experimental evidence for each of ~:hese hypotheses is studied. The information comes mainly from the decays of the D mesons (Section 2.3) and v interactions. Unfortunately the charm quark is contained within hadrons together with other quarks and their interactions often confuse the simple predictions of Fig. 49. This wiI1 be a major preoccupation of Section 5.2 where other possible diagrams and final state interactions have to be considered. 5o~to The V A e a ~ r e ef the c~rre~t In principle the decays of the D meson D --+ K * e v

can demonstrate the existence and relative strengths of the vector and axial vector components of ":he currents. However, the data is sparse, consisting of the electron m o m e n t u m spectrum only, and is insufficient to give any definitive result. (~ (The decay D --+ K e y only occurs by the vector component of the current). Within a V A sckeme the p u r d y leptmaic decays (to approximateiy massless •eptons) of the D are suppressed (just as in K decay)--none has been observed. The best evidence (sl~ for the V A structure comes from v interactions of the type vN --,/~-#+ + . . . ~#

(5.1.1)

e++...

where the positively charged iepton is assumed to originate from the weak decay of a charm particle. The V A nature of the current then implies a flat y distribution (y = E~ - E ~ / E ~ = Eh~d/E~) for the processes v+d--+ #

+c

v+s--* # - + c .

tn Fig. 50 this y distribution from high energy v interactions, is shown together with the modifications due to the apparatus acceptance. These results are clearly consistent with a predominantly V - A structure of the current.

The C u r r e n t Status of C h a r m

287

35 30, ~25 20 C

e, t5

t0 5 0

0

0.2

0.6,

X

0.6

0.8

1.0

0

0.2 0.4 0.6 X

0.8

1.0

0

0.2

0.8

1.0-~

2 °1

c5

0

0.2

0.~ 0.6 Y

0.8 1.0

0.4. 0.6 Y

Fig. 50. The x and y distributions in v and v induced reactions leading to #-/~ ~ final states.

Thus all the evidence points to a V-A n a t u r e for the weak current, a I t h o u g h m o r e precise d a t a w o u t d allow m u c h m o r e q u a n t i t a t i v e statements to be made.

5°2° The weak e~rree¢ a~d its q a a r k straet=re The various weak decays of c h a r m particles to leptonic, semi leptonic a n d h a d r o n i c final states p r o v i d e a large a m o u n t of i n f o r m a t i o n on the structure of the w e a k current a n d the effective H a m i l t o n i a n . F u r t h e r i n f o r m a t i o n is also available from v interactions. 5.2.1. Meson decays

Lepto•ic decays. The decays D - , #v~

(# = e, #)

are suppressed in the V-A scheme (cf. ~z--+ ev, K--, ev) as i d d i c a t e d in (5.1). F o r massless fermions the decay rate w o u l d be identicaffy zero.

Semi leptonic decays. The m e c h a n i s m leading to these decays is s u m m a r i z e d in Fig. 49a. PPNP

7 - S

288

R.J. Cashmore

The partial lifetime (or partial width) can be estimated from muon decay u4'~6)

T'(C--+ e')e-]-...) = (j~f#~5 leading to the result for D mesons that

z(D-+ev+...) ~ ( m ~ ~. r(# --, evv) \mD/ However, owing to the large exponent (5) small changes in masses unfortunately produce large variations in the partial lifetime, making the estimate only semi quantitative. A measurement of the ratio F(D ~ rcev)/Y(D --, Key) would be the most sensitive test of the Cabibbo structure of the weak current. It is predicted to be tan 2 0 (up to phase factors which in this case are approximately the same for the two decays since both Q values are ]arge). Similar studies of the Cabibbo structure in decays to hadrons alone are confused by questions of non leptonic enhancement. Since the transition c --, s#v~ is At = 0 then there is an equality between D O and D + semi leptonic decay channels, e.g. F(D ° ~ K e+%)=F(D + ~ K ° e + v ~ ) ['(D O--, Korc-e+v~) = F(D + ~ K - g + e+Ve) and the semi teptonic width is expected to be the same in both cases. The experimental evidence for these decays is substantial leading to m o m e n t u m spectra (for the single lepton) shown in Fig. 30. Un;ormnately from these distributions a precise value for the D ~ "aev component cannot be obtained. The results are consistent with the Key and K*ev dominance expected. (4) Since the semi leptonic decays of the D O and D + should be the same, measurements of the semi leptonic branching fractions in each case can be converted into the relative total decay rates of the two mesons. The results summarized in Table 7 suggest that the (branching fraction) for D + ~ e + is substantially larger than that for D o ~ e +. This then implies different total lifetimes for the two mesons which must be associated with different purely hadronic decays. This important observation is returned to in the next sections.

Hadronic weak decays. The weak decays leading to hadronic final states are obtained via the processes indicated in Fig. 49(b). Taking a naive view of these decays would lead to the result that c ~ q e v e : C ~ q l ~ v u : c ~ q q l q 2= 1:1:3 where in the latter case an extra factor of 3 is due to the 3 colour possibilities in the coupling of the W + to the qlq2 pair. The total lifetime of the charm quark would then be given by ~(c)_ t (m~ s r(~)

A kmc/

where A = 1 + 1 + 3 = 5. This approach thus leads to

B(D ~ Xev) ~ 20 ~o in the absence of any strong interaction enhancement of the non leptonic decays. This result is not wildly inconsistent witt~ the observed branching fractions, although the recent measurements of the D o and D + semi leptonic branching fractions (which differ

The Current Status of Charrn

E [ ~Sq

C U 20

289

÷

tJ

84

Fig. 51. Schematic representation of charm quark decays lying in 20 and 84 representations of SU(4).

substantially) suggest that the situation may be more complicated. In the corresponding case of strange particle decays there is considerable non leptonic enhancement. When the S U(4) structure (~2) of the weak non leptonic Hamiltonian, eqn. (5.2), is studied it is found to contain two pieces, oae transforming as a {20} representation and the other as an {84}. This can be represented as shown in Fig. 51 where the first term is antisymmetric (the 20) and the second symmetric (the 84)° The decomposition of these representations into their S U(3) sub groups is given in Table 27. In K decay the tra•skion K + ~ rc+r~° is suppressed compared with K ° - , rt+rc -. Since the former has to be a AI = 3/2 transition, which belongs to an S U(3) 27, which is only found in the S U(4) 84, h is natural to expect the 20 component to be enhanced over .the 84 component of the Hamikonian. If this enhancement occurs in charm decay then the simple predictions of Fig. 49 wouid no longer follow. The new properties are conveniently expressed in terms of V-spin content o2 the transition. The first term of Fig. 51 corresponds to V = 0 (u and s lie in V = ½ state and the antisymmetric combination must give V = 0) and thus if this dominates only AV = 0 transitions will be observed. The AC = _+ 1 transitions, due to the _6 and 6* pieces (83/of the 20, lead to very specific predictions based on the S U(3) structure of these operators: (i) there wo@d be no Cabibbo enhanced decays (c~cos ~ 0~) of the D + to a pair of pseudoscalars (e.g. R0~+) or vectors (K,0p+) since the negative sign (of Fig. 51) leads to a cancellation. (Or alternatively the D + has V = 0 while a 2g;°~z+ or ~ , 0 p + system must, to preserve Bose statistics, have V = 1 and thus these states cannot be connected via a AV = 0 transition.) Only those decays to pseudoscalar pZus vector (KT°p+) would exist;

@) r(P +) ~ ~(D°). However, within this approach more sophisticated (not necessarily correct) calculations of the matrix elements suggest that there is only mild enhancement of the 20 over the 84 leading to resu]ts such as (!61 F(D + --+ K°zc +) ~ U(D ° --+ K-~z + ) B ( D , F --+ ~ + v ~ + h a d r o n s ) ~ 0.1-0.25 B ( D --+ ~"+ v e + K ) ~ 0.03-0.08 B ( F - - + ~ + v ~ + ~ l ) ~ 0.02 0.05 B(DO _+ K - r r + +Ro~o) ~ 0.03-0.18 B ( D + --+/,~%r+ ) ~ 0.02-0.10 B ( F + --+ rVc + + K + K °) ~ 0.02-0.12

with the Cabibbo enhanced decays still of the greatest importance, i.e. the naive results of Fig. 49 will stand.

R. J. Cashmore

290

c

l

s W÷

DO

Do

W+

(a)

(hi

c W+

D+ W

F+ g

u

~

d

(d)

Ic)

Fig. 52. Other possible contributions to the decays of D and F mesons.

The introduction of other processes, (841 as in Fig. 52, could lead to dramatic changes in the predictions for decays containing charm quarks. For example, no diagram such as Fig. 52a can be drawn for D + decay and hence an immediate enhancement of D o decays over D + decays is obtained. However, it should be pointed out that the decay D o ~ sd is suppressed in the case of massless quarks (cf. Section 5.t and 5.2.1) and thus the emission of a soft gluon from one of the quarks in the D O (Fig. 52b) has to be invoked to avoid this difficulty. Thus an alternative to 20 enhancement exists if ~(D ° --, E:°rc 0) << ~(D + ~ K % + )

which impiies :

(i) ~(F +) < ~(D+); (ii) the F might no longer decay predominantly to strange particles since diagrams of the type of Fig. 52c would lead to non strange final states. Models which also include the W annihilation graphs (Figs. 52c and d) lead to further possibilities. Table 27. SU(2) structure of weak Hamiltonian in charm decays AC

20

84

2 1 0 -1 --2

6 8 6*

5* 3 " + 15,~ 1+ 8 + 2 7 3+15M 6

Whatever the exact structure of these interactions, a~l models imply a variety of final states are possible. The results of one such model, (sS) the statistical model, are summarized in Fig. 53, indicating the enormous number of channels available and the iaigh multiplicity

The Current Status of Charm

291

230 decay

(o)

(stafisfica[ mode[)

8 u

20

K+

-

' K ° 2r~ o

E cJ

~s

8 13_

2

3

4

5

6

-~7

Number of finc[ Dc~rfic[es (b)

30

D- decay (sfa,fisfica[ mode[)

I/]

cJ

W

K°2 rc°r~-I

i~
20

,KU 3~m° E7 i

K+r~o 2 _lK+2rc ° 2rc-[

~d 8 K°~+2 I%- I ,

2

3

,K+T~+T~° 3T~

5

6

--7

Number of finer parficies Fig. 53. The results of a statistical model for the decays of the D meson.

of particles in these decays. In these circumstances it is unlikely that any specific exclusive channel will exceed a few per cent in branching fraction. Finally a more 'mundane' effect, final state interactions, could change the reiative rates of the decay. K, for example, there is a resonance iv. a particular channel, e.g. KTr, near 1.865 GeV, this could lead to a dramatic increase in this decay of the D. Thus in studying these decays it is difficult to unravel tSe effects of Cabibbo enhancement in the current from effects due to the strong interactions which can lead to both a variety of new diagrams and non leptonic enhancements as well as final state interactions. Such effects must be present if the different semi ieptonic D branching fractions are to be understood. With this background the weak non leptonic decays of the D's can be discussed, although

292

R. L C a s h m o r e

the assertion of Section 5.2.2 that a true test of the Cabibbo structure will only be obtained in the semi leptonic decays must be remembered. The k n o w n weak decays of the D o and D + mesons were summarized in Table 7. The most obvious features are: (i) The smalt percentage of identified decays consistent with statistical model type approaches (
727[

D : - - = 0.03 _+0.015 KTr o

Kn

- 0.11 _+0.04

D+ . K / ( _ 0.24 _+0.14 K~z indicates deviation from the expected values of tan 2 Oc ~ 0.05. Of course there are phase space corrections and it is not clear that SU(3) breaking effects are totally accounted for by the use of physical masses (in the phase space calculations),. Furthermore this is an example of where no account is taken of final state interactions which are u n d o u b t e d l y differen~ in the Krr, 7[~zand K K final states and which could change the predictions dramatically (s6) {due to the presence of a factor sin 2 6, where 6 is the corresponding KTc, ~zn or K £ ~ phase shift). (v) Taking into account the differing lifetimes F(D ° -+ K n + + K:°rr °) > 8F(D + -+ K'°7[ + ) once again indicating either 20 enhancement or the presence of other processes, e.g. Fig. 52a. These last four o:aservations all point in the direction of either 20 enhancemen~ or the presence of V / exchange and annihilation diagrams, and it is worth summarizing the distinctions between these two approaches as a guide to future i m p o r t a n t experimental measurements. (s4~ (i) 20

dominance

This oniy has a major effect on the D + decays so that F + and D o decays (the F + and D o lie in the same V = ½ m u k i p b t ) are not dramatica!ly affected " c ( V ) ~ +(D °) << r(D + ) B ( F + --+ e + + X )

~ B ( D ° --+ e + + X )

B(D ~ ~ no /~° or K

)~0.2

0.3.

The Current Status of C h a r m

293

(ii) W e x c h a n g e dominance This can only have a major effect in the D o decays ieading to ~(p+) ~ ~(D + ) >> ~(D °) B(F + ~ e + +X)

~ B ( D + -+ e + + X )

B ( D + -* no /~° or K

)~0.05.

(iii) W annihilation + e x c h a n g e The processes of Figs. 52c and d produce further effects in ":he D + and F ~ decays leading to

v(D ° ) < "c(F+ ) < r(D +) ~ ( D ° --, e + X ) < B ( F + ~ e + X ) ~ m D + B(D +-+no

/c° or K

~ e*~)

)~0o35

B ( F + ~ K's or ~'s) reduced.

The D + decays indicate that either (i) or (iii) are the more ~ikely, although a distinction can only be made t h r o u g h the lifetime or decays of the F + (on the extremely tentative (!) basis of ~ 3 events it appears tha': r(F +) ~ r(D°)). However, it should be stressed that the F m a y not decay preferentiatiy to ~7 or K / ( final states and an open mind should be kept in searching for its decay channels. D° D ° m i x i n g

As in the case of the K °,/~o system the possibility of D°D ° mixing exists. {~4's7) If this is induced by charm changing neutral currents, e.g. 67'½(1 _+75)u coupled to the Z ° boson, then A M ( D ° , D °) - G e M ~ >> F(D ° - , all) - G } M ~ and D°/i] ° mixing will he complete; i.e. the D °, D O system wi!l develop in time as DO+//] o

,/~

DO_~ o and

,/5_

Thus a D o meson will decay equally often to K's as to /('s or akernatively as often to e - as e +. However, if these IAC] = 2 transitions are second order (G}) processes, e.g. D o ~ n + n - _, ~ o then the mixing wiil be less but possibly sdt] appreciable. This p h e n o m e n o n has been studied by both Iooking for ~ike strangeness K ' S (53) o r like sign leptons 'ss) in the region of DD production, tn ali cases there is no evidence for AC = - A S decays and the upper limits on the violation of the AC = AS rule from the experiments are ~ 17 G(s6) and ~ 5 G
294

R.J. Cashmore

cos 2 0~) and from the valence d quarks (at high x and proportional to sin s O~). 2~hus lktle increase, ~5~o, is expected in the total cross-sections, as observed, (s9) and the charm particle production she'~ld be associated with low x. Charm particles produced from the processes

v+d~-+c v+s-~ #-+c can then be expected to decay giving S = - 1 kaons and positively charged leptons. Further K's are expected from the #quark of the sea. This process is the origin of the # - e + and g - # + dilepton events observed in v scattering. As shown in Fig. 50 the x distribution for tkese events is indeed peaked at small x which is indicative of large sea contributions. Had the weak current not possessed its Cabibbo structure many more events would be expected at large x. In the case of antineutrino scattering charm production can only occur from the sea antiquark distributions

£+~-* #+ 4-6 g+d-* I~+ + 6 and there is no valence quark contribution. Due to the Cabibbo enhancement more N's are expected than in v interactions where there is a contribution from the d valence quark. These comments are consistent with the observations) 8z) Finally there is no evidence for charm production in r.eutral current v and ~ reactions at high x indicating the absence of charm changing neutral currents. (9°} 5.2.3. Summary There is a clear preference for K's in the D O and D + decays which is consistent with the Cabibbo structure of the weak current. However, quantitative ~tests are obscured by the undoubted presence of either 20 enhancement in the non leptonic decays or W exchange and annihilation graphs, as indicated by the D O and D + branching fractions and lifetimes. The only true test of this Cabibbo structure is meson decays will come with the measurement of Key and ~zev branching fractions and more experimental information will be essential in unravelling the complicated physics of the weak decays. Similarly, v interactions imply that the weak current does indeed have the desired Cabibbo structure although the evidence is somewhat more qualitative. Finally there is no evidence for charm changing neutral currents, although the limits against these are far from small. 5.3. ~he s~reng~h e£ ~he i~¢erae¢io~ Within the G~M mechanism the strength of the charm quark decays is given by GF, the same factor which determines # decay. The expected decay rate for a charm quark is

192~ 3

\m~}

where A is the factor to account for the extra final states available compared with muon decay. This leads to charm particle lifetimes z(charm) ~ few x 10 -xa sec

The Current Status of Charm

295

with large uncertainties due to the charm quark mass and to the poor understanding of A (see Section 5.2). At present the lifetimes estimated from D decay and observations in emMsions are not inconsistent with this estimate but a true test will only be possible when there are precise measurements of both 1tot and B(D -> e+vx). Even then the uncertainty of the charm quark mass wi~.l remain to confuse the situation. Fi:~saliy the fact that the increase in the v and ~, cross-sections is vanishir..gly small arg~aes against a coupling much larger than that hypothesized. 5°4° S e t , mary All results are consistent with the G t M model for the charm weak current, eqn. (5.t) and in particular the evidence supports properties (4), (5), (6) and (7) of the charm quark listed in Section L2. Unfortunately the quality of the information does not allow a precise verification of the major points. The experiments necessary for such a proof are very hard to perform so that the current status will probably exist for a substantial length of time~

6.

HADRON~C, P H O T O - A N D E L E C T R O P R O D U C T ~ O N O F C H A R M

The prod-action of charm is confused both theoretically and experimentally. Akhough there is a substantial body of information on ~ production there are few observations of D production. What observations there are of open charm lie in different kinematical regions and hardly altow any definite conclusions to be drawn. Only with more complete experimental results will there be a guide to which are the correct phenomenological models at present used in describing both charm and @ production. The discussion in this section will be brief to avoid confusion, and begins with hadronic @ production, the best measured process.

6Jo Ha@ron~epro@r~etionof ~'s There are now numerous measurements of @ production in pp, #p, and ~zp collisions, (ls'9z-9s) although in general the fulZ kinematic regions are not covered making comparisons difficult, tn Fig. 54 an example of a p.+/~ invariant mass spectrum is

10 ~ lO z L~J

lO

2.5

3.0

3.5

M~

4.0

4.5

@eV/c z

Fig. 54. The g+/~ massdistribution in ~75 GeV/c 7c p collisions (Ref.94).

R. J. Cashmore

296

p p ~

............... q~

Fig. 55. Parton model for production of ~. shown. (9¢) One immediate observation is that the ~' production rate is much tower than that of the q (approx. a(~')/~(~) ~ 2 G), a result common to all experiments. All models attempt to explain the production of the ~ by interaction between constituents (partons) of the colliding hadrons as indicated in Fig. 55. The cross-section is then given a s (96)

2E dcr

dxf

8n 2

M 2 (g2/47~)A~(xl)Afl(x2)O(M2-xlx2s)

where gc is the coupling constant between A,4 and the ~, x 1 and x 2 are the momentum fractions carried by A and A and A~(xl), Afl(xz) are the structure functions for A and A in the particles ~ and ft. Then ~2

~

X1X2 S

X f ~- X 1 - - X 2

and if A and Z are quarks or gluons then

A~(x) = xq~(x) etc. The most naive assumption would be to assume A and A are in fact c quarks from the quark sea in the hadrons. However, this would imply that the remnants of ~ and fi would contain c and ( quarks (unless in some final state interaction they combine to give light quarks which seems unnatural). The ~9 production would then always occur together with DD production, i.e. ~DI), leading to leptons (from the D decays) accompanying the ~. There is no experimental evidence for this (~DD/O ~< 2 %)~97~ and hence either this process does not exist or some long range final state interaction occurs to neutralize the free charm. Alternatives are to consider gluon fusion and light quark fusion as indicated in Fig. 56.

(o)

(c)

(b)

Y

(d)

Fig. 56. Diagramsof gg and qq contributions to Ikand 7.production in hadronic collisions.

The Current Status of Charm

297

Since the ~ cannot couple to two gluons alone it either has to be produced together with a soft gtuon or via an intermediate Z state followed by cascade decay to 7¢. This then gives an attractive explanation for the Iow ~' yield--there are no Z states from which it may be produced. Which of these processes dominates can be studied experimentally. If qq fusion is dominant then ~ production in/~p collisions would be much greater than in pp collisions by a factor of 20-50 (due to the increased number of antiquarks in the ,6), whereas if gluon fusion is important then similar rates wou2d be expected. The experimental resuh (92) is

~;(pp -> ,~ ) - 0.15 _+0.08 at , ~ = 8.75 GeV indicating that both mechanisms (qq and gluon fusion) are probably necessary with neither dominating. To confirm the gluen fusion ideas the associated °/-rays, from the Z decays, can be sought. Here there are conflicting results on the proportion of ¢'s derived from Z states (i) pp at tSR 43 _+2~ ~o(93) and l~+~oo/I9s) 15 / o (ii) ~ - N at 215 GeV ~99) 70 -+28 ~ Z(35i0) (iii) ~ - N at 175GeV (94~ 36-+5~o Z(3510),Z(3550 ) However, the last two results are not necessarily incompatible as they cover different x I regions, (iii) being at lower x I than (ii). ~ndeed an explanation can be obtained if the mechanisms of Figs. 56b and c are both operative. Then the Z(3550) and the X(3510) (which cannot couple to two massless gluons) are produced at high xy (Fig. 56c) and the gluon fusion (Fig. 56b) is obtMned at low xy where the gluon sea predominates. This model is consistent with the observed xy distribution which can be fitted with structure fur~ctions for the 7r and proton of the form ~=(X)cZ(1 - - X ) 23 + 0"3 Ap(x)c~(1

- x ) 51 -0.6. + ~s

100-pN-~ ;t@+X A

10

£ O. 0.01 0.001

,

0

10

, 20

p 30

, 40

F 50

, 60

V~ (feV} Fig. 57. The inclusive ~ production cross-section as

a functionof energy. The curve is taken from

Ref. 96.

Thus a sensible phenemenological explanation can be found for the ¢ production, although both light quark fusion and gluon fusion have to be invoked. The ¢ production, shown in Fig. 57, as a function of s is well reproduced by such models. As these analyses are refined and the experimental data improved it will clearly become possible to use production together with Drell-Yan lepton pair production as a probe of the parton (gluon and quark) structure of the colliding hadrons.

298

R.J. Cashmore 6.2, Ha4re~ic preduct~e~ ef charm

In analogy with ¢ production, predictions for central charm production have been derived from the diagrams, Fig. 58, with b and c dominating. (1°°) These lead to I) production cross-sections of ~ 1 gb at s ~/a = 27 GeV so that the cross-section is rather small. Similar values are obtained from o~her models in which D production is predicted by scaling from ~ production and accounting for the large mass increase. (~°1)

(a)

(b)

(c)

Fig. 58. Charm production mechanismsin hadronic collisions. Estimates of production rates for the peripheral region (x > 0.5) also exist but these are even smal!er, (1°2) e.g. o-(~ p ~ D - CO-) ~ 0.5 nb a(Trp ~ D + . . . ) ~ 60 nb. The experimental evidence to confront these predictions is very poor. Production cross-sections appear to be ~ 1 0 - 4 0 g b as derived from beam dump experiments/1°3/ However, production in ISR experiments (63 6s) is apparently much larger being in the region of ,-~100 1000gb (assuming branching fractions for the observed channels and models to extend the measurements to the whole kinematical range). These two measurements are not necessarily in conflict, due to somewhat different kinematical regions, bu.t certainly the size deduced from the diffractive production is remarkable. The situation is of course confused by the different targets (and the need to assume a specific A dependence for the cross-section), the uncertain branching L'actions (e.g. C 0- - ~ p K * ) and the various kinematical regions and the consequent need for models. However, there is a suspicion that the model predictions for cross-sections are somewhat smaller than those observed. This is rather surprising as these models are similar to those used in ¢ production and electroproduction (Section 6.4) which are comparatively successbal. Clearly better experimental data is eagerly awaited. 6.3. Phetopro~etion of ~ an4 charm The earliest measurements of 0 photoproduction from heavy targets were important in demonstrating that the 0 was indeed a ha&on. The photoproduction cross-section is related to 0 N --, 0 N by (2s'1°4) da 322 + do" d / ( T N -~ 0 N ) = x?d~, F(0 --' e e- ) d r (0N -~ 0 N ) where 2 allows for a variation in the °/0 coupling with q2 (2 = 1 in a naive vector dominance model). By using the optical theorem (dcr/&) (ON ~ 0 N ) can be related t o o-tot(@N) so that this quantity can be estimated (assuming a value for 2 to be ~ 0.4). The result is consistent

The Current Status of Charm

299

with O-tot(@N)~ 3.5 _+0.8rob obtained from studying the A dependence of ~, photopr)duction from heavy targets. F r o m a kr.owledge of ~, photoproduction and the use of unitarity an estimate can be obtained for the cross-section a(yN --+ charm), assuming that O'tot(~tN) ~ O-tot(~/N --~ charm), o-(?N -+ charm) > 370nb/(1 +e)e(i +3)2 where 3 is the ratio of the real to imaginary forward amplitude in ~ N -~ @N and e is a measure of the violation of the Zweig rule. If ~ and 6 are both small then cr(TN -+ charm) > 350 nb. Alternative techniques using Q C D arrive at similar results/~°s/ There is some evidence for a rather large total photoproduction cross-section, o-tot(gp), at high energies/*°6) However, to infer that the excess ( ~ 2 6 ~b) over what is expected (from V D M extrapolations) is due to charm is not very reliable and it is much desirable to observe specific charm particles in the final states. Unfortunate]y in these cases conflicting or surprising resuits are reported. Probab]y the first observation (Fig. 37) of a charm antibaryon, Co, was made in high energy photon interactions in the reaction (62) ~-+X

7p~Arc+rc

but the non observation of the baryon Cg has remained a diNculty. The search for charm mesons has led to conflicting reports. Recent results from CERN, {sT) giving a value of the charm cross-section of ~ 800 _+200 rib, seem to indicate that only D states are produced and not D's. The evidence from the KTr spectra is shown in Fig. 59. This suggests that the dominant mechanism_ might be 7P ~

DC+X

....

However, measure:'nents (*°7) of D* production at F N A L with higher energy photons indicate equal numbers of D* and D*, implying processes leading to , , p --+ D D

K + % - + K+TC-

>

+ X ..

-i~0

K- ~++ K-~ + r~°

1500 x>~ m

15k00

~> lOO°r

1000

'N

\ 500 L,--1.683

1.863 2.043 Mass (GeV)

1.683

1.863

2.043

HQss {SeV}

Fig. 59. Production of D mesons in photoproducdom A peak is observed in (K%z- +K%z-~z °) but not in (K rc=+K rc+)z°).

300

R.J. Cashmore

with a cross-section a(D) ~ 300 _+ 100 nb. Clearly these two results are in conflict, akhough the different photon energies may lead to a reconciliation. The only other result (sT) of note in photoproduction is that of the F meson which is observed (Fig. 34) in various decay modes, e.g. ~3~r with a ' B = 30_~0 n b20. + Observation of charm is obviously difficult in photoproduction too. Higher statistics and more refined experiments are clearly necessary for these various conflicts to be resolved and tentative observations substantiated.

6.4o M ~ o n an~ e~eetropreduet~on of ~he ~, and charm Charm production can be expected in inelastic electron and muon scattering and will lead to changes in the structure functions (e.g. Fz(x, Q2)) when the charm t h r e s h d d is passed. However, these changes will probably be gradual due to propagator effects, characterized by ~ like masses (i.e. Fz(x, Qz)c~(1/Q; +M~)). Indeed a large fraction of the rise in vW z at low x can be accounted for in this way. (~°8~ There now exist many observations of multimuon production from high energy muon beams, (~°9) e.g.

I~+Fe ~ #+ p- +...

(6.4.1) (6.4.2)

#+/~ /~+ ....

A substantial ~b signal is observed in reaction (6.4.2) as shown in Fig. 60, together with a large continuum. These data have been interpreted within a photon gluon fusion model (~~o) of Fig. 61, where if Mcc < 2MD then ~, ~' and other bound states are produced. {~**) The production cross-section is summarized in Fig. 62 where it is compared with photoproduction experiments and the predictions of the model/**°) Encouraged by this success

500

200 1oo

so Z

2O

g

2

1

2

3

~

5

~L+ ~t- Mass (GaV/c 2 I Fig. 60. ~ production in #+p ~ / ~ * # + # - + ....

T h e C u r r e n t S t a t u s of C h a r m ~x / / /

301

/ Fig. 61. The photon gluon fusion model.

100 10

/

--:3-

/ Y

0.1

/ [I

,

10

.....

,,I

Ey (GeV)

,

100

Fig. 62. Photoproduction of ~ mesons observed in both 7P and/zp reactions. TEe curve is taken from Ref. i 10.

10-35 {

L..-.-3

~, { P-+N-~'P-+ IJ,D X 10-35 ' ~ 4

P"* N_.~ #+ ( p.+#.-) X

10-36 'X~ie\{

DD decay

DD decay lO3,

q

% 10 -37 "1:3

10-37 10-38

1

I

I

2

I

t~

q2 (5eV/c}2

M

I

I

6

4

I

I

I

8 12 I; 20 2/+ 28 q z {GeV/c} 2

Fig. 63. Fits to trimuon and dimuon final states using the DD production on the photon gluon fusion model. t h e m o d e l c a n be u s e d to a c c o u n t to°9) for the d i m u o n a n d r e m a i n i n g t r i m u o n s a m p l e s in t e r m s o f o p e n c h a r m p r o d u c t i o n r e s u k i n g in t h e c u r v e s o f Fig. 63. T h e a g r e e m e n t is excellent. T h u s an a p p a r e n t l y successful d e s c r i p t i o n of t h e m u o n a n d e t e c t r o p r o d u c t i o n of c h a r m exists.

302

R.J. Cashmore 6°5° Summary

Clearly the data on open charm production is poor and often conflicting, representing both the difficulty of the experiments and the small cross-sections. The ~ production is, however, in much better standing, tndeed it is already being used as a probe of hadron structure in both hadronic and e!ectroproduction reactions. Little of the physics of charm has been derived from observations in these processes. In fact as more substantial information becomes available it will continue to be used to reveal the nature of the colliding particles and their constituents rather than the physics of charm itself. Thus in this case charm has already passed into the category of a particie physics probe of the quark and gluon compositions of hadrons. A valuable future can be expected from this approach to h a & o n structure.

7. C O N C L U S I O N S Since the discovery of the J/~ in 1974 there have been tremendous advances in our understanding of the basic constituents of matter, "zhe quarks and leptons, and their interactions. Charm has been a cornerstone in these achievements. Atl of the postulated properties of the charm quark (Section 1.5) have been qualitatively and, in m a n y cases, quantitatively substantiated. There remain some outstanding questions, in particular the rather tenuous evidence for the existence of the F meson, and the need for yet more quantitative confrontation of the charm hypothesis with experimental evidence. The cC bound state system is not quite the hydrogen atom of hadron physics, the meson wavefunctions being mainly determined by the quark confining potential rather ~han the Q C D potential. None the less this bound system and its decays (that is, gluon counting rules) has been a great spur for QCD, leading to many advances and the need for the calculation of higher order corrections, tn fact the cC system is the prototype for our approach to al! o',:her heavy quark bound systems. Our expectations for the b/7 system, and hopefully future tFsystems, are now even greater and should lead to further advances in our understanding of the colour force between the quark constituents of matter. Turning to the weak interactions, the qualitative success of the S U(2)L × U(1) classification of the charm quark and the G I M hypothesis has led to a dearth of other models of the electromagnetic and weak unification. In fact, in current views, flavour is now a confirmed weak interaction phenomenon, a dramatic change from 15 years ago. However, the detailed quantitative confrontation of the G t M hypothesis is confused, probably not because of weak interaction phenomena, bv.t rather through the hadronic interactions of final state quarks. These non leptonic enhancements will, hopefully, lead to a better appreciation of the strong interactions~ The knowledge of the production of charm, both bound and free, by particles other than e+e - and neutrinos remains primitive. Even so, ~) production is playing a useful role in the investigation of hadronic structure and a valuable future can be foreseen for these processes. After these enormous initial successes, it is to be hoped that further experiments, although difficult, will lead to a deeper understanding of the quarks and their composire structures, the hadrons.

Acknowledgemems--Inpreparing this review t have made extensiveuse of the excellent reviews of 2". Appelquist, R. M. Barnen and K. D. Lane/2s)and B. H. Wiik and G. Wolf. (29) ~ have benefited immensdy from conversations

The Current

Status of Charm

303

with my colleagues in Oxford, DESY and CERN and been helped by many experimentaiists. In particular I would like to thank L Bigi, E. Bloom, I. C. Brock, J. K. Davies, J. Ellis, G. Myatt, G. G. Ross and G. Wolf. Finally D. Pollard and the members of the drawing office in Oxford did an excellent job in creating the final document.

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