Semileptonic decays of heavy mesons

Nuclear Physics B (Proc . Suppl.) 21 (1991) 384-391 North-Holland

SE ILEPTONIC DECAYS OF HEAVY

ESONS

Alex Nippe Deutsches Elektroren-Synchrotron, Notkestrasse 85. D-2000 Hamburg 52, Germany Experimental results on exclusive semileptonic decays of B and H mesons are presented and their role as a probe

of the hadronic structure of weak decays is reviewed. 1.

INTRODUCTION

not affected by the light spectator quark q,. Hadronic

ileptonic decays of heavy mesons provide a

b at for testing the hadronic structure of weak decays, From the theoretical point of view they are relatively simple to interpret since only two valence quarks are involved. On the other hand, the undetected neutrino makes them difficult to study experimentally. so in this review I will include a briefsketch of the various experimental techniques used to analyze semileptonic decays . These measurements are not restricted to the determination of rates, but investigate other quantities, such as angular distributions, which are more sensitive to the underlying hadronic dynamics and are independent on the weak coupling . The understanding of the hadronic structure is of particular interest for a reliable extraction of the Cabbibo Kobayashi Maskawa elements from exclusive semileptonic decays. I will not go into more detail on the latter point but concentrate on the first one . After a theoretical overview I will discuss experimental results on B and D decays involving b -~ c and c -* s transitions . Due to lack of statistics it is not possible to extract information on the hadronic structure from Cabbibo suppressed channels . 2.

THEORETICAL BACKGROUND

In the spectator model (Fig.1), the semileptonic decay of the heavy meson M into the lighter X via emission of a virtuel W-boson, is described by the under lying quark transition Q -+ qlv, where this process is

qs

9s

Figure 1: Spectator diagram for semileptonic decays dynamics enters only as soft forces binding the quarks into mesons . The transition amplitude is derived as: A(M --> 1'lv) = ~VQ9 - L"H,,

(2.1)

where the leptonic current L" is calculable exactly . In contrast the hadronic current H" =< X'IJ"IM > cannot be derived from first principals, but has to be estimated by phenomenological models . This problem turns into the calculation of form factors appearing in the lorentz invariant decomposition of the hadronic matrix element . These form factors depend only on q2, the square of the momentum transfer to the lepton-neutrino pair. It is expected that the total semileptonic rate is dominated by the two lowest lying mass states, the pseu.doscalar P and the vectormeson V . Neglecting lepton masses, one arrives at the following expressions for the decay rate of these processes:

0920-5632/91/$03 .50 © 1991 - Elsevier Science Publishers B.V . (North-Holland)

A. Nippe/Semileptonic decays of heavy mesons (a) pseudoscalar meson (X = P) dI' = GFI?

4a32

One expects b --"

K

(2 .2)

3 Fr(g 2)2.

VQq is the appropriate Cabbibo Kobayashi Maskawa matrix element and K the momentum of the meson V in the frame of 111. The decay rate depends on only one vector form factor Fl( q 2 ). (b) Vectormeson (fi = T') The partial width can be expressed in terms of three

helicity amplitudes H where i = (+, -, 0) refer to the two transverse and the longitudinal polarisation state of V:

dT ti(IH+12 +IH_12 +IH01 2).

(2 .3)

The amplitudes are given by 2 2 H±(g) _ (Alm + 111v)AI(q)

Ho(g2)

=

Alai K

q?(Mar

, 2 + lth)t (q )

(2 .4)

1 ar~ - g 2 )(1lIAq + MI )AI(g 2 ) 2Mvgf(~lsr A112fK2 (2.5) MvA2(g2)) . 4 Mat +

Here MAr and lbly denote the masses of the initial and final mesons ; q is -1 for positive and +1 for negative charged quarks . One is left with the calculation of two axialvector form factors AI(g2) and A2(g 2 ), and one vector form factor V(q2 ).

Recently N .Isgur and M .Wise 1 have shown, that in the so-called heavy mass limit, there exists a model in-

dependent description of hadronic matrix elements : as quark masses go to infinity (the spectator quark stays light), the velocities of the heavy quarks Q and q are not affected by soft binding forces . Moreover the spin of

these quarks fully decouples from its dynamics. Therefore the overlaps of the initial and final mesons, i .e .

the form factors, are all equal at maximum momentum transfer . This new spin symmetry leads to definite relations between the transitions M -+ Plv and 11I --> Vlv. Model dependence enters the calculation through cor-

rections to the heavy mass limit. (For further details see J.Körner in these proceedings.)

F

transitions to be close to this limit .

so that the theory should be correct to within V.-_ on the other hand for c , s transitions. the s-quark is no longer heavy enough, to make this approximation reliable . Here we have to rely on more p models, which are discussed widly in literature 2.3 .4 .5, Although their approaches are different (e .g . nonrelativistic and relativistic quark models ; helicity matching),

the predictions are the same on the 20'`ßa level. This allows me to avoid discussion of individual models, and to refer to their collective results as 'theory' . (For b ---, c transitions the models are also in a ' agreement with the predictions of the heavy quark limit .) In the theoretical framework givers above the angular dependence of the decay rate is already integrated out . In principal there are three angles involved which, in combination with the q2 distribution . a for a direct determination of the individual form factors. The angles are

1. 0`r - the angle between one of the pseudoscalar decay

products of j' and the direction of M. in the l'-frame . 2. 0E - the angle between the lepton and J1 in the lepton-neutrino system .

3. X - the angle between the lepton-neutrino plane. and the plane formed by the two pseudoscalar decay products of V, measured in the 111-frame.

Instead of giving explicit formulas, I would like to point

out that 0v distinguishes between transverse and longitudinal polarisation of V, and 0E between its positive

and negative helicity. ., appears only in the interference terms of Ht , H_ and Ho. To include the

q2

dependence of the decay rate into

the studies one has to make assumptions about the

q2

behaviour of the form factors. Usually one assumes a

single pole dominance with, for example, a monopole type formfactor

F( q2 ) =

F(0) , 1 - g2/ntporE

etc.

(2 .6)

where the pole carries JP = 1 - quantum numbers for vector (Fl , V (q2 )), and JP

=

1+ for axialvector form

A. fppe/Semileptonic decays of heavy mesons fact

(A ;. A_). Experimentally one can extract the

malisations F(O) from a simultanious fit to the three angular distributions and the q2 distribution . As we will see later, the complication arises from the unseen neutrino, because one has to obtain the full kinematics from ay products . Therefore it has not just the observed always n possible to perform the full study, and one has only restricted information in the form of the ratio r, and the ratio of pseudoscalar to vectormeuction. Branching ratios can be compared to if i Qq is determined independently, which holds for c - s transitions .

RESULTS h -, clr, TRANSITIONS In this section I will first explain the experimental technique used to study the decays P - D`+I _ v and -~, D'V!9 , and then discuss the theoretical implicati of the results. Up to now there are only two experiments, ARGUE and CLEO, contributing measurements to semileptonic B meson decays . Since both produce the B's in e+c_ annihilation via T(45) --~ BB, they use almost the same experimental method to investgate these decays. This technique . the so-called 'missing-massmethod' exploits the fact, that the B's are produced almost at rest. Therefore, all the kinematical quantities needed to calculate the neutrino mass as the recoil mass of the D'+I- system, are known: 3.

M2

=

s y _ py

s

Figure 2: Mr of D`+I_ combinations from ARGUE 10 The full line is a fit with a gaussian and a parametrisation of the background contribution, shown as a dotted line . eie 0 v

`0 .5 z

0 .4

0 .0 -1 .0

-0 .5

0 .0

0 .5

1 .0

cos 8.,

Figure 3: Strong decay angular distribution 0v in B -+ D`+I- v (ARGUS10 ). Fitting Eqn . (3.5) yields rlong/rtrans = 0 .85 f 0.45 .

E2

- [EB -

(ED. + E1)1 2 -

( PB -

(PD" + P1)I2 (3 .1)

Using EB = Ebea,n and neglecting pB (which is about 340 MeV/c) one obtains M2

[cev2 /C - ]

P, .(®- a - )

~ = [Ebea,n - (ED* +

El)] 2 -

(PD" + pl) 2 .

(3 .2)

Fig.2 shows the ARGUS9 measurement displaying the recoil mass, where one can see a clear peak arround M,? = 0, as expected for B --~ D'+l'v decays .

The background consists of uncorrelated combinations, faked leptons, faked D's, continuum and mixed events . The resulting branching ratio is listed in Table 1 (together with other results discussed below) . To get deeper information on the hadronic structure of the decay process, a more detailed study has been performed, measuring the alignement r1ong/rtrans = I'o/(r+ + r_) of the D'+ . This can be obtained by investigating the distribution of the strong decay angle 9 v in the decay D'+ --4 it+Do.

A . Nippe/Semileptonic decays of heavy mesons

387

The relations dr * - sin dro - cos

29yJH_ 1 2 20t,

IH012

(3.3) (3 .4)

leads to an angular dependence of the form dR'

. 0.,;0V -

1 +

with rlong~rtrana

acos2fly

= 1 4- n

B -->

60 30

(3 .5)

(3.6)

The experimental distribution (Fig.3) shows no pronounced angular dependence, thus I'oa g ::Z rtransCombining the ARGUS 10 result with a more recent measurement of CLE06 yields r,~g /rtrans = 0.84 ± 0.29 in good agreement with the theoretical expectations of about 1. The same principal has been applied to the investigation of the decay B -+ D+1- v , where the recoil mass of the D+V system is calculated. Here additional background arises from the decay cascade B --+ D` + l-v , followed by D'+ -+ D- (y, 7r°) . These events peak at values slightly above zero in the recoil mass spectrum. This can be seen in Fig .4, where the missing mass of D+1 - is shown: points with error bars are background corrected data, the curves correspond to the signal process D+l- v and the feedthrough from D'+l - v . To suppress the latter, a tight momencut of PD > 1.5 GeVlc was applied; the remaining tum contribution was not taken as a free parameter in the fit, but its form and absolute value was fixed from the study of B -+ D'+1 - v , already described above. These processes, and the corresponding decays of the charged B's, have now also been studied by CLE07. The latter are investigated by fitting the D° 1 - recoil mass distribution with theoretical predictions for the shape of the D'° and D° components simultaniously, leaving their normalisations as free parameters . In addition the ratio VIP was constrained to be the same for B° and Bdecays . From the results listed in Table 1 one can conclude:

B -->

N

-30

-2

-i

0

1

2

reco¬l

Figure 4: 111,1,, of D+ I- combinations from ARGUS1a. The dashed curve shows the contribution from the cas. cade B -" D'+I - v --- D+(y .rr°)1-v . Table 1: Summary of the decay rates in B decays. To calculate the branching ratios.it was assumed that Band B° are produced with equal rates from T(4S i decays.

B --+D+1 -v B --) D*+I-v B- -->D°I-v

B- -;D'°I- v

ARGUS CLEO 1 .6t0.5±0.5 1.8i0.6=0.3 5.4~0.9±1.3 4.6~0.5y0.7 1.6t0.6-0.3 4.1~0.8~0.9

(a) The ratio of vector to pseudoscalar agrees with the theoretically predicted value of about 3 (this is not 'naive' spin counting, because this would imply r[ong/rtrans = 0-5)(b) Adding up the vector and pseudoscalar branching ratios gives only about 70% of the inclusive branching ratio, measured to be (10 .3 f 0.5)% 8.7 . What makes up the difference? CLEO claims to see weak evidence for B -+ D'+Xl- v at at rate of (2.0 i 1.2)`%. This process is difficult to observe, since it appears only as a small enhancement at positive values in the D'+lrecoil mass spectrum (Fig.5) . The broadening of this

r1. Nippe/Semileptonic distribution due to the neglection of the B momentum in Egn .(3.2) prevents a cleaner seperation of the differ-

decays of heavy

mesons

E691 . a photoproduction experiment, isolates charm

ent contributions .

10

®

i

6

11';1'k

w

~~III,p w

t

0

_

r, .I

-0.2 -0.1 0 0.1 0.2 0.3 U (K-e+v hypothesis) (GeV)

Figure 6: ~llree of K - c - combinations from MARKII I 16

(histogram) . The solid curve shows Monte Carlo D' - a K c+ v events (normalized to data) and the contribution ( x 100) from D° -4 K- ;r'c+v . decays by reconstructing well seperated secondary ver_ of D"1 combinations from CLE06. (a)

Figure 5:

right sign,(b)gong sign combinations. The fit contri butions are described in the text . The dotted histogram in (a) is the contribution from B --+ D"+ ß'1-v.

RESULTS ON c --4 slv TRANSITIONS

Here I will discuss the decays D° --~ K - etv and D+ --~ hoc'v . Some remarks on D; -~ ¢e+v are also made. 4.1 .

THE DECAY D° -~ K-c+v

Results on

D

°

-->

K

- et v are published from the

MARKIII and E691 collaborations . These experiments are different in their charm production mechanisms and therefore in their analysis techniques. MARKIII produces the D mesons in e+e' collisions via 0(3770) -4 DD . The semileptonic decays of the D's are observed

using the recoil mass of the K- e+ system . In contrast to the analogous method in B transitions, the momen-

tum of the semileptonically decaying D can be fixed by reconstructing the other D meson in the event . The corresponding recoil mass distribution is shown in Fig. 6.

tices. In this case they make use of the decay cascade

D'+ -+ 7r+D°, followed by D° --~ K-e+v . From the

direction of the D meson (given by the secondary ver-

tex of K-e+), the momentum of the neutrino can be

determined up to a quadratic ambiguity. Including the neutrino momentum, the (K - c+ v) mass is constrained

to the D° mass. In combination with a a+ the whole invariant mass of this system is required to equal the D.+ mass .

Background is subtracted using wrong charge

combinations .

The results of both experiments together with the the-

oretical expectation are summerized in Table 2. As a conclusion, there is a remarkable agreement between the experiments and theory . E691 has also analyzed the q2 -dependence of this transi-

tion . As_uming a single pole dominance as in Eqn. (2 .6) the distribution was fitted, treating the pole mass q2

mpoce as a free parameter. Theoretically one expects the lowest lying ca-pole with vector quantum numbers, which is the D ; at a mass of 2.11 GeVlc 2 . The fit gives a mass of 2. 1+ 0 4 GeV/c 2 consistent with this prediction . 0.2 *

A. Nippe/Semileptonic decays of heavy mesons

389

Table 2: Summary of the decay rates in D decays . The experimental rates are normalized using BR(D + -> K- 7r+ar - = (9 .1 ± 1.3 î 0.4)% and BR(D° -> K- 7r+ = (4.2 î 0.4 î 0.4)% 17 . T[10'°s- lj D° -~ K-e+v

7.8

exp./ theory

î 1 .2 î 0.9

8.8î1 .2î1 .4 D+ --> K`°e+v Do

8R(D; -Oe+ to BR(D, -~ oir+ )

theory 2,3

4.2 î 0.6 i 0.4

E691 1

ARGUS 12

3.5 î 0.9 î 0.9

CLE0 20

9.1, 9.5

theory23 E691 21

< 0.45090%Gc.l . 0.49 î 0 .10+00 :1140 0.57 î 0.15 î 0.15

1

4.2 .

E691 15

8.4, 8.3

4.6 î 0.6 ± 1.1

K' - c+v

IVIARKIII"5

CLE020 ARGUS 12

WBS3

THE DECAY D+ -+ Îs`°e+v

In 1988 the E691 Collaboration presented a study

of the decay D+ --"

h°e+v

, using a method similar

to the one described above . They looked for (K- ar+)e+

combinations pointing to a common vertex, and analyzed the resonance structure of the (K -7r+) invariant mass. Subtraction of background was mainly per-

formed by investigating (K - ar+)e - wrong charge com-

binations. The invariant mass of both charge combina-

Figure 7: Invariant masses of Kar right charge (solid histogram) and wrong charge (dashed) combinations (E69113 ) for standard (a) and tight (b) cuts. production in semileptonic D decays . One arrives at

hO

I'(D+

-4 e`v) _ 1 r(DO --i K-e+v) ^- 2'

tions is shown in Fig. 7.

where theory predicts a value of about 1 (not 3 as in

shape for the resonant part plus an s-wave nonresonant

of the vectormeson rate).

BR(D+ -> K*O e+v ) =

CLEO (for simplicity the presentation will be no longer chronological) . These experiments have a more compli-

Fitting the remaining distribution with a Breit Wigner

background parametrisation yields a branching ratio of (4 .5

î 0.7

î 0.5)% .

The non-

resonant contribution is determined to be only about 10% of the resonant .

In what follows I will talk in terms of partial widths rather than branching ratios, making a common interpretation of semileptonic D+, D° and D, decays pos-

sible. For example one expects from SU(2) invariance that I'(D° -+ K- e+v ) equals I'(D+ -+ be+v) . This enables a comparison of vectormeson and pseudoscalar

B

decays because of a stronger phase space suppression Recently this result was confirmed by ARGUS and

cated experimental enviroment, since the D's produced in nonresonant e+e - annihilation at a center of mass

energy of 10 .5 GeV are accompanied by other parti-

cles from the fragmentation process. To study semileptonic decays one can exploit the relatively hard momesons, which leads to small opening angles between the daughter particles. Conmentum spectrum of

D

A. IN°ippe/Semileptonic decays of heavy mesons sequently, ARGUS12 searched for events containing a *0 and an electron, requiring an opening angle be-

40

the combination of less than 90°. The backt ground consists mainly of faked electrons and uncor-

related combinations . Wrong charged combinations `~c arise from almost the same mechanism, but not

from charm decays. and are taken as a test of the back-

ground determination. The CLEO technique" to investigate D' --= fï - e~r, requires the invariant mass of the rat

-t

-

z W

20

w

combination to be less than the D° mass

than a cut on the opening angle. The results,

suns i ed in Table 2 are in very good agreement . Applying a similar method CLE0 20 and ARGUS12 observed the decay D; --, o; -v , with a branching ratio relative to the channel D; ---~ o-° of 0.49 ± 0.14,,â and 0,57 ± 0,15 =0.15, respectively. For a rough comparison

one can take the estimate from ref. 19 of BR( D,' -+ 6-') = (2 .7 0.7) , which yields a branching ratio for D;

oc 'g, of {1,4

(3.? ± 1,1) x 10 r° s-r .

0.5) t or r(D; --+ oe-v )-

1

0 Cos

1

1

IA

Figure 8: Distribution of (E69113 ) 01for D} --+ Îi so et y candidates . The solid curve is the fit to the signal plus background .

From SU(3) arguments this

value should equal r(D' -->

K"c'v ), but phase space

should suppress the former by about 0.8318 . The exper-

imental ratio of 0.76 ±- 0.3 agrees well with this number .

As a conclusion present form factor models are in disagreement with the rates for D -~ T'ev .

To understand this discrepancy a more detailed study of the reaction D. --> Fi °e~v was performed by E691 . As mentioned above, one can exploit the angular distributions in k, (91 " , 0, and the

92

dependence to measure

the form factors. For this analysis it is necessary to know the momentum of the unseen neutrino, which can be de-

rived from the direction of the D meson. Zv91 obiains

this from the reconstructed decay vertex (ARGUS and CLEO do not have such information) ; as a step towards

the full analysis they presented in 1988 the measurement of the alignement

01 -1,0

rlong/rtrans

of the _K'° . The

corresponding distribution (Fig .8) in 0y shows a pronounced angular dependence, different to the situation for B mesons . The fit to the data with a parametrisation as Eqn. (3 .5) results in r,ng/rtrans = 2 .4+ 1.7 0 ±0.2,

whereas theory predicts 1 . Recently the other distributions were included in the

analysis by performing a simultanious fit as discussed in

the section 2. Since (V,( is well known one can take the total decay rate as an additional constraint, leaving only

two free parameters in the fit. Experimental complications arise from the different lepton momentum spec-

tra for positive and negative helicity states since clean

seperation from background requires hard cuts on the lepton momentum .

The comparison of the result with the models (Tab.3) çhowç

a marked disagreement in all form factor nor-

malisations, especially in A2 . Thus the discrepancy is

localized, but not yet explained. Note that this anal-

ysis also gives a new value for

rlong/rtrana

with much

reduced errors . As a remark, I would like to mention,

that the authors of 18 treat one of the overlap integrals

as a free parameter. Fixing this only by the total decay rate of D+ --+ R' {° e+v they obtain good agreement with all measured form factors within errors . Moreover,

A. Nippe/Semileptonic decays of heavy mesons Table 3: Measurerrjgqnt of the form factors for D+ -, Îi ° E+ v (E691"*) . Result are given for q'- = 0 and q2 - q2mar' GS5 E691 IS 2 BW3 KS 4

A1(0) A2(0) 1'(0)

A1(q.f ) AA 92N) 1'(gM) rtrmns

.46± .05± .05 0.8 0.0±0.2±0.1 0.8 0.9 ± 0.3 ±0.1 1.1 .54 ± .06 ± .06 1 .0 0.0±0.2±0.1 1 .0 1 .2±0.4 ± 0.1 1 .4 1 .8-0.4 s 0.3 1.1

the model then predicts

0.9 1 .2 1 .3 1.1 1.4 1.7 0.9

BR(D; ~ar' t,) BR(D, -. Q~+ )

0.8 0.6 1 .5 0.9 0.7 1 .9 1.2

1.0 1.0 1 .0 1 .2 1 .2 1 .3 1.2

^- 0 .45 close to

the experimental value. However, this does not provide further information about B meson decays . In general one can conclude. that the model predic-

tions have to be mistrusted for semileptonic transitions into lighter quarks, which will be especially true for -~ u decays. Here the measurement of form factors h=*oc'v for D+ --> gives an important input for future extraction of 1L 6 from exclusive semileptonic b -4 u b

transitions since Isgur and Wise is a relation between

5.

b -~ u

1

have shown that there

and c --+ s form factors.

SUMMARY

In semileptonic B meson decays the measurments --D++l - v ) show good agreeand BR(B of 1F /1F BR(B -+D+ 1- v ) ment with the theoretical predictions . This is expected transitions are close to the heavy mass limit. Here the full investigation of angular distributions, i.e . the determination of the individual form factors, is desince b

--~ c

sireable .

The situation for c -+ s transitions is not so harmonious. Only the decay D° -4 li - E+v is well described

by models . In contrast there is disagreement for the decay D+ --~ Ii ` ° c + v : the rate turns out to be half

that predicted and the alignement to be about twice. This difference is also reflected in the measurement of the form factors for this process. Currently there is no

391

explanation of the source of this discrepancy REFERENCES

1 . N.Isgur and M.B.Wise, Phys. Lett. B232 (19,89)

113 and Caltech preprint CALT-68-1 8 and CALT-68-1625.

2. N .Isgur, D.Scora, B.Grinstein and M .B .Wi ,

Phys. Rev . D39 (1989) 799 and N .Isgur, D.Sc a. Phys. Rev. D40 (1989) 1491 .

3. M .Wirbel, M.Bauer and B.Stech, Z. Phys. C2 (1985) 637 . 4. J.G .Kârner and G.Schuler, Z. Phys. C3¬3 (19

511 and Erratum in Z. Phys. C41 (1989) 6

)

5. F.J .Gilman and R .L .Singelton Jr ., Phys . Rev. D41 (1990) 142. 6. D.Bortoletto et al . (CLEO Collab .), Phys . Rev. Lett . 63 (1989) 1667 . 7. D.Cassel (CLEO Collab.) . CLNS 90/1014. 8. H.Albrecht et ai . (ARGUS Collab .), DESY 90-088 . 9. H.Albrecht et al . (ARGUS Collab .), Phys . Lett . B197 (1987) 452. 10 . H .Albrecht et al . (ARGUS Collab.), Phys . Lett . B219 (1989) 121. il . H.Albrecht et al . (ARGUS Collab.), Phys. Lett . B229 (1989) 175. 12 . H .Albrecht et al . (ARGUS Collab.), contributed paper to Singapore 90 . 13 . J.C .Anjos et al . (TPS Collab .), Phys . Rev. Lett . 62 (1989) 722. 14 . J.C .Anjos et al . (TPS Collab .), FERMILAB-Pub90/124-E . 15 . J.C .Anjos et al . (TPS Collab .), Phys. Rev. Lett . 62 (1989) 1587 .

16 . J .Adler et al . (MARKIII Collab .), Phys . Rev. Lett . 62 (1989) 1821 . 17 . J .Adler et al . (MARKIII Collab .), Phys . Pe:- . Lett. 60 (1988) 89 . 18 . M .Bauer and M.Wirbel, Z . Phys . C42 (1989) 671. 19 . Particle Data Group, Phys . Lett . B239 1990 1.

20 . J.Alexander et al . (CLEO Collab .), Phys . Rev. Lett .

65 (1990) 1531.

21 . J.C .Anjos et al . (TPS Collab .), Phys . Rev. Lett . 64 (190 ')) 169 .