Charm production by weak neutral currents

Nuclear Physics B123 (1977) 132 1 4 6 © North-Holland Publishing Company

CHARM PRODUCTION BY WEAK NEUTRAL CURRENTS * V. B A R G E R

Physics Department, University of Wisconsin, Madison, WI 53 706, USA R.L. K I N G S L E Y , R.J.N. P H I L L I P S a n d D.M. S C O T T

Rutherford Laboratory, Chilton, Didcot, Oxon, England Received 13 December 1976 (Revised 19 February 1977)

We discuss quantitatively the production of charm in uN and v-N neutral current interactions, and the anomalous lepton events that follow from semi-lcptonic charm decay. Diagonal neutral currents, in the Weinbcrg-Salam model and similar models, predict associated charm production with small cross sections: e.g. o(vN ~ vccX)/o(uN ~ ~ - X ) -~ 10 -2 at high energy. The meagre data on vN ~ ve+X are consistent with a rate of this order. Non-diagonal neutral currents, if present, could give larger cross sections via valence p ~ c transitions. It should be possible to distinguish diagonal from non-diagonal contributions by their x- or u-dependences, where u = x(l -.v). We calculate the expected energy distributions of the leptons in characteristic uN ~ ~,t:+X and uN -÷ u~+~-X charm decay cvents using simple models, and disct,ss some practical problems in neutral current measurements.

1. Introduction The n e u t r i n o - i n d u c e d d i m u o n a n d ~e events [1,2] are t h o u g h t to c o m e m a i n l y f r o m the p r o d u c t i o n o f c h a r m e d particles [3] via the weak charged c u r r e n t (CC), w i t h s e m i l e p t o n i c c h a r m decay [4]. Similarly, m u - i n d u c e d d i m u o n e v e n t s [5] m a y be a t t r i b u t e d to c h a r m p r o d u c t i o n via the e l e c t r o m a g n e t i c c u r r e n t [6]. In the present p a p e r we discuss q u a n t i t a t i v e l y w h a t a n a l o g o u s effects m a y be e x p e c t e d f r o m c h a r m p r o d u c t i o n via w e a k n e u t r a l c u r r e n t s (NC), in ~,N a n d u-N s c a t t e r i n g , using the q u a r k p a r t o n m o d e l (QPM) f r a m e w o r k . I f the n e u t r a l c u r r e n t s c o n s e r v e c h a r m , as in the Weinberg-Salam (WS) m o d e l [7] for i n s t a n c e , c h a r m m u s t be p r o d u c e d in association w i t h a n t i c h a r m f r o m the target sea. The c u r r e n t strikes a c h a r m e d q u a r k c, leading typically to a fast c h a r m e d

* Work supported in part by the University of Wisconsin Research Committcc with funds granted by the Wisconsin Alumni Research l.'oundation, and in part by the Energy Research and Development Administration under contract E( 11-1 )-881, COO-574. 132

V. Barger et al. / Charm production

133

particle in the current fragmentation region; the spectator quark V gives a slower anticharmed particle in the target fragmentation region. Alternatively the current may strike V, leading to a fast anticharmed particle, etc. The charmed particles can decay semileptonically via the basic quark transitions c ~ X(n)~+v,

~- ~ X(~)~-k-,

(1)

giving events of the' forms vN -~ vX

(2a)

-~ v~+X

(2b)

-+ v~+~-X,

(2c)

(and similarly for V ~ F) according to whether none, or one, or both charmed particles decay semileptonically. Here £ denotes e or/a, the two leptons in (2c) may be of different kinds and we have ignored D o - D ° mixing that is small in the 4-quark model [8]. The lepton charge shows whether it came from c or ~-; when one lepton is fast, we can tell whether c or ~- was struck. When a decay lepton matches the beam quantum numbers, these events will masquerade as CC interactions, e.g., ruN ~ Vula-X vu#- ~+X,

(3a) (3b)

where (3a) appears normal and (3b) appears as charm production by the charged current. If the momentum of the hadrons X is measured, however, transverse momentum balance tests will usually unmask these events. If no decay lepton matches the beam, however, the events will stand out as special NC effects, e.g., ruN ~ pu#+X

(4a)

rue +-X

(4b)

vue+e-X

(4c)

vwu+e-X.

(4d)

These cannot be interpreted as CC events without violating lepton number or muon number or both. However, a neutrino beam is neverpurely vu, V~,, Ve or V-e: there is always some contamination from the other three components. To detect a significant effect of the type in eq. (4) require~ both a big enough signal and a pure enough beam. A background to process (4c) is expected from NC trident production in the Coulomb field of the nucleus: however, this should give "quiet" events with little hadronic excitation. Charm-changing neutral currents, absent from the Weinberg-Salam model, are

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V. Barger et al. / Charm production

still an important possibility [9,10]. If they include substantial terms like C-R')'uPR + ~RTuCR, allowing c-production from valence p-quarks, striking consequences follows: (i) charm production is strongly enhanced; (ii) the enhanced component is charm, not anticharm; (iii) x-distributions differ strongly from sea-quark processes; (iv) one charmed particle is usually produced, not two; (v) single charm decay can yield two charged leptons via c -+ p~+ 2-. (vi) complete D o - b ° mixing occurs. These effects should be observable, or at least testable, in various ways.

2. Experimental observables In NC events the final neutrino is unmeasurable, so it is hard to determine some of the usual deep inelastic scattering variables. From measurements of the recoifing particles, with due allowance for missing neutrals, one can estimate approximately the total hadron energy and momentum: P x H ~- E H = V = E y ,

(5)

p2 n ~- 2 M E x y ( 1 - y ) ,

(6)

where Px and Pt are longitudinal and transversa momenta relative to the incident beam axis. These equations are based on a small angle approximation for the scattered neutrino. In heavy liquid bubble chamber experiments one might also determine the hadron invariant mass squared W 2 = E~H - p ~ = 2 M E y ( 1

- x) + M 2 .

(7)

Here Ell and PH have to be known accurately, since the leading terms o f order E 2 cancel out in eq. (7), and the result is also sensitive to the measurement of the energy of the neutral particles. For fully identified events in which W2 can be reliably determined, eqs. ( 5 ) - ( 7 ) determine E, x, y completely. In a narrow-band dichromatic beam, the incident energy E is determined uniquely when E H exceeds the lower beam energy. Most NC experiments can measure E H and hence y in a rangey/>Ymi n (withymin ~- 0 . 1 - 0 . 5 depending on details of the beam and distance from the beam axis). Bubble chamber and fine-grain calorimeter experiments can also measure the hadron shower angle OH ~Ptll/PxH and hence the complete set x , y , E . With a wide-band beam, E cannot be determined and we are left usually with E H and pt2H. Neither of these is a scaling variable. To work with them, we have first to know the incident spectrum and then to compute spectrum-integrated distributions. Alternatively, it is interesting to consider the single scaling variable that can be

V. Barger et aL/ Charm production

135

formed from eqs. ( 5 ) - ( 6 ) , namely [11] u = x(1 - y )

~- 02HEH/(2M).

(8)

In a Bjorken scaling region, u-distributions are independent of the incident neutrino spectrum. This variable is analogous to v = x y , that can be measured independently from E in CC processes. How accurately, can one measure u? For a typical fine-grained calorimeter [12] (bubble chambers should do better), standard deviations AE H = 0.55 (MEH) 1/2 and A0 H = 0.1 (M/EH) 1/2 are expected, which imply Au -- 0.14 u 1/2 + 0.55 u(M/EH) 1/2 .

(9)

At high energy this promises an accuracy of +-0.02 at u = 0.02, and +0.05 at u = 0.15, suggesting that u may indeed be a useful variable. Note also a threshold effect. Charm can be produced only for W > Wc, where W 2 = M 2 + 2MEy(1 - x ) is the invariant recoil mass squared and Wc is the charm threshold. This implies an upper bound U1/2 < 1 -- [([412 -- M2)/(2ME)] 1/2

(10)

for charm production, that bites severely near threshold. For events in which the charm particles decay semileptonically, the measured hadron quantities cannot include the momentum carried by the decay neutrino. However, this is usually a small fraction of the total hadron energy-momentum, so that "visible" quantities Xvis, Yvis, Uvis defined via eqs. (5), (6), (8) should not differ much from the true x, y, u.

3. Diagonal neutral currents In this section we calculate associated charm production cross sections from diagrams in which the neutral current couples to gc; contributions from other associated charm production diagrams in which the neutral current couples to non-charm quarks are more difficult to estimate. In the WS model [7] the weak neutral current conserves charm. Some other gauge models have similar left-handed couplings plus additional right-handed terms [9,10,13]. For such models the gc component of the weak neutral current has the form J~ = gLC-L')t#CL + gRCR"//aCR ,

(11)

gL = 1 -- ~3 sin20w ,

(12)

gR = ")' -- 4 sin20w ,

(13)

where 0w is the Weinberg angle. In the WS model "), = 0; in gauge models [9, 10]

V. Barger et al. / Charm production

136

where CR transforms as the upper member of a doublet, 3' = 1 Diagonal NC cross sections in the scaling limit for striking c or ~- separately are [14]

d o / d x d y ( v N ~ vcX) = do/dxdy(v-N -+ ~ )

= ~ ' ( x ) x [g[ +g~(1 _y)21 ,

(14)

d o / d x d y ( v N ~ vc-X) = do/dxdy(v-N ~ ~-cX)

= l~'(x) x [g~, +g[(1 - y ) 2 l ,

(15)

in units of G2ME/rr where G is the Fermi constant, E is the incident energy and ~'(x) = c(x) = b-(x) is the charmed paxton distribution in the nucleon. These distinct cross sections are equal if')" = 1, or in the WS model [7] with 3` = 0 when sin20w = 2. Note that the y-dependence reveals the gL/gR ratio. These cross sections may be compared directly to the electro- or mu-production of charm, via the electromagnetic current [6]

do/dxdy(,uN -+/acX) = do/dxdy(laN -+ lac-X) = ~9a27r(MExy2) -1 ~'(x) (2 - 2y + y 2 ) .

(I 6)

A measurement o f the electromagnetic process would determine ~'(x) and hence the weak cross sections. Since the electromagnetic and weak excitation of charm should give very similar hadronic final states, with the same fraction of leptonic decays, the one- and two-lepton event rates should also be directly comparable at given E, x, y. Since the V / A interference cancels out in the sum of processes (14) and (1 5), the expression for the cross section ratio

[da/dxdy,(vN -+ vcX) + d o / d x d y (vN -+ vc-X)] /[2do/dxdy(/2N -+ ucX)] = [3GMExy/47ra]2(g[ + g ~ )

(17)

is valid in a much wider context than the quark parton model: i.e., in any theory where the matrix elements (N[ Vc(x) Vc(0)[N) and ~ [ A c ( x ) A c ( O ) [ N ) are equal at short distances. As charm is conserved in these processes, the experimental signal is clearer for the sum of processes (14) and (15) than for either of them separately. Charm production can only occur above threshold, so the cross sections should be understood to contain a factor O(W 2 - W2e), where W2 = 2 M E y ( 1 - x) + M 2 is the invariant recoil mass squared and 1,9c is the charm threshold. The charmed meson mass [15] suggests a value Wc 2 M + 2mD --~ 4.7 GeV; taking the charmed meson plus charmed baryon mass [16] instead gives We -~ 4.1 GeV. The precise value of Wc is unimportant if we also introduce a slow rescaling variable z, that gives suppression near threshold. Following ref. [17] we take

z = x + m2e/(2MEy),

(18)

V. Barger et al. / Charm production

137

where m e = 1.5 GeV is the charm quark mass. The factors representing x,y dependence in eqs. ( 1 4 ) - ( 1 6 ) are then modified as follows

~'(x)x -+ ~'(z) [z(1 - y) + xy] ,

(19a)

~'(x)x (1 - y)2 _+ ~,(z) [z(1 - y ) + x(y 2 - y ) ] .

(19b)

In the scaling limit z -+ x and the original form is recovered. Let us compare the NC charm production with the total vN and F N CC cross sections, in the 4-quark model [3]. The latter involve valence and uncharmed sea quark distributions t;(x) = ½(p + n - ~ - ~ ) and ~(x) = p = n = k = ~ , assuming SU(3) symmetry for ~. The integrated cross sections involve the integrals V = fxvdx, S = fx~dx and S ' = fx~'dx, as follows:

o(vN ~ u - X )

= 2V+ ~S+

2 ,, 7S 2

o(FN-+u+X)=~V+~ S+3S

r

(20)

,

(21)

o(vN --* vcc-X) = -3(gL 2 2 + g~) S ' ,

(22)

in units G2ME/~r. Eq. (22) is the sum of eqs. (14) and (15) integrated, and includes both fast and slow charm quark production. These are asymptotic scaling expressions. Relative to the total CC, the associated charm production rates are approximately

o(vN-+vcc-X) ~ 1 o(uq~q -+vc~X) o(vN-+/~-X)

3

1

2

[ ~ [ ~ SS'

o(FN'-*/I+X)~3(gL+ g 2 ) ~ - - V ~ - S - J '

(23)

where we have neglected higher order terms in S/V. Inclusive NC measurements below cC threshold indicate a value of sin20w ~- 0 . 3 - 0 . 4 , so that g2L + g~ ~ 3. From QPM descriptions of inclusive electron and neutrino structure functions, the sea to valence ratio is estimated [18] as S / V ~- 0.06. Thus we obtain

o(vN -+ re+X) ~ 10_2 (S'/S)B, o(vN -~ tt- X)

(24)

where B denotes the mean branching ratio for electronic or muonic decay of the produced charmed particle. This estimate holds for both the WS m o d e l a n d 3' = 1 model. An optimistic choice o f S ' / S = 1 with B ~ 0.2 yields

o(vN -~ re+X)

2 X 10 . 3 .

(25)

o (vN -> t t - X) Alternatively, if the mu-induced dimuons of ref. [5] are ascribed to charm production using eq. (16), a value (S'/S)B ~- 0.07 is found [6], which is consistent with other estimates [2,4,19] that B and S'/S may each be of order 0 . 2 - 0 . 3 . On this basis the "anomalous lepton" NC events of eq. (4) make up a very small fraction of

138

II. Barger et a L / Charm production

order

o(vN -+ re+X) ~ 0 . 7 × 10 - 3 . o(vN -'* It- X)

(26)

However, the acceptance cuts on the mu-dimuon experiment are drastic, so this latter estimate could conceivably be too pessimistic. In practice there will be some reduction in charm production from the threshold cut W > We, from slow rescaling and from the usual lepton energy cutoffE~ > E m i n (especially severe for present muon experiments). However, the above formulas show the order of magnitude. We now discuss some assumptions contained in eq. (26): perhaps the sea component is too small; perhaps the charm suppression factor S'/S should be a function of O 2 not a constant. There are various ways to approach these uncertainties. (i) We can normalize to the mu-induced dimuons [5]. Since precisely the same assumptions go into the analysis [6] of these events, we largely avoid the uncertainties this way, at least for comparable conditions E ~ 100 GeV, ( O 2 ) ~ 5 - 1 0 GeV 2. However, the mu-dimuon data are very preliminary and the acceptance cuts for that experiment are severe. (ii) We can see how far the estimate can be increased by reasonably optimistic assumptions. The sea could be bigger with a (22 dependent charm component rising toward ~' = ~ as (22 -+ o~. Let us take the results of ref. [20] for the O 2 dependence, with normalization x~(x) = 0.2 for x -+ 0 and the power of (1 - x ) given by dimensional counting [21 ], which gives x~ ~ (1 - x) ~. The resulting cross section for NC charm production vN -+ vcCX is shown in fig. 1 : the calculation includes a threshold We = 4.7 GeV and slow rescaling. The asymptotic cross section is o(vN -+ vcCX) = 0.8 X I 0 - : (G:ME/rr). This could be compared with the CC cross section o(vN-+ I t - X ) = 0.5 (G 2ME,/rr). (iii) We can be pessimistic. There is no direct quantitative evidence for the charmed sea, apart from the mu-dimuons, so S'/S could be very small. Experimentally, the BCHW group [2] found three possible vN -+ ve+X events out of 5000 vN interactions with Spx > 5 GeV/c; one of these could be a v-e -+ e + event (it satisfies momentum balance), but the other two are not likely ~e events. The uncorrected experimental rate is around the expected level for the WS model. The asymptotic expression eq. (24) with (S'/S)B = 0.07 predicts 2.8 vN -+ ve+X events for 4000 CC events: this number would be reduced by the threshold cut and the Ee > 0.8 GeV cutoff. The Q2 dependent sea calculation of fig. 1 gives about the same as eq. (24), for the 2 0 - 4 0 GeV region, but here the threshold cut is included. In the CERN narrow-band vu beam, the ~-u contamination is expected to be less than 10 - 4 ill flux (and even less in CC cross section). A NC charm production signal vN -+ vIt+X at the level of 1 0 - : - 10 - 3 should therefore be visible above the VN -+ It+X background here, even without momentum balance checks. It is interesting also to display anomalous NC events as a fraction of CC dilepton

11. Barger et al. / Charm production

139

10-2 . . . . . . . .

' Asymptotic

volue

I0 {.)

l

10-3

Z v

b

10-4 I0

10 2

10 5

E (GeV)

Fig. 1. Cross section for NC charm production o(vN~ vc~X) iq units G2ME/zr, versus neutrino cnergy E, assuming the charm sea to be Q2 dependent as in ref. [20]. The asymptotic value is 8.3 X 10-3 G2ME/Tr. This should be compared with the CC cross section o(uN ~ ~-X) = 0.5 (G2ME/Tr).

events, since the branching ratio B cancels out here. For the 4-quark model [3] we obtain o ( v N ~ ve+X) 2 2 + g2R)S," (S'/S) o(vN-+/~-e+X) = 2 [ V s~(gL i n 2 0 c + S + 3 r_-•]j ~- i 1 + 2 ( S ' / S )

(27) '

with our previous notation and assumptions. The SU(4) limit S' = S gives the ratio --

1

13.

All our estimates in this section have been for charm production by diagonal ~-c neutral currents; these estimates do not include possible contributions from associated~harm production diagrams in which the neutral current couples to a noncharm quark and a ~-c pair appears in the final state. Some models postulate further new quarks b, t, etc. with diagonal NC couplings bb, tt, etc. Although details may differ, the corresponding associated production cross sections will all be of the same order of magnitude as charm production well above the appropriate thresholds. Finally, it is interesting to display the expected energy spectra of the charm decay leptons. Fig. 2 shows the spectrum dN/dEQ+ for the process vN ~ u~+X, assuming D-meson production from the fragmentation of a struck c-quark with D -+ K*£+v decay, with Wc = 4.7 GeV and slow rescaling, exactly as in ref. [6]. We here assume the WS model with sin20w = 0.33. The Q- spectra from ~ ~ ~-~-X are very similar (they would be identical if sin20w = 3). In these model calculations, the fraction of events that survive the cutoffs E~ > 2.5 GeV and EQ > 0.8 GeV, typical of muon

140

V. Bargeret aL/ Charm production 10 -I

i

i

i

J

i

~

I

10-2

"N

I0 -3

a

Z

I0 -4

I0-5 10

20

3O

40

Ea (GeV)

Fig. 2. Lepton energy spectrum dN/dE~ for vN ~ v~+X at incident neutrino energies E = 50, 100, 150 GeV, with diagonal NC. We assume that a c-quark is struck and fragments to a D-meson, with D --+K*Q+v decay, foUowing ref. [6]. The Weinberg-Salam model is assumed, with sin20w = 0.33. The ~- spectra from vN ~ v~-X are rather similar. and electron measurements, are

N ( E u > 2.5 GeV)/N(all Eu) = 0.29, 0.47, 0.57, N ( E e > 0.8 GeV)/N(allEe) = 0.71, 0.80, 0.84, where the numbers refer to E = 50, 100, 150 GeV, respectively.

4. Off-diagonal neutral currents In some models [9, 10] the neutral current does not conserve charm, and allows off-diagonal ~-p couplings to valence p-quarks, with greatly enhanced cross sections. This is single, not associated, charm production. Consider for example an off-diagonal current term J.

= hL (/~L')'#CL

+ C-L ' ) ' / 2 P L )

+ hR(/)R')'/~CR

+ b-R"/uPR)

•

(28)

In SU(2) × U(1) gauge models with doublets and singlets h L is already made small ( h i ~< 10 - 2 ) by requiring universality for the p-quark CC coupling compared to the lepton couplings. We therefore concentrate our attention firstly on h R effects and put h L = 0.

v. Barger et al. / Charm production

141

For NC p -> c and ~ -+ ~- transitions, leaving a charmed (anticharmed) particle in the current fragmentation region, the cross sections are

do/dxdy(vN -+ vcX) = ½x(v + ~)h~.(1 _ y ) 2 ,

(29)

do/dxdy (u-N -->~-cX) = -{x (v + ~ ) h ~ ,

(30)

do/dxdy(vN -+ uCX) = ~x~(x)h 2 ,

(31)

do/dxdy (~N--> gc-X) = ½x~(x)h2(1 - y)2 ,

(32)

in units G2ME/n, in the scaling limits; v(x) and ~(x) are the valence and uncharmed sea distributions from sect. 3. The complementary case with hR = 0, h L 4 : 0 is found by writing h L in place of h R and interchanging the y-dependences 1 ~+ (1 - y ) 2 , in eqs. (29)-(32). There are also c -+ p and c -+ p transitions, leaving an anticharmed (charmed) particle in the target fragmentation region; these cross sections are given by eqs. (14) and (15), respectively, with gL and gR replaced by h L and hR. We are particularly interested in the enhanced cross sections eqs. (29), (30), containing the valence distribution v(x). Previous remarks about thresholds and slow rescaling still apply, except that the threshold here is for single charm production: Wc = m N + m D = 2.8 GeV is appropriate. Integrating eqs. (29), (30) and comparing to CC, we obtain

o(vN -+ vcX)/o(vN -+ g - X )

~- l1~ h 2R ,

o(~-N_+~-cX)/o(~-N_+/J+X) _~ ~h R 32

,

(33) (34)

neglecting terms of order S/V. Note that the relative effect is an order of magnitude bigger for u-hi. The existence of the charm changing current depends on a mixing of p and c states, and h R may be expressed in terms of the mixing angle ~bas [9,10] h R = cos q~sin q~.

(35)

The maximal value of h 2 is ¼; inclusive neutral current measurements at low energy further limit the possible range to h i < 0.2. Thus we find

o(vN -+ ve+X)/o(vN -->/J-X) ~ 0.02 B ,

(36)

which for B ~- 0.2 gives o(vN -+ ve+X)/o(vN ->/J-X) < 4 × 10 - 3 .

(37)

Thus valence excitation of charm could give significant enhancements over the associated charm production rates in eqs. (25), (26), especially for gN. Even if non-diagonal valence transitions are not evidenced by a greatly enhanced rate, they may still be distinguished from diagonal sea transitions by their x-dependence. Valence-dominated processes have x-dependence similar to CC events, with

142

V. Barger et aL / Charm production i

°\

~~

~

[

I

I

"",, diagonal ~c NC

~

~''(hL#O' hR=O) non-diagonol ~p NC ............" ~ ....................."...-.......,,, ..,.~ R:¢:O,hL=0 )-,,,.)

,,

I

0

I

t

0.1

~

"

I

0.2

0.3

J

0.4

U

Fig. 3. u-distributions for NC charm production, m the scaling limit, for the cases of diagonal ~c) and non-diagonal (c-p) neutral currents.

(x) ~ 0.25, while sea processes have ( x ) ~ 0.1 typically. The different x-dependences reflect into different u-dependences, which can be more easily measured. Fig. 3 shows calculated u-distributions for the following cases, in the scaling limit. (a) Diagonal NC uN -~ vc~-X. This is the sum of eqs. (14) and (15); in the WS model these two distinct contributions have rather similar u-dependence. (b) Nondiagonal NC vN -~ vcX with h R only, h E = 0. (c) Nondiagonal NC uN -+ ucX with h b only, h R = 0. The corresponding mean values are (u) asymptotically = 0.05 (a), 0.21 (b), 0.14 (c). The minimum decay-lepton energy cutoff has little effect on the u-distribution, but the W > We cut plus slow rescafing gives a strong bias near threshold. To illustrate this we quote below the corresponding mean values at E = 20 and 100 GeV, calculated with We = 4.7 for case (a), Wc = 2.8 for case (b), and case (c). (u) at 20 GeV = 0.015 (a),

0.09 (b),

0.08 ( c ) ,

(u) at 100 GeV = 0.04 (a),

0.16 (b),

0.12 ( c ) .

Given the expected measurement accuracy of eq. (9), it may be difficult to distinguish in this way between diagonal and non-diagonal processes at energies below E = 20 GeV, but should be feasible in beams with a higher mean energy.

5. Leptons from

target fragmentation

We wish to estimate the distribution of charmed particles and their decay leptons, coming from target fragmentation. We therefore construct a simple model for diago-

Is. Barger et al. / Charm production

E

N

+

143

c

N

Fig. 4. Model for diagonal NC charm production, including the charmed targ_et fragments. The quark-partons c and c are taken to fragment independently, yielding D and D mesons.

10 3

10 2

E

Z "~ 101

~o °

0

5

10

15

Et (GeV) Fig. 5. Energy spectrum dN/dEQ of leptons from the decay of charmed D-mesons, produced by target fragmentation according to our model, at the typical kinematic point v = 100 GeV, Q2 = 10 GeV 2.

V. Barger et a L / Charm production

144

nal NC production from the c~- sea of the nucleon, as shown in fig. 4. The charmed quarks fragment independently into charmed D-mesons, with probability [22] D(z) o: (1 - z)/z 1/2, where z = ED/Ec, with the cutoff z/> z o = rnD/Ec and normalization flzoD(Z) dz = l. All particles are treated as spinless; g has q~ quantum hum2 --F , where k bers. We assume that the gc~- vertex function is damped as ( - k 2 + mc) is the momentum in the virtual quark line, and describe the lower vertex by a scaring structure function F(x). We perform an asymptotic calculation, as in ref. [23], neglecting mg and mn compared to p and Q2 but retaining the large masses m D and m e (taken equal for convenience). This model gives the spectrum of D-mesons produced in the target fragmentation region, for given ~, and Q2 of the current J,

dN dF D

~ cc

dE D(ED/E) / E3+21,

mD

F(z)dz

(38)

7,3+21, , z0

where E is the energy of the slow quark, and

z o = x + m~)/[2ME(1 - E/u)].

(39)

We fold in the lepton distribution from D -+ K*~, decay, as in ref. [6]. Fig. 5 shows the resulting lepton spectrum dN/dE~, calculated at a typical kinematic point for NC charm production: u = 100 GeV, Q2 = 10 GeV 2. We choose F = 0 and F(x) ~x ( 1 - x) 4 here, but other choices give qualitatively similar results. Note that cuts at E~ = 0.8 and 2.5 GeV, corresponding to typical electron and muon experiments, remove 35% and 66% of the events, respectively, in this example. At high lepton energies, the current fragmentation mechanism dominates (fig. 2), but at lower energies target fragmentation becomes important, and the two contributions cannot be distinguished experimentally.

6. Summary Our results suggest the following conclusions. (i) Diagonal neutral currents, as in the WS model, predict associated charm production at the level 10 -2 of CC uN events at high energy. Charm cross sections for uN and FN are equal. They give anomalous one- or two-lepton final states by semileptonic decay. Our estimates are based on diagrams in wttich the neutral current couples to the charm quark. (ii) The BCHW pN -+ ue+X candidate events are consistent with charm production in the above range. (iii) Non-diagonal ~-p neutral currents could in principle give much bigger cross sections, via valence p ~ c transitions, favoring e + and/~+ decay leptons. However, at least in SU(2) × U(1) gauge models, theoretical constraints limit non-diagonal c-production to the level ~< ? × 10 -2 of CC events for vN, ~< 2 × 10 -1 of CC events

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for gN. A fraction B -~ 0.2 might be expected to yield e + (or equally/a +) decay leptons. (iv) Relatively small non-diagonal neutral currents could still be distinguished from diagonal neutral currents by the different x- and u-dependences as illustrated i n fig. 3.

(v) The y-dependence of NC charm production reveals the ratio of left handed to right-handed couplings. (vi) The expected energy spectrum of current-fragmentation charm-decay leptons are as shown in fig. 2. (vii) An illustrative model for target fragmentation gives the charm-decay lepton spectrum shown in fig. 5.

We are grateful to D. Nanopoulos, J. Mapp, D. Reeder and W. Venus for discussions and to G. Weller and T. Gottschalk for computations.

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