On b-flavour production by neutrinos

Nuclear Physics B153 (1979) 475-484 0 North-Holland Publishing Company

ON b-FLAVOUR PRODUCTION BY NEUTRINOS

R.J.N. PHILLIPS Rutherford Laboratory, Chilton, Didcot, Oxon, England Received 27 February 1979

Quantitative estimates are given for b-quark production by neutrinos and antineutrinos in the standard sixquark model, including realistic threshold suppression. The feasibility of identifying b-decay leptons by their transverse momentum is examined critically with discouraging conclusions. Production by flavour-changing neutral currents in a fivequark model is also evaluated.

1. Introduction

Neutrino production of b-quarks (the presumed constituents of upsilon mesons) could be an important way to explore their role in fundamental gauge models. The phenomenology has been extensively studied in the standard six-quark SU(2) X U( 1) model [l] and other models [2]. Upper limits have been set [ 1,3] for the mixing angles that control b-production by weak currents. However, at presently accessible energies it is essential to take account also of threshold suppression effects, and these have received little discussion. In the present paper, the threshold effects are calculated explicitly using the best available techniques: for production from light quarks (u + b, ii+ 6) the quark parton model is used, with QCD-corrected distributions [4,.5] and a slow-resealing variable [6]; for production from heavy quarks (c + b, t + b, etc.) the current&ton fusion model [7,8] is used. Results for charged current processes are given in sect. 2: small mixing angles and threshold factors combine to keep b-production well below 1% at presently accessible energies. There is also the question of identifying b-quarks. The most promising signature [9] for neutrino b-production is the transverse momentum of the secondary muon in opposite-sign dimuon events. Because of the big energy release, leptons from bdecay can have large momenta pl transverse to the production plane, whereas the background leptons from c-decay have smaller mean pb However, if the b-signal is relatively weak, as predicted, it will not dominate until rather large pl where the statistics are poor and the predictions are model dependent. This is a quantitative question; it is examined in sect. 3, with rather discouraging conclusions. Another 475

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R.J.N. Phillips/ b-jlavourproduction

possible b-signature is same-sign dileptons, where the secondary lepton comes from cascade decays b + c + SQZJ, etc. (or alternatively from B”-@’mixing). The background here comes mainly from 71and K decays; in principle this can be separated by extrapolating the target density dependence, but it would be nice if pl dependence could also be used to help the separation. Sect. 3 examines this question, again with discouraging conclusions. Trilepton rates from cascade b-decays are well below the present experimental bounds [lo]. The calculations above assume the standard six-quark model, based on three left-handed doublets. Another non-standard model [ 11,121 assigns the b-quark to a singlet with d and s mixing. Here the limits on charged current u + b, c + b couplings are the same as in the standard model, but additional non-diagonal d --f b, s + b neutral current couplings appear. Upper limits for the corresponding cross sections are given in sect. 4.

2. Charged-current b-production In the standard six-quark SU(2)L X U(1) model, an extra doublet (t,b’)L is added to the established doublets (u, d’)L, (c, s’)~ of the GIM model. Here d’, s’, b’ are related to the physical d, s, b states by the Kobayashi-Maskawa matrix [ 131, containing three mixing angles 8i and a Cp violating phase 6: -S1C3

-s1s3

(ClCzC3 -s2s3ei6)

(ClCzS3 +s2c3ei6)

(ClSzC3 +c2s3ei6)

(ClSzS3 - c2c3ei6)I

rdl

(1)

where si = sin Bi, ci = cos Bi. Analysis of d +uands+udata [1,3] giveslsrl-0.23 and sets the limit lssl < 0.5. The success of a calculation of the KL, KS mass difference requires [l] Is2I < 0.3 (for mt > 10 GeV). Thus the u + b and c -+ b couplings are at most 0.1 and 0.7 respectively, in modulus, relative to the standard Fermi coup ling strength; however, the t + b coupling can be essentially unity. Charged-current b-production proceeds via Vu + p+b, 2rc-+ p’b. trt + p+b, E-t p-6, E+ /.L%, VT+ p-5. Only the first of these uses a valence quark, the rest rely on sea quarks. Production from ordinary u, U quarks can be calculated in the quark parton model framework; here threshold suppression comes from the kinematical restriction 2&Zv- e2 + @ > (M + mb)2 and from the use of a slow-resealing [6] variable x’ = x t m~/2Mv. Fig. 1 shows the resulting cross sections for an isospin average nucleon target, as fractions of the total charged current cross section: The calculations use the QCD-corrected parton distributions of Owens and Reya [5] (taking their counting-rule solution) with maximum mixing s:si = 0.013. The parton distributions of Bums and Gaemers [4] give very similar results. Note that the b-threshold is just below E = 20 GeV. At E = 100 GeV threshold

R.J.N. Phillips/ b-fi’avourproduction

417

NEUTRINO

losb

’ ’ “““’ E GeV

I 1000

30

1

I

,I

1

100 E GeV

Fig. 1. Charged current b-production from an i-spin average nucleon target, as a fraction of the total charged current cross section, for neutrinos and antineutrinos. Maximal mixing angles are assumed for each contribution.

effects still cost a factor 2 even in the favouredlu + b case: at 40 GeV they cost a factor 10. For production from heavy c and t quarks, the best available model seems to be current&on fusion [7,8]; here a single QCD gluon essentially generates the heavy sea, g + CC,g + t?. Threshold suppression is directly related to phase space, through the heavy quark masses. General formulae are given by Leveille and Weller [8]. Fig. 1 shows the resulting cross sections calculated for the maximum allowed c --f b and t + b couplings, assuming m, = 1.87, mb = 5.1, mt = 15 GeV and taking the running gluon coupling constant %(P~) = 12 nr/]23 1n(3/A2)1,

(2)

appropriate for 5 active flavours, with A = 0.5 GeV. The calculations shown take cu,scaled by the invariant mass square for the produced quark pair, but it makes little difference if (y, is scaled instead by the momentum transfer Q2 following ref. [ 81. A standard counting-rule gluon distribution g(x) = 3x-r (1 - x)’ is assumed. The t-quark mass is simply a guess, but it scarcely matters since the corresponding cross section is negligible anyway. The c and b masses are chosen to give physical phase-space limits. It can be argued that smaller quark masses should be used and that the diquark invariant mass need not by itself exceed the physical flavour threshold [ 141; if so, the results here should be scaled up somewhat.

The most promising ahollt

~tnvs

blnw

Gek,

cnmpared

to

b-prndllctinn

channel js ohvinunlyvll

0.3% of the tntal charged-cllrrent

113-15% fnr charm prodllctinn

4

p’b.

hut even this

cross sectinn fnr E = 100-200 [221. Since the relevant

semi-

of the opposite-sign antinelltrino dimllnns in this energy range can he expPcterl to cnme frnm h-prndllctinn_ in the standard theory. Fnr nelltrino rlimllnns the figllre is n.l-1%.

leptnnic

branching

ratios shnllld he cnmn,nmhle.

at mnq? 3%

After production the b-quark fragments into a B-hadron. within which the bquark finally decays. Many authors have studied the lepton signals from b-decay [1,&o-12,15-171. An important feature is that b -+ cllv and b + uRv transitions give leptons with high momenta pt transverse to the line of flight of B. In zeroth approximation, this line of flight is the axis of momentum transfer from the current: however, B shnuld have apt distribution relative to this axis. Conservatively, we may expect B to have the universal pt dependence ohserved in other hadrnn production processes [ 181

cwldp:-

exp{-A(p:

+ ~2:)~‘~) ,

with A = 5 GeV-‘. However, in the current-gluon fusinn model. a broader distribution withA = 2.5 GeV-’ is found [S] for heavy quarks: with approximate &function fragmentation expected [19], a similar distributinn would hold for B-particles. This range of A deserves study. In practice it may be better to study momenta pl transverse to the production plane defined by the beam axis and the direct muon. Fig. 2 shows the predicted pl distributions for B + cPv decay leptons, assuming an initial pt distribution for B given by eq. (3) with A = 2.5 or 5.0 GeV-‘. The inclusive decay is ca.lculated with bare-quark V-A matrix elements, which should be approximately valid for = 5.1 GeV and m, = 1.87 GeV to give heavy quark decays [ 1,201, with masses rn,, realistic phase-space limits. Lepton mass is neglected. The alternative b + uRv decay gives almost the same syectnlm. (For the mechanics of semileptonic decays, see, e.g., ref. [21]). Fnr comparison fig. 2 also shows the pL spectrum from D + XPv charm decay. Here the initial pt distriblltinn nf D is again taken from eq. (3) with the same two values of A ; D-decay is represented by equal proportions of D + KQv and D -+ K*Qv as in ref. 1171. Experimentally the problem is to distinguish a b-signal such as GN + P’bX, b -+ R-X’ from the charm background FN + p%‘X, C -+ Q-X’. In fig. 2 the relative normalization of signal to background is chosen to be 1 to 30, representing the most optimistic expectation for E = 100-200 GeV according to sect. 2 above. If we take the most favourahle example, with A = 5.0 for both B and D initial distributions, the signal dominates over background (by a factor > 2) only for pl > 1.5

Fig. 2. Opposite-sign dilsntnn events: denmdance on the momentum pl tranwerre Ientnnq frnm D ductinnTlane for leptnns frnm B + QX decay and hnckgrolrnd valuesA = 2.5, 5.0 GeV-’ for eq. (3) RW ilhlWated.

to the proQX.

Prrameter

GeV, a region where only 9% of R-decays occur. If instead A = 2.5 for bnth R and D, the signal dominates over background only for pI > 2.5 GeV, where only 1% of the R-decays lie. Either wa,y, the useful fraction of R-dccnvs is smrll. and the tail of the spectrum where these events lie denends strongly on the initial pt &tributinn. It appears that at least 100 h-dimllnns may he needed to eatahlich a cnnvincing signal of this kind. corresponding to IO3 b-productinn events and 106 antineutrino interactions at the high energies nf interest. This cnnclllsinn

is much mnre discnllraging

thaq thnt of Alhright

and Smit.h [9],

because they assume a much narrower initial LQdiWihn+inn for D-prndnc the shape of tion dN/dp: - exp(-4 p:). Present dnta do nnt accurately rl+-mine the initisl ptD distribution, especinlly in the tail. Fnr COWS dimunn events [22], mean values of p6 for the secnndaw mm-m relative to the mnmentum trnnsfer axis are reported: (ptu) = 0.76 + 0.04 and 0.64 + 0.05 &V/c for VN and m events

essentially

480

R.J.N. Phillips / b-fikvour production

respectively. (ptr)

The calculated = 0.35 GeV/c

values for various initial ptr, distributions for

dNd&

are as follows,

- 6 (P,“D)

= 0.36 GeV/c

- exp(-4

= 0.38 GeV/c

- exp(-5(p&

= 0.41 GeV/c

- exp(-2.5(&r

PLJ + rn~)“‘) + &)“*).

The comparatively large experimental values presumably reflect measurement uncertainties, and do not discriminate well between the models. Cascade decays b + c -+=SPVcan give same-sign dileptons. The transverse momentum of the second-stage lepton is much less. Fig. 3 shows the pl distribution calculated as follows. The initial pt distribution of B is given by eq. (3); the inclusive B + CX decay is calculated with free-quark V - A matrix elements; c + D fragmentation is described by a flat (uniform) fragmentation function [23] ; D-decay is

\ K,H-wl

background

---__-__

,

Ki6 0

1

I

1

2

\ 3

P,G~V

Fig. 3. Same-sign dilepton events: dependence on the momentum pl transverse to the production plane for leptons from cascade b -+ c-e SQVdecays and background leptons from n and K decays. Parameter values A = 2.5, 5.0 GeV-’ are illustrated.

R.J.N. Phillips/ b-jlavourproduction

481

represented by D + KQv,K” Qvas before. For comparison, the background from ?T and K decay leptons is shown: this is taken to have the usual pionic diV/dp: exp(-6pt) dependence, translated into pl dependence normal to the production plane. The signal to background normalization is 1 to 1. It can be seen that transverse momentum is no help in discriminating the signal. One has to rely on target density extrapolations to remove the rr and K decays. Unfortunately the expected same-sign dimuon signal is at most of order 3 X lop4 @N) or lO-5-lO-4 (vN) for energies E = 100-200 GeV, smaller than reported signals [24]. Alternatively, same-sign dileptons can arise from B”-Bo mixing, if it occurs. In this case the secondary lepton has a component similar to the signal in fig. 2 (the n, K background shape is very similar to the D background with A = 5 in this figure). If the rr, K background can be reduced by density extrapolations to a level comparable with the signal, the latter may be extracted by its pt dependence. Signal limits are like cascade case. Cascade decays can yield two leptons b + QTQ;X with branching ratios of order 10M2 for each QrQ2assignment. The corresponding trilepton event rates are of order 10m4 form, 10v5 for vN in the range E = 100-200 GeV. The CDHS trimuon experiment [lo] sets an upper limit 0.7 X lo-’ for VN trimuons from this source (from the observed invariant masses of the secondary muon pairs), averaging over a broad-band spectrum with E > 30 GeV. Converting this to a limit for E > 100 GeV instead, as seems reasonable from fig. 1, yields on upper bound for b-cascade trimuons of 6 X lo-’ instead, well compatible with the present theoretical estimates.

4. Non-standard five-quark model Suppose the new b-quark is assigned to a left-handed singlet, with d and s mixing [ 11,121. The most general mixing of charge -i quarks is still as in eq. (1), but some flavour-changing neutral currents are now implied since b’is a singlet. The bounds on s + d couplings are so severe, however, that we may assume them to be zero in lowest order, as a first approximation: i.e., either d or s decouples from b’. We then get two possible parametrizations (these correspond to the two solutions of Barger and Pakvasa [12]), with just two mixing angles and no complex phase. Class (a)

(4)

Class (b)

I

IO’0 E GrV

E

c.xv

Fig. 4. iueuual ~UIIWI d - to a11ds - b proclucuon m rhe kveyaark nloudr [ 11 ,121, as a fraction of the tolal charged cun’ut CXN section. Maximal mrxmg anyies ale a~~eci. Neutral culrtrkt bb prouucclon m tile sra~~crard mod [8] is snown tar comparison.

R.J.N. Phillips / b-fluvow producmm

Although v@N -+ e’ X, production). and hard to

483

neurral current b-production has mteresrmg srgnaturas, such as they are not unique and can be faked (e.g., ‘by neutral current cc The smallness of the d + b coupling keeps the cross section small identify.

5. Conclusiuns (i) Threshold factors are important, even at five times the threshold energy; they are especially important for production from sea quarks. (ii) Small mixing angles and threshold effects combine to keep b-production at presently accessible energies well below 1% for irplJ, below 0.1% for vN. (iii) In opp osr“t e-sign d’1l ep t on events, the transverse momenrum of leptons from b-decay can be distinguished from c-decay background only at very large pl values, where the signal is severely depleted. (iv) In same-sign dileptons, the transverse momentum of cascade leptons from b-decay is not readily distinguishable from the background from rt and K decays. A direct lepton signal (via possible B”-B” mrxing) could be distingunshed by pl, but only if the background is not too large. (v) Flavour-changing neutral current production of b-quarks is small, in a nonstandard five-quark model.

References [l] [2] [3] [4] [S] [6]

J. Ellis et al., Nucl. Phys. B131 (1977) 285. C.H. Albright, R.E. Shrock and J. Smith, Phys. Rev. D17 (1978) 2383. R.E. Shrock and L.L. Wang, Phys. Rev. Lett. 41 (1978) 1692. A. Buras and K.J.F. Gaemers, Nucl. Phys. B132 (1978) 249. J.F. Owens and E. Reya, Phys. Rev. D17 (1978) 3003. R.M. Barnett, Phys. Rev. Lett. 36 (1976) 1163; H. Georgi and H.D. Politzer, Phys. Rev. Lett. 36 (1978) 1281. [7] J. Babcock and D. Sivers, Phys. Rev. D18 (1978) 2301. [8] J.P. Leveille and T. Weiler, Nucl. Phys. B147 (1979) 147. [9] C.H. Albright and J. Smith, Phys. Lett. 77B (1978) 94. [lo] T. Hans1 et al., Nucl. Phys. B142 (1978) 381. [ 111 G. Branco and H.P. Nilles, Nucl. Phys. B15 1 (1979) 529. (121 V. Barger and S. Pakvasa, Phys. Lett. 81B (1979) 195. [13] M. Kobayashi and T. Maskawa, Progr. Theor. Phys. 49 (1973) 652. [ 141 C.E. Carlson and R. Suaya, Phys. Lett. 81B (1979) 329. [15] A. Ali, 2. Phys. Cl (1979) 25; A. Ali and Z.Z. Aydin, Nucl. Phys. B148 (1979) 165. [ 161 C. Quigg and J.L. Rosner, LBL-7961. [17] V. Barger, T. Gottschaik and R.J.N. Phillips, Wisconsin report COO-881-82. [18] J.D. Bjorken, SLAC-191 (1975); B. Alper et al., Nucl. Phys. B87 (1975) 19.

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R.J.N. Phillips / b-flavour production

[ 191 M. Suzuki, Phys. Lett. 68B (1977) 164; J.D. Bjorken, Phys. Rev. D17 (1978) 171. [20] M.K. Gaillard, FermilabConf-78/64; M. Suzuki, Nucl. Phys. B145 (1978) 420. [21] V. Barger and R.J.N. Phillips, Phys. Rev. D14 (1976).80; V. Barger, T. Gottschalk and R.J.N. Phillips, Phys. Rev. D16 (1977) 746 [22] M. Holder et al., Phys. Lett. 69B (1977) 377. [23] R. Odorico and V. Roberto, Nucl. Phys. B136 (1978) 333. [24] M. Holder et al., Phys. Lett. 70B (1977) 396; A. Benvenuti et al., Phys. Rev. Lett. 41 (1978) 725.