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# Flavor Changing Neutral Scalar Currents at $mu^+mu^-$ Colliders

SLAC-PUB-95-6962 BNL-

arXiv:hep-ph/9507416v1 26 Jul 1995

Flavor Changing Neutral Scalar Currents at ?+ ?? Colliders David Atwooda , Laura Reinab and Amarjit Sonib

a) Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309, USA b) Department of Physics, Brookhaven National Laboratory, Upton, NY 11973, USA

Abstract: The prospect of observing the ?avor changing decay H ¡ú t? of a neutral Higgs boson produced via s-channel and its c subsequent decay into t? is considered at a ?+ ?? collider. Nuc merical estimates are given in the context of a two Higgs doublet model with ?avor changing couplings. It is found that for many values of the model parameters such tree-level ?avor changing decays will be produced at an observable level. In addition studies of the helicity of the top will allow the determination of the relative strengths of the ?avor changing Higgs couplings and these may be measured with about 103 events.

Submitted to Physical Review Letters

* This work was supported by US Department of Energy contracts DE-AC03765F00515 (SLAC) and DE-AC02-76CH0016 (BNL).

The suppression of ?avor changing neutral currents (FCNC) is an important feature of the Standard Model (SM). Thus, the measurement of such currents provides an important test which can discriminate between the SM and various models of new physics. In the SM, the relative largeness of the top mass [1, 2] leads to a measurable rate of FCNC¡¯s in the down type quark sector through penguin processes [3]. In fact recent experiments at CLEO have observed the reaction b ¡ú s¦Ã. At least in part due to the fact that no correspondingly heavy down type quark is thought to exist, similar FCNC processes within the up sector (e.g. t ¡ú c¦Ã) are highly suppressed in the SM[4]. Since we do not know of a conservation law that enforces the absence of such FCNC¡¯s their continual search is clearly warranted. These considerations have, of course, fueled the searches for ? ¡ú e¦Ã, KL ¡ú ?e etc. for a very long time. The extraordinary mass scale of the top quark has prompted many to advocate that FCNC involving the top quark may well exist [5]. An important class of models where FCNC¡¯s can occur among up type quarks are those where ?avor changing occurs in an extended neutral Higgs sector. In previous works [6, 7], the observation of FCNC¡¯s (due to penguin graphs involving such a Higgs sector) was considered in the processes t ¡ú c¦Ã or cZ and e+ e? (or indeed ?+ ?? ) ¡ú ¦Ã or Z ¡ú t? respectively. In this Letter c we suggest that the tree level coupling of such ?avor-changing neutral Higgs bosons [8] to t? may be probed by ?+ ?? ¡ú t? at suggested muon colliders c c (MUCs). Although very much in the notion stage at present, the MUC has been suggested [9]-[12] as a possible lepton collider for energies in the TeV range. The advantage of such a MUC would be that the much heavier muon su?ers appreciably less energy loss from synchrotron and beamstrahlung radiation. The obvious disadvantages include the fact that muons eventually decay as well as the new accelerator technology development needed to produce and control such beams to the necessary degree to reach high luminosities. If MUCs are eventually shown to be a practical and desirable tool for exploring physics in the TeV range, most of the applications would be very similar to electron colliders. One advantage however is that they may be able to produce Higgs bosons directly in the s channel in su?cient quantity to study their properties directly [9, 13, 14, 7]. In particular, a simple but fascinating possibility that we wish to explore here is when such a Higgs, H, has a ?avor-changing Ht? coupling then the process ?+ ?? ¡ú t? will give a c c signal which should be easy to identify, is likely to take place at an observable 1

rate and yet has a negligible SM background. Thus the properties of this important coupling can be studied in detail. The crucial point is that in spite of the fact that the ?+ ?? H coupling, being proportional to m? , is very small, if the MUC is run on the Higgs ¡Ì resonance, s = mH , Higgs bosons may be produced at an appreciable rate [9, 13, ¡Ì 7]. 14, At s = mH , the cross section for producing H, ¦ÒH , normalized to ¦Ò0 = ¦Ò(?+ ?? ¡ú ¦Ã ¡ú e+ e? ), is given by: R(H) = 3 H ¦ÒH = 2 B? ¦Ò0 ¦Áe (1)

H where B? is the branching ratio of H ¡ú ?+ ?? and ¦Áe is the electromagnetic coupling. If the Higgs is very narrow, the exact tuning to the resonance implied in equation (1) may not in general be possible. Let us suppose then that the energy of the beam has a ?nite spread described by ¦Ä:

where we assume that s is uniform about this range. The e?ective rate of Higgs production will thus be given by: mH ¦Ä ¦£H R(H) (3) arctan mH ¦Ä ¦£H We now consider an extended Higgs sector which admits FCNCs. In refs. [6, 7], for instance, a minimal FCNC Higgs model with two Higgs doublets ¦Õ1 , ¦Õ2 is considered. We assume, without loss of generality, that ¦Õ1 is aligned with the vev so that ? R(H) = < ¦Õ1 >= 0 ¡Ì v/ 2 , < ¦Õ2 >= 0 (4)

m2 (1 ? ¦Ä) < s < m2 (1 + ¦Ä) H H

(2)

¡Ì 1 where v = ( 2GF )? 2 . There are three neutral mass eigenstates denoted by H, h, and A which are [6, 7] ¡Ì 2[(Re¦Õ0 ? v) cos ¦Á + Re¦Õ0 sin ¦Á] H = 1 2 ¡Ì 0 h = 2[(?Re¦Õ1 ? v) sin ¦Á + Re¦Õ0 cos ¦Á] 2 ¡Ì A = ? 2Im¦Õ0 2 2

(5)

where the mixing angle ¦Á is a parameter determined by the Higgs potential. The Lagrangian for the Higgs-fermion interaction is [6, 7]: ? ? ? ? L = ¦ËU Qi ¦Õ1 Uj + ¦ËD Qi ¦Õ1 Dj + ¦ËL Li ¦Õ1 Ej ij ij ij D ? L? U ? ? + ¦Îij Qi ¦Õ2 Uj + ¦Îij Qi ¦Õ2 Dj + ¦Îij Li ¦Õ2 Ej + h.c.

(6)

Here the ¦ËU,D,L couplings turn out to be proportional respectively to the ij quark and lepton mass matrices, while the ¦Îij couplings are arbitrary and ?avor non-diagonal. For de?niteness, we will assume that the magnitude of the parameters ¦Îij are as suggested by the ansatz of [15], ¡Ì mi mj (7) |¦Îij | ¡Ö g Mw Let us now consider that a Higgs H of mass mH is under study at a MUC. For illustrative purposes we take H = h in the above model where ¦Á = 0 (case 1) or ¦Ð/4 (case 2). The main distinction between the two cases is that in case 2 the decays H ¡ú ZZ, W W are possible while in case 1 they are not. Thus case 1 is very similar to H = A. In general the coupling of h to ? f f is: Re¦Îf f + i¦Ã5 Im¦Îf f g mf gmf ¡Ì sin ¦Á + ¦Öf ei¦Ã5 ¦Ëf cos ¦Á ¡Ô 2 mW 2mW 2

Chf f = ?

(8)

while the coupling to ZZ and W W is given by: g sin ¦Á mZ g ?¦Í ChW W = g sin ¦ÁmW g ?¦Í cos ¦ÈW Finally the ?avor changing Higgs ?t? coupling is given by: c ¡Ì g mt mc 1 ? (¦ÖR PR + ¦ÖL PL ) Chtc = ¡Ì ¦Îtc PR + ¦Îct PL cos ¦Á ¡Ô 2mW 2 ChZZ = (9)

(10)

where ¦ÖL and ¦ÖR are in general complex numbers and of order unity if (7) applies. The decay rates to these modes given the above couplings can be readily calculated at tree level by using the results that exist in the literature [16]:

3

2 3gW m2 mH t ? ¦Ât ¦Ât2 + (1 ? ¦Ât2 ) sin ¦Ët ¦Ö2 ¦£(H ¡ú tt) = t 32¦Ðm2 W 2 3gW m2 mH 2 b ¦£(H ¡ú b? = b) ¦Öb 32¦Ðm2 W m4 g 2 m3 Z H 2 ¦ÂZ (¦ÂZ + 12 4 ) sin2 ¦Á ¦£(H ¡ú ZZ) = 128¦Ð m2 mH Z g 2 m3 m4 H 2 ¦£(H ¡ú W W ) = ¦ÂW (¦ÂW + 12 W ) sin2 ¦Á 64¦Ð m2 m4 W H

(11)

where ¦Âi = 1 ? 4m2 /m2 . i H The decay rate to t? is thus: c
2 3gW mt mc mH 32¦Ðm2 W

¦£(H ¡ú t?) = c

(m2 ? m2 )2 H t m4 H

|¦ÖR |2 + |¦ÖL |2 2

(12)

? and, ¦£(H ¡ú t?) = ¦£(H ¡ú ct) at the tree level that we are considering for c + ? now. The decay rate to ? ? which we require in equation (1) is ¦£(H ¡ú ?+ ?? ) =
2 gW m2 mH 2 ? ¦Ö? ; 32¦Ðm2 W H B? = ¦£(H ¡ú ?+ ?? )/¦£H

(13)

For the purpose of numerical estimates let us take the following sample choices of parameters: ? Case 1: ¦Á = ¦Ëc = ¦Ët = 0, ¦Ö? = ¦Öb = ¦Öt = 1 and ¦ÖL = ¦ÖR = 1 ? Case 2: ¦Á = ¦Ð/4, ¦Ëc = ¦Ët = 0, ¦Ö? = ¦Öb = ¦Öt = 1 and ¦ÖL = ¦ÖR = 1 ? In ?gure 1 we plot R( H) with ¦Ä = 0, 10?3 and 10?2 in the two cases as well as
H H ? ? Rtc = R(H) (Bt? + Bct ) ? c

(14)

? ? Note that in case 1 if mH is below the tt threshold Rtc is about .01 ? 1 ? and in fact tc makes up a large branching ratio. Above the tt threshold Rtc drops. For case 2 the branching ratio is smaller due to the W W and ZZ threshold at about the same mass as the tc threshold and so Rtc is 4

around 10?3 . For a speci?c example if mH = 300GeV , then ¦Ò0 ¡Ö 1pb. For a luminosity of 1034 cm?2 s?1 , a year of 107 s (1/3 e?ciency) and for ¦Ä = 10?2 case 1 will produce about 5 ¡Á 103 (t? + tc) events and case 2 will produce c ? about 150 events. Given the distinctive nature of the ?nal state and the lack of a Standard Model background, su?cient luminosity should allow the observation of such events. If such events are observed one would like to extract the values of ¦ÖL and ? ¦ÖR . What is measured initially at a ?+ ?? collider is Rtc . One is required to know the total width of the H and the energy spread of the beam in order to translate this into ¦£(H ¡ú t?). This then allows the determination of c 2 2 |¦ÖL | + |¦ÖR | . To get information separately on the two couplings we note that the total helicity of the top is: Ht = ?Ht = ? |¦ÖR |2 ? |¦ÖL |2 |¦ÖR |2 + |¦ÖL |2 (15)

from which one may therefore infer |¦ÖL | and |¦ÖR |. Unfortunately in the limit of small mc the helicity of the c-quark is conserved hence the relative phase of ¦ÖL and ¦ÖR may not be determined since the two couplings do not interfere. Of course the helicity of the t cannot be observed directly, however following the discussion of [17] one may obtain it from the decay distributions of the top. In particular if X is a particle arising in top decay let us de?ne the forward-backwards asymmetry AX = ¦£(cos ¦ÈX > 0) ? ¦£(cos ¦ÈX < 0) ¦£(cos ¦ÈX > 0) + ¦£(cos ¦ÈX < 0) (16)

where ¦ÈX is the angle between PX and ?PH in the t rest frame. For each particular choice of X we de?ne ?X to be the correlation with the polarization de?ned by:
t ?X = 3 < cos ¦ÈX > t where ¦ÈX is the angle between X and the spin axis of a polarized top. In terms of ?X the asymmetry AX is thus given by:

(17)

1 AX = ?X Ht . 2 Let us now consider the following decays [17]: 5

(18)

? 1) for t ¡ú W b, W ¡ú l+ ¦Íl where l = e, ? then ?l = 1 and the branching fraction for this case is B1 ? 2 . 9 ? 2) For t ¡ú W b, W ¡ú hadrons then ?W = (m2 ? 2m2 )/(m2 + 2m2 ) ¡Ö t W t W 7 0.39 and the branching fraction for this is B2 ? 9 . The number of t? events needed to observe the top helicity with a signifc icance of 3-¦Ò is [17]: N3¦Ò = where Et = 36 Et2 H2 t ¡Ö 107 H2 t (19)

Thus at least 102 events are required to begin to measure the helicity of the top and hence the relative strengths of ¦ÖL and ¦ÖR . In the above numerical examples it is clear that for some combinations of parameters, particularly if the luminosity is 1034 cm?2 s?1 , su?cient events to measure the helicity may be present.

B1 ?2 + B2 ?2 ¡Ö .58 W l

(20)

This work was supported by US Department of Energy contracts DEAC03-765F00515 (SLAC) and DE-AC02-76CH0016 (BNL).

6

Figure Captions ? Figure 1: The value of R(H) is shown as a function of mH for scenario 1 ? (dash-dot) and for scenario 2 (dots). The value of Rtc is shown in case 1 for ?3 ¦Ä = 0 (upper solid curve); ¦Ä = 10 (middle solid curve) and ¦Ä = 10?2 (lower ? solid curve). The value of Rtc is shown in case 2 for ¦Ä = 0 (upper dashed ?2 curve) and ¦Ä = 10 (lower dashed curve).

7

References
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[11] W.A. Barletta and A.M. Sessler, ibid, p. 36; A.G. Ruggiero, ibid, p. 45; S. Chattopadhyay et al., ibid, p. 53. [12] R.B. Palmer, preprint, ¡°High Frequency ?+ ?? Collider Design,¡± SLACAAS-Note81, 1993. [13] V. Barger, M. Berger, K. Fujii, J.F. Gunion, T. Han, C. Heusch, W. Hong, S.K. Oh, Z. Parsa, S. Rajpoot, R. Thun and B. Willis, Working group report, Proc. of the First Workshop on the Physics Potential and Development of ?+ ?? Colliders, Sausalito, CA, preprint MAD-PH-95873 (BB-9503258). [14] V. Barger, M. Berger, J. Gunion, and T. Han, hep-ph/9404330. [15] T.P. Cheng and M. Sher, Phys. Rev. D35, 3484 (1987); M. Sher and Y. Yuan, Phys. Rev. D44, 1461 (1991). [16] J. Gunion, H. Haber, G. Kane and S. Dawson, ¡°The Higgs Hunters Guide,¡± published by Addison Wesley. [17] D. Atwood and A. Soni, SLAC-PUB-95-6877.

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