Physics Letters B 299 (1993) 312-314 North-Holland PHYSICS LETTERS B

t6H production for an intermediate mass Higgs

Alessandro Bal les t rero INFN, Sezione di Torino, 1-10125 Turin, Italy

and

Ezio M a i n a Dipartimento di Fisica Teorica, Universit~ di Torino, and INFN, Sezione di Torino, 1-10125 Turin, Italy

Received 14 July 1992

We study the contribution of the t6H channel to Higgs production in the intermediate mass range for which conflicting results have been published. We conclude that t~H production does not significantly increase the chances of discovering the standard model Higgs.

The search for the Higgs boson will be a central is- sue for the next generation of colliders. I f this fails, we will known that new physics exists beyond the simplicity of the standard model at a scale of about 1 TeV. Several studies [ 1 ] have shown that LEP I and II will explore the mass range rnl4<~ 80 GeV using e - e + ~ Z H . Larger masses will have to be studied at hadron supercolliders. For rnn>~ 130 GeV the four lepton channel H ~ Z Z ~ 4l will allow detection up to masses o f several hundreds GeV, the precise reach depending on machine energy and luminosity [2,3 ]. The most difficult range to cover is the so-called in- termediate mass region. It has only recently been es- tablished that, for 80 ~< rnn~< 130 GeV, the associated production of the Higgs with a W b o s o n [4] or a t/- pair [ 5 ], followed by the decays H ~ y 7 and W ~ h,, has promising event rates and not too large backgrounds.

In a recent paper [ 6 ] it was claimed that the pro- cess gq--,tSHq' has a cross section comparable to t[H and W H production. The contribution of the tH final state was estimated from the cross section for gW-- . t~H convoluted with an appropriate W lumi- nosity, in the so-called equivalent W approximation

Work supported in part by Ministero dell'Universith e della Ricerca Scientifica.

[ 7 ]. The only possibility of explaining such a result would be that the large W H coupling compensates the smallness of single t production compared with t/- production [ 8 ]. In view of the relevance of this result for an assessment of the required luminosity and de- tector capabilities, we have performed the calcula- tion of the exact matrix element for gq~t6Hq ' . Our results are in disagreement with those ofref. [ 6 ] and in fact about a factor of five smaller. In the meantime new results have appeared [ 9 ] which contradict the claim of ref. [ 6 ]. In ref. [ 9 ] the b quark was consid- ered a massless constituent of the proton. The exact matrix element for bq-~ tHq' was computed, avoiding the use of the equivalent W approximation. In this approach the fact that the dominant contribution to the cross section for gq--. t6Hq' are those in which the final b is collinear to the incoming gluon is exploited, and the collinear logarithms are summed up to all or- ders in the leading and next-to-leading approxima- tion. The rates obtained in ref. [9 ] are about ten times smaller than those reported in ref. [ 6 ]. As a further check, we have repeated the calculation of ref. [ 9 ] with whose results we are in agreement.

The Feynman diagrams describing the matrix ele- ment at tree level can be conveniently divided into two gauge invariant sets according to whether the gluon attaches to the heavy or to the light quark line.

312 0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.

Volume 299, number 3,4 PHYSICS LETTERS B 28 January 1993

The cross section obtained squaring the sum of the diagrams in which the gluon attaches to the heavy quark line is finite. The remaining contribution, in- cluding the interference between the two sets, is di- vergent in the limit of a final light quark collinear to the incoming gluon. The collinear region has to be considered with the higher order corrections to qq'--,t6H in order to get a finite answer. We have checked that with a 10 GeV cutoff on the light quark transverse momentum the contribution, interference included, of the collinearly divergent diagrams is nu- merically negligible. Therefore we believe that the re- sult obtained considering only the nonsingular dia- grams is a good estimate of the relevance of the tH final state to Higgs production and detection. Since only this term was also considered, in an approxi- mate way, in ref. [ 6 ], the two calculation should be directly comparable.

The calculations have been performed at the am- plitude level following the method of ref. [ 10 ]. All results include the charge conjugate states. The HMRSB set of distribution functions has been used [ 11 ] throughout. The strong coupling constant and the distribution functions have consistently been evaluated at a scale equal to the subprocess total in- variant mass. We have used the two loop expression

• ( 4 ) for ors with A ~-g = 190 MeV and five active flavors. Changing the scale and/or the distribution functions should not affect the predictions by more than a fac- tor of two.

We have not applied cuts to our results. All pre- vious experiences indicate that for a realistic choice of cuts, about 50% of the events will be lost.

Our results are presented in fig. 1. The cross sec- tions for bq~tHq' and gq~tGHq' are given for both LHC and SSC energies, with the top mass at 100 GeV and 200 GeV, conveniently bracketing the range al- lowed in the standard model by recent LEP data. We typically obtain that the cross section for the former process is twice the cross section for the latter. Not unexpectedly, this difference is larger than the 10% to 35% discrepancy obtained in ref. [9] comparing the cross section for pp~gq~t6q' with the one for pp--,bq--.tq'. Indeed log(m~/g) is on average larger in our case than in the reactions considered in ref. [ 9 ]. The expectation that the cross section is strongly influenced by the Higgs coupling to the W boson is confirmed by the decrease, except for small ran, of

lo"

b

i0-'

~l i i i i i

"x/s=40 TeV"

mr=20 0

" " ; - - " . . . . . . . . . . mt=100 x/s=16 TeV

" ' ' - . mt=200 . . . . . . .

i i ! r I i

7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0

M H (GeV)

Fig. 1. Cross sections a(gq--*t6Hq') (solid lines) and a(bqotHq') (dashed lines ) at SSC (upper four curves ) and LHC (lower four curves) for mr= 100 GeV and mr= 200 GeV as indicated.

the cross section for increasing top mass. This is to be compared with the behaviour of the gg--. ttH cross section for similar mn and mr, where the increase in the Higgs-top coupling compensates the larger center of mass energy required by larger top masses. In fact there is a substantial cancellation between the dia- grams in which the Higgs couples to the heavy quarks and those in which the Higgs couples to the W.

When the appropriate branching ratios are folded in, the cross sections reported in fig. 1 correspond to between 0.5 and 5 events per year at LHC ( L = 105 pb -~) and SSC (L=104 pb - l ) before cuts, and therefore do not significantly modify the expected number of H(-*77) + I events.

As a byproduct of the calculation described above, we have computed the contribution of and gq-, t{Hq' including only Z exchange between the two fermion lines. We obtain cross sections of 5-20 fb at LHC and 40-130 fb at SSC which are totally negligi- ble compared to gg--, ti-H or qq'--* WH.

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Volume 299, number 3,4 PHYSICS LETTERS B 28 January 1993

In conc lus ion Higgs p r o d u c t i o n in assoc ia t ion wi th

a single t qua rk does no t y ie ld a substant ia l n u m b e r

o f even t s at had ron i c coll iders. In a g r e e m e n t wi th ref.

[9] we f ind tha t this channe l gives O ( 1 ) even t pe r

year.

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