On the associate production of a neutral intermediate-mass Higgs boson with a single top quark at the LHC and SSC

Physics Letters B 299 ( 1993 ) 315-320 North-Holland

PHYSICS LETTERS B

On the associate production of a neutral intermediate-mass Higgs boson with a single top quark at the LHC and SSC G. Bordes Laboratoire de Physique Corpusculaire, Coll?ge de France, F- 75231 Paris, France

and B. v a n Eijk 1 CERN, CH-1211 Geneva 23, Switzerland Received 23 July 1992

The typical behaviour of the semiweak single top quark production mechanism in hadron-hadron collisions in comparison with heavy quark pair production suggests that boson-gluon fusion may lead to important associated Higgs cross-sections. This is of particular interest for the interval in which the Higgs mass is close to the mass of the Z ° and well below 2 Mzo. In this region experimentally significant signals are expected to be small, while complicated to extract due to large backgrounds. In two recent papers, studies have been presented in which contradicting results have been reported on the magnitude of Higgs production in association with a single top quark. We present an independent analysis and trace the origin of the discrepancies.

Although data in high energy particle interactions collected over the past decade show striking agreement with predictions from modern gauge theories, many principles essential to these theories remain as yet not probed. All models describing electroweak interactions through the mechanism of symmetrybreaking contain physical particles of the bosonic type. They predict that the boson sector will consist of at least one or more spinless so-called Higgs boson(s) which through the Higgs mechanism are responsible for mass generation. None of the models however, provide predictions on the mass of these scalar particles. Direct searches for scalar particles at existing experimental facilities have been negative while the most stringent limit on the mass of the standard model [ 1 ] neutral scalar (H °) has been derived by

i Supported by the "Netherlands Organization for Scientific Research (NWO)", The Netherlands.

the ALEPH Collaboration at the Large Electron Positron (LEP) accelerator at CERN: Mno/>57 G e V / c 2 [2 ]. No upper bound for Ho can be derived from experimental data, however, there are strong theoretical indications that its mass should not exceed ~ 1 TeV/c 2 [3] (or even: MHo<700 G e V / c 2 [4]). LEP200 will certainly improve the present lower bound, but its sensitivity is most likely to decrease rapidly above Mno ~ 80 G e V / c 2. Unless the Higgs is discovered at LEP200, present experimental facilities will not be sufficient to probe deeper into the symmetry breaking mechanism and new accelerator facilities are therefore indispensable. Although e + e - colliders have proven to be relatively clean and precise laboratories for new particle searches, with accelerator technologies as of today one is not able to construct electron machines which will both extend into the (multi) TeV centre-of-mass regime and provide enough luminosity to produce observable event rates at the same time. Hadron colliders such as the proposed Large Hadron Collider

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

315

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( L H C ) at CERN and Superconducting Super Collider (SSC) in Texas provide laboratories for studying interactions that are less clean, but after careful analysis, turn out to allow for exploitation of parton interaction centre-of-mass energies into the multi TeV region. Luminosities at these colliders will be sufficiently large to allow for a scan for (neutral) scalars with a mass up to ~ 1 TeV/c 2 [ 5,6 ]. However, for an important mass window, 80~< Mi-io <~120 G e V / c 2, which covers the lower part of the so-called intermediate Higgs mass interval, 80 GeV/c2 ~< MHo ~<2 Mzo, it will be extremely difficult to resolve an experimentally significant signal from the background. The rate for Higgs decays into four leptons is much too low in this region to be useful whereas the decay H°--,y7 puts severe constraints on photon detection resolution in order to survive the two-photon background from quark-antiquark annihilation and gluon-gluon scattering in the reconstruction of the Higgs mass [7 ]. Alternative production mechanisms have been studied for which backgrounds are sufficiently small. One should bare in mind that total signal event rates per unit of integrated luminosity are very limited and demand highly efficient detectors. The main two processes considered are [ 8,9 ] PP--',qF1'---, W * ~ W H o ,

(I)

where the W decays leptonically and Ho--,)7 ( H ° ~ z + z - seems to be very difficult experimentally [ 10 ], but is interesting enough to justify further study) and a Higgs produced in association with a heavy quarkantiquark pair: p p ~ gg ~ QQ_.H° .

(2 )

For a sufficiently large quark mass (mQ > M w ) , the heavy flavour will decay into an on-shell W and a quark with a substantially smaller mass than the decaying quark Q. Leptonic decays of the W will then provide additional tagging possibilities. Signal to background ratios for these mechanisms are of order 3-4 [9,11 ] at both the LHC and SSC operating at design luminosity, while the total number of events (in which decay branching ratios for H °, Wand heavy quark have been properly included) does not exceed 50 events per year of data taking. Single heavy flavour production has been discussed at length in the literature [ 12 ] and proceeds 316

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through the mechanism of boson-gluon fusion. The fact that the emerging event contains only one very heavy flavour reduces the overall hadronic activity with respect to heavy flavour pair production. A similar argument holds if one compares the production of a Higgs in association with a single heavy flavour or with a pair of heavy quarks. Obviously, also here the heavy flavours will generate a considerable amount of hadronic fragments. Diaz-Cruz and Sampayo [ 13 ] have therefore studied the process pp--, Wg--, Q Q ' H ° ,

(3)

where mQ >> mQ,, arguing that this process may lead to event rates comparable with the ones from the process in (2). Using the effective W approximation, they predict of order 30 lvTy events per running year at LHC. This result seems, a priori not unreasonable if one follows the arguments presented in ref. [ 12 ]. In comparing the shapes of the total cross-section for single top quarks and heavy flavour pair production as a function of the heavy quark mass, one concludes that for a relatively small top quark mass ( m r ~ 100 GeV/ c2), pair production clearly dominates. However, increasing the top mass illustrates the different behaviour of the two mechanisms as a function of the invariant mass of the hard scattering process. The matrix element squared for the boson-gluon fusion mechanism varies with 1/~ (due to the t-channel exchange of the W), while the Q(~ production crosssection is proportional to 1/g. Both mechanisms become equally important for mt ~ 250 G e V / c 2. One may argue that for associate Higgs production where m r ~ 100-200 GeV/c 2 and MHo ~ 100 GeV/c 2, process (3) may compete with the heavy flavour pair production mechanism. Stirling and Summers [ 14 ] have explicitly calculated the semiweak process as well and obtain a result in striking contradiction with [ 13 ]. They claim that W-gluon fusion leads to a negligible contribution to the heavy flavour associated Higgs production crosssection, while increasing the top quark mass at a fixed value of the Higgs mass decreases the cross-section even further. As the origin of the discrepancy between the results of refs. [ 13,14 ] is not apparent, we have performed an independent calculation of the matrix element squared. Diaz-Cruz and Sampayo have applied the

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effective Wapproximation in order to obtain numerical results for the W-gluon scattering process. In ref. [ 14], the authors have used tile helicity formalism extended to heavy quarks to calculate pp-,qb-~ q'H°t [ 15 ]. This method is well suited to include the matrix element for the decay of the top quark as well al. In order to verify the total cross-section for producing a top quark and a Higgs and to understand the disagreement with ref. [ 13 ], they have repeated the calculation using the effective W approximation. They find that they cannot reproduce the results of ref. [131. Since the discrepancies between the two calculations appear at the top quark production level, we have computed the matrix element for the process

pp--,qb--,q'tH ° ,

(4)

using standard Feynman rules. Here we use that since the ratio rob~mr is small, convolution of the O ( a 2) matrix element with the bottom quark distribution function in the proton gives excellent agreement [ 16 ] with calculating the more complicated graph where a bb-pair is produced from gluon splitting [ 12 ]. The set of Feynman diagrams forming the basis of the calculation by Diaz-Cruz and Sampayo then reduces to a much smaller an simpler set of graphs. They are depicted in fig. 1. In the following we will show that although each of the graphs in fig. 1 give potentially large contributions to the cross-section, a huge interference term is arising which is destructive. Let us consider the subprocess W(k)b(pl ) ~H°(pl4)t(p2), thus ignoring the upper vertices in fig. 1. Conventional Feynman rules lead to the following expressions for these matrix elements:

#~

We wish to thank David Summers for forwarding his calculations. q

~

b

~,

¢..,

.~

W ~ ...... .,

(a)

q'

q

~

b

~

H0 t

L,

~

W (~

q' • H0

-~

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Ma = - i ( i g w ) (igwwH)

u(P2)Yu( 1 - ys )u(Pl ) (Pl -p2)2-M2w

X(gU,._ (P,-P2)u( (P,-P2)~) Mzw

Mb = i ( i g w )

e.,

(5)

(ig..)

X a(pz) (gl + ~ + mt)yu(1 -YS)u(Pl )

(p, + k ) Z _ m z

eu ,

(6)

where the couplings among fermions, Higgs and W are specified through their indices (gw is taken to be universal to all fermion doublets, thus ignoring offdiagonal Cabibbo-Kobayashi-Maskawa matrix elements). The high energy behaviour of these amplitudes becomes worse when the incoming W are longitudinally polarised. Then, for a W with fourmomentum k, the polarisation vector can be written as eu = ku/ Mw + 0 ( M w / ko ). Substitution in eqs. ( 5 ) and (6) and taking the high energy limit in which masses may be neglected, the amplitudes reduce to

Ma = - i gwgww~i ( a(P2) mr( 1 - Ys) u (p, ) Mw \ 2MZw -

a(p2)~(1-y,)u(p,)~) '

(7)

gwg,I4 { Mb = - i ~ ~u(P2) (1 -ys)u(p, ) a(p2)m,~(1- ys )u(p, ).] +

2pl .k

]"

(8)

Substitution of the couplings g,n = - g m # 2 M w and gWWH=gMw (with g defined as the SUa gauge coupling), finally shows that the magnitude of the leading terms in both amplitudes are equal and cancel satisfying the unitarity constraint [ 3,17 ] ~2. It is interesting to note that this result is also applicable to extensions of the standard model such as minimal SUSY, where the strength of the top-Higgs coupling depends on the choice of the mixing angle fl (defined by the ratio of the two vacuum expectation values) and angle a (from the diagonalisation of the scalar mass matrix). Unitarity imposes [ 18 ]

t

(b) #2

Fig. 1. Feynman diagrams contributing to the processqb~q'tH°.

We wish to thank Ronald Kleissfor an illuminating discussion (see also Kleissin ref. [ 17]. 317

Volume 299, number 3,4 mt 2 M 2 gwwngwtb

PHYSICS LETTERSB 10.2

-

-

gwnhgwtb = g,ngw~b ,

pp ~

(9)

where h denotes the charged scalar field. After squaring the amplitudes of the graphs in fig. 1, we obtain relatively comprehensive expressions for the contributions from both diagrams and their interference [ 19 ]. Convolution with structure function parametrisations and phase space integration is performed numerically using the Eurojet simulation package [ 20 ]. The scale at which the structure functions are evaluated is chosen to be Q2=g, the total invariant mass of the partonic sub-process squared. We use the Eichten et al. [ 21 ] structure function parametrisations (set 1, A = 0.2 MeV). Since the amplitude squared does not contain any intrinsic divergences, integration can be carried out over full phase space. In figs. 2a,2b, we present total cross-sections as a function of the Higgs mass at LHC and SSC energies respectively. We have chosen three different values for the top quark mass in order to illustrate the crosssection dependence (lower set of curves: mr= 100 (solid), 137 (dashed) and 200 (dotted) G e V / c 2 respectively). For comparison purposes, we have also computed cross-section estimations for the boson fusion mechanisms without associated heavy flavours (upper solid curve: WW-fusion, upper dashed curve: ZZ-fusion), which are rather straightforward to obtain. For increasing M n o , the amplitude containing the ti'H ° coupling becomes less important due to its 1/g dependence and with it the interference term becomes smaller (in absolute value) [ 19 ]. At small Mno, the ti-H ° amplitude takes over and a further decrease of the Higgs mass leads to a decreasing contribution from the interference term. In the intermediate region, that is at mt ~ M n o , destructive interference reaches its peak value. Apart from being larger at the SSC, the cross-sections fall less rapidly for increasing Higgs mass than at the LHC. Evidently, for a small top quark mass, the cross-section is dominated by the process containing the W W H ° coupling. Although we have argued that cancellations should occur naturally, it is quite striking to see that the magnitude of the interference term rapidly rises as a function of the top mass at a fixed Higgs mass. In fig. 3 we show this behaviour for M n o = 2 0 0 G e V / c 2, 318

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H° X o t , / s =

16TeV

(a)

£urojet

10"~

10"4

-5

lO

H° mass [GeV/c2~

10"1 pp ~

H° x a t . / s

= 40TeV

Eurojet

qqH~(W~) lO" I b I

10-3!

lO" 1000

H° mass [GeV/c ~1

Fig. 2. Higgsproduction cross-sectionsat the LHC (a) and SSC colliders (b) (v/s=16 GeV and x/s=40 TeV respectively) through boson-boson fusion without (top curves) and with (bottom curves) associatedtop quarks.

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References

10 "2

pp ~

t H°X at ~/s = 16TeV m. = 200 CeV/c: Eurojet

10 "-~ qb

-->

qtH*.

interference term

-

--

iiiiiii:

.

--

........

b

/

qb --~ qtH~

/; ,' ql~ ~.) qtH °, ttH° coupling only

0

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100

200

300

=lO0

500

Top quark mass [GeV/c 21

Fig. 3. Higgs production cross-section at the LHC with Mn0 = 200 GeV/c 2 as a function of m, The increasing importance of the till ° coupling leads to an increase of the cross-section at larger values ofrnt (the absolute value of the interference term is drawn ). v a r y i n g the t o p m a s s b e t w e e n 50 a n d 450 G e V / c 2. In c o n c l u s i o n , we f i n d o u r c a l c u l a t i o n s in perfect a g r e e m e n t w i t h Stirling a n d S u m m e r s a n d t h e r e f o r e agree w i t h t h e i r c o n c l u s i o n that this c h a n n e l is barely o f r e l e v a n c e at the n e x t g e n e r a t i o n o f h a d r o n colliders. T h e results o b t a i n e d by D i a z - C r u z a n d S a m p a y o are i n d e e d q u i t e different. T h e i r cross-sections are i n c r e a s i n g for an i n c r e a s i n g t o p q u a r k mass a n d are larger t h a n the c o n t r i b u t i o n f r o m the g r a p h w i t h t h e W W H ° alone. It t u r n s out that c h a n g i n g the sign o f t h e i n t e r f e r e n c e t e r m in o u r e x p r e s s i o n for the m a trix e l e m e n t s q u a r e d exactly r e p r o d u c e s t h e i r results. C o m p e n s a t i o n is n o t u n e x p e c t e d since, for sufficiently large t o p a n d Higgs mass, the two c o n t r i b u t ing F e y n m a n d i a g r a m s will e a c h give rise to e v e n t s p o p u l a t i n g o v e r l a p p i n g regions in phase space. M o r e o v e r , in o r d e r n o t to v i o l a t e unitarity, c o m p e n sation is b o u n d to occur.

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[ 17 ] C.H. Llewellyn Smith, in: Proc. 5th Hawaii Topical Conf. on Particle physics, eds. P.N. Dobson et al. (University of Hawaii Press, Honolulu, HI, 1973); R. Kleiss, in: Physics up to 200 TeV, ed. A. Zichichi (Plenum, New York, 1991 ). [18] J.F. Gunion, W.E. Haber and T. Wudka, Phys. Rev. D 43 (1991) 904.

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