HIGGS BOSON PRODUCTION AT LARGE TRANSVERSE MOMENTUM IN QCD 4. Stanford Linear Accelerator Center Stanford University, Stanford, California

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1 SLAC-PUB-2197 COO September 1978 (T/E) HIGGS BOSON PRODUCTION AT LARGE TRANSVERSE MOMENTUM IN QCD 4 Risto Raitio* Stanford Linear Accelerator Center Stanford University, Stanford, California and Research Institute for Theoretical Physics University of Helsinki, Helsinki, Finland Walter W. Wadat Stanford Linear Accelerator Center Stanford University, Stanford, California and Department of Physics The Ohio State University, Columbus, Ohio ABSTRACT We estimate the Higgs boson production cross sections duldy and dcr/dydqg in p(p3p-collisions by calculating the subprocess gluon + gluon - Higgs boson + heavy quark-anti- quark pair. (To be submitted to Phys. Rev. D.) *Supported by the Department of Energy under Contract No. EY-76-C and the Academy of Finland. tsupported in part by the Department of Energy under Contract No. EY-76-c *000.

2 The problem of Higgs boson (H) production has been studied earlier. 5 Because of the lower bounds on the mass of H that have been proposed, it the possibility of its production and detection would be restricted to energetic e+e- annihilation ~4 and pp collisions of several hundred GeV3 of the next generation proton storage ring facilities. In Ref.3 the two-gluon analog diagram of the Drell-Yan mechanism (Fig.l(a)) arising from the fusion of two-gluons into H through the quark triangle diagram is calculated. While this subprocess obviously gives relatively large cross sections, it only con- tributes at small transverse nwmenta (qt) of the produced H, say (qt)w300 MeV, in which kinematic region the background problems are most severe. Therefore, we find it desirable to invest-lgate also other processes that might give measur- able cross sections in the 14q T ~~10 GeV region. The process that we have investi- gated in this work is the external and internal bremsstrahlung production of H off heavy quark-antiquark pair from two-gluons in pp collisions. The re- levant diagrams are given in Fig.2. The resulting cross section is of order a2 S same as that of Ref.3 (Fig.l(a)). To this order there are other dia- grams that can lead to non-vanishing qt, such as that in Fig.l(b). However, because of the small heavy quark content of the nucleon, these are expected to be dominated by the process under consideration (Fig.2). In this note we cal- culate the differential cross sections do/dy and do/dydqg at y=o, where y referes to-the rapidity of H, for p(c) +p-hhanything arising from the sub- process gluon+gluon-h+heavy quark pair. We assume the simplest spontaneously broken gauge theory6 involving one physical H. Its coupling constant to quarks is given by f-4 $9 %I = mq 2 GF' (1)

3 3 I where mq is the quark mass and GF the Fermi coupling constant. The fact that gh is proportional to m Q makes it that its couplings only to heavy quarks c, b, and t are appreciable. - The amplitudes corresponding to the diagrams of Fig.2 for ga(pl) +gb(p2) -H(q) +Q(k$ +a(k2> is of the fo- with (2) I? = ab T T A" abl + TbTaA;"+ TaTbAzV + TbTaAtv (3) + TaTbA;;" + TbTaAgV + ifabctc AFV + AIV >, where g is the gauge coupling constant of QGD, a and b refer to the octet of gluons, Ta = *ha with ha the Gell-Mann matrices, and f abc the structure constants in [Ta,Tbl = ifabctc* It is straightforward to construct the amplitudes AyV...AiV in accordance with the diagrams in Fig.2. These are given in the appendix. Assuming on-shell gluons in the protons, the square of the amplitude (2) should be summed over only the transverse polarizations of the gluons. Contrary to QED in which photon is always compled to conserved charged current, because of the diagrams (7) and (8) in Fig.2 in which self-couplings of gluons take place, the gauge-invariance conditions familiar in QED, p TPv = p2v?al = 0, 1~ ab in fact do not occur. As was pointed out previously7, this has the consequence that the condition in the Feynman gauge,& h hh E = -g would introduce spurious contribu- PV WV tions coming from the longitudinal polarizations. A method to circumvent the com- plications resulting from this was proposed previously8, according to which the terms in APv and APv proportional to py and pl are to be dropped, since the difference7between8til of (3) and?" ab thus obtained is proportional to pyep(pl) "

4 4 and p's (p ) 2v 2 and the amplitude is unchanged for the physical polarizations. It is then found p p" = p2v!?ib = 1~ ab 0, allowing the usage of the Feynman gauge for the phyacal gluons. Needless to say, the square of the amplitude (2) should be averaged over the physical polarizations and the octet degrees of freedom of 9,lO the gluons. The coupling constantols(=g2/4n) of QCD should depend upon Q2, where Q is an appropriate mass scale of the system. It may be approximated by8 as(q2) = 4ll 9!h(Q2/A2> ' (4) where A = 500 MeV. If one takes Q2 to be equal to the mass square of the three particles produced, Crs(Q2) is found to be in the range for Q2= GeV2. Because of the considerable uncertainty in assigning the value for Q2 in (4) in the present situation, we have adopted the value for as commonly used in QCD cal- 11 culations, i.e. as*0.3. The cross section for p+p -H+anything is now obtained by convoluting the differential cross section for g+g -H+Q+~ over the gluon distribution functions according to da = s dxldx2 F(xl) F(x2) da(xlp1,x2p2,kl,k2,4), where pl and p2 are the c.m. momenta of the protons, and F(x) the gluon dis- tribution function which is taken to be F(x) =,tl-x)5, X (6)

5 5 I corresponding to (x f-n) = 0.5. The resulting h cross sections da/dy(at y=o) are shown in Fig.3 as functions of /.s at two Higgs boson mass values % = 5 and 10 GeV. Contributions from three quarks c, b, and t with masses 1.5, 5, and 15 GeV, respectively, are summed. Of these, c and b quarks contributions are found to be approximately equal, while that of the heaviest quark is roughly 5% of the total. Thus, additional heavier quarks, if exist, should increase the cross section only slightly. The differential cross section do/dyqg (at y=o) for % = 10 GeV and &=400 GeV is shown in Fig.4. A comparison of da/dy obtained with that arising from the triangle diagram3 shows that the present cross section for H production arising from the bremsstrahlung offheavy quarks is smaller by one or two orders of manitude at all Js. This disadvantage may perhaps be compensated by the relatively large qt, as seen in Fig.4. As has been emphasized by the previous authors l-4, the most serious problem in the search of the Higgs boson is the experimental signal for its identifiaation. Its decays into pairs of leptons, hadrons, and photons have been discussed previously. l-4 An interesting situation arises if mh 211 GeV. It is then expected that the Higgs boson decays predominantly into a pair of b6 jets. For an appreciable qt, say qtb5 GeV/c, these b6 jets will be accompanied by a pair of heavy quark-antiquark jets with corresponding transverse momenta. The structure of these events in momentum space is non-coplanar. If the meson pairs from the decay containing heavy quarks, i.e. bii, b3, etc., are stable, then the signal for the Higgs boson is expected to be relatively clean.

6 6 Finally, we would like to mention that our cross section valuesnare - sensitive to the largely unknown gluon structure function. These un- _ certainties are typically factors of two (squared in this case). - In sunxnary, it seems to us that the production of the Higgs particle in multihundred GeV proton rings at large transverse momenta may possibly provide another avenue for its search. Acknowledgements We thank S. J. Brodsky, J. Ellis, P. H. Frampton, and E. Takasugi for useful discussions. We are grateful to Professor S. D. Drell for the warm hospitality extended to us at the Stanford Linear Accelerator Center Theory Group where this work was carried out.

7 7 APPENDIX Amplitudes AyV, AgV, and,ag' are given below. The corresponding amplitudes in tiich2he two gluons are crossed, A ClV AclV, and Ai', respectively, are obtained 2' 4 by the simultaneous interchanges p,*v and pl*p2. AVV = C(kl) 1 2Wl) +G 1$" -$2yv + 2k; 2(p2k2) V(k2) ACIV = C(k1) 3 2ky-Tfil 4-2m 2(Plkl) YV Uqk2) +g wq APV = G(kl) 5 2ky - hl $2~v - 2k; 2(plkl) 2(p2k2) W2) AC"" 7 +A"= ' 8 2(PlP2) C (-Pl+P2)pgtiV + (2Pl+P2)v gpp- (Pl+2P2)pgvq l u(kl) yp - yp W2).

8 8 REFERENCES 1. J. Ellis, M. K. Gaillard, and D. V. Nanopoulos, Nucl. Phys. B106, 292 (1976), and references therein. 2;" F. Wilczek, Phys. Rev. Lett. 2, 1304 (1977). 3. H. M. Georgi, S. L. Glashow, M. E. Machacek, and D. V. Nanopoulos, Phys. Rev. Lett. 40, 692 (1978). 4. P. H. Frampton and W. W. Wada, Phys. Rev. (to be published). 5. S. Weinberg, Phys. Rev. Lett. 36, 296 (1976); A. D. Linde, JETP Lett. 2, 296 (1976), and Phys. Lett. 7OB, 306 (1977); P. H. Frampton, Phys. Rev. Lett. 37, 1378 (1976). 6. S. Weinberg, Phys. Rev. Lett. l-9, 1264 (1967); A. Salam, in Elementary Particle Physics, ed. N. Svartholm (Almquist and Wiksell, Stockholm, 1968), p R. Cutler and D. Sivers, Phys. Rev. Dz, 196 (1978). 8. H. M. Georgi, S. L. Glashow, M. E. Machacek, and D. V. Nanopoulous "Charmed Particles from Two-Gluon Annihilation in Proton-Proton Collisions,11 Harvard -- preprint (1978). 9. The trace of the squared matrix element was obtained by the computer pro- gram REDUCE. The xl9 x2, and phase space integrations were carried out by the Monte Carol program SHEP. 10. We have approximated the numerators in the square of the sum of the amplitudes by setting quark mass m Q 10. We checked the case for da/dy (y=o) using =5 GeV at /s=400 GeV. The result was 27% increase of cross section commq pared to the m =0 case. For other quark masses considered the effect upon Q do/dy was smaller G. Altarelli, G. Parisi and R. Petronzio, Phys. Lett. z, 356 (1978); H. Fritzsch and P. Minkowski, Phys. Lett. m, 80 (1978); K. Kajantie and R. Raitio, Nucl. Phys. B139, 72 (1978).

9 I 9 1. FIGURE CAPTIONS 8 Diagrams of order asgf for H production in hadron collisons. 2. >Diagrams for gluon+gluon -H+heavy quark-antiquark pair. 3. The cross section do/dy at y= 0 in nb for pp-h+anything as a function of /s with Higgs masses %=5 and 10 GeV, and as=0.3. In dashed line we show for %=lo GeV the different quark contributions with the quark masses 1.5, 5 and 15 GeV indicated. 4. The differential cross section do/dydqc in nb/gev2 for pp-hkanything at Js=400 GeV with %=lo GeV and as=0.3. The various quark contributions are shown in-dashed line with quark masses indicated.

10 I a -- W 9-78 (b) Fig. I

11 I. P+--k2 2. pq \ \ XE L- r--<, ~3 Fig. 2

12 I I I s 6 (GeV) Fig. 3

13 \ mq = I IO qt (GeV) Fig. 4