γ, Z, W γ, Z, W q, q q, q

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1 DESY ISSN July 1995 HIGGS BOSON PRODUCTION AND EAK BOSON STRUCTURE ojciech S LOMI NSKI and Jerzy SZED Institute of Comuter Science, Jagellonian University, Reymonta 4, Krakow, Poland Abstract The inuence of the QCD structure of the weak bosons on the Higgs boson roduction in e- scattering is studied. The energy and Higgs boson mass deendence of the cross-section, following from the new contributions, is calculated. ork suorted by the Polish State Committee for Scientic Research (grant No. PO3B ) and the Volkswagen-Stiftung.

2 1 Introduction In our recent aers [1, ] we have introduced the basic roerties of the and Z boson structure functions. In analogy to the hoton case [3] it has been shown there, how the quark and gluon content of the intermediate bosons aears due to the QCD cascade. The corresonding evolution equations have been solved in the asymtotic regime with the solutions develoing logarithmic Q growth of the quark and gluon densities. The form of weak coulings forces these densities to deend strongly on sin and avour. It is extremely interesting where the QCD structure of weak intermediate bosons may be observed exerimentally. In the systematic investigation of ossible rocesses we start with the Higgs boson roduction. The question ut forward in this case is to what extent the inclusion of the 'resolved' and Z can modify the redictions known before. e concentrate on the Higgs boson roduction in e- scattering, quoting the e + e scattering, where one should not exect large contributions, for comleteness. The aer is organized as follows. In Section we recall the formalism introduced before to study the QCD structure of gauge bosons and quote the main results concerning and Z, comared to the hoton case. Section 3 resents the calculation of the cross-section for the Higgs boson roduction in e- scattering at selected energies. The results are comared with the dominant roduction channel [4, 5](-fusion) and earlier calculation of the 'resolved' hoton contribution [6]. Summary, comments and conclusions are given in Section 4. QCD structure of and Z bosons In the standard model weak intermediate bosons are elementary (oint-like) articles. Nevertheless, when observed by a very high Q article, they can reveal QCD structure by collinear quark-gluon Bremsstrahlung. In this sense they become \comosite". The evolution equation for unolarized arton A density, f B A (x; t), inside a comosite weak intermediate boson B reads df B A (x; t) dt = X B P AB (x; t) f B B (x; t) ; (1) where t = ln(q =Q 0) and the scale Q 0, which deends on the articular rocess, will be discussed later. P AB (x; t) are slitting functions and the convolution is dened as (P f)(x) Z dx1 dx P (x1) f(x) (x x1x) : () For weak bosons the indices A; B go over quarks, antiquarks, gluons and oint-like, and Z. In the following we will consider the leading-log QCD and 1-st order electroweak case. Denoting weak intermediate bosons by uer case letters and QCD artons by lower case ones, we have f AB (x; t) = AB (1 x) ; (3) P ib (x; t) em P ib(x) ; (4) P ik (x; t) s(t) P ik(x) : (5) 1

3 Substituting this into Eq.(1) we arrive at the following non-homogeneous evolution equations for the QCD content of a weak intermediate boson: df B i (x; t) dt = em P B i (x)+ s(t) X k P ik (x) f B k (x; t) (6). In the lowest s order the slitting functions of the longitudinal and Z bosons vanish and the transverse ones read PqZ? (x) = P qz? (x) =z q P d? (x) = Pu+? (x) = 1 sin s(x) ; (8) with s(x) =[x +(1 x) ]=. The QCD slitting functions are taken in the standard form [7]. In the leading-log aroximation with s(t) s(t) = s(x); (7) bt ; (9) (b =11= nf=3 for nf avours) the t deendence of the equations (6) can be factorized out f B k (x; t) ' em leaving integral equations for the x deendence ~f B i (x) = P B i (x)+ 1 b X k=q;q;g ~f B k (x)t (10) P ik (x) ~ f B k (x) ; (11) Numerical solutions to the above equations can be found in Ref. []. They show in general that, aart from the t-deendent factor which at sub-asymtotic momentum transfers might be dierent (see discussion in the next Section), the quark and gluon structure of the weak bosons is reacher than that of the hoton. In the above review we have summed over the arton and weak boson olarizations (leaving out the longitudinal bosons which do not contribute in leading-log aroximation). The same considerations can be reeated keeing the arton and boson olarizations xed [8]. In fact, due to the articular form of weak coulings, we shall use in the following calculations artonic densities of given olarization inside olarized and Z bosons. 3 Higgs roduction in e- scattering The dominant mechanism of the Higgs boson roduction in electron{roton scattering is the - and Z-Z fusion (see Fig. 1a) [4, 5]. The new diagrams, which involve gauge boson structure, are shown in Fig. 1b{c. The case with the 'resolved' hoton has been already studied some time ago [6]. Here we include in the calculation the and Z bosons. The aroximations made in the following considerations require a word of warning. First, we will be using the equivalent boson aroximation, known since long for the hoton [9], and introduced in Ref. [10] for the and Z. In the case of massive weak bosons, out

4 e γ, Z, H γ, Z, a) e γ, Z, e γ, Z, G H q, q H G q, q b) c) Figure 1: Diagrams contributing to the Higgs boson roduction in e- scattering: a) dominant - fusion; b) gluonic art of the electroweak boson structure; c) quark art of the electroweak boson structure. of the three ossible olarization states only the transverse degrees of freedom develo the logarithmic factor, characteristic of hoton emission. The density of transversely olarized gauge bosons inside unolarized electron f e B(x) / 1 x ln Q max + M B Q min + M B with x the boson momentum fraction, M B the gauge boson mass and Q the negative momentum squared of the emitted gauge boson. One sees that whereas in the hoton case the logarithm is scaled by the electron mass, coming from Q min, in the weak sector it is the mass M B which sets u the scale (exlicit forms used in the considered rocesses are given in the next Section). Consequently, due to the large weak boson mass, the above logarithmic factor is resonsible at resently available energies for the fact that there is more 'equivalent' hotons in the electron than 's and Z's. The accuracy of the 3 (1)

5 equivalent boson aroximation has been tested in the rocesses where exact calculation is also ossible [5]. For examle the ratio of the aroximate to exact results in the Higgs roduction in e + e scattering varies between a factor of two and few ercent in the energy range between 500 GeV and 50 TeV and aroaches 1 with increasing Higgs boson mass. Taking into account the above remarks one should treat the numerical results at energies corresonding to the existing accelerators only as estimates. Another roblem is the Z- interference. In general the neutral current exchange contains a coherent mixture of the Z and the hoton. However in the robabilistic aroach used here these ossible interference terms are neglected. The next aroximation concerns the quark masses. In the QCD evolution equation all masses are neglected, they are used solely as thresholds, oening new avour evolution when increasing Q. A more delicate treatment requires the b quark threshold in the structure evolution. In rincile it aears already above the b quark mass due to the bu roduction. However only after the channel b t oens ( Q > 180 GeV), the Kobayashi{Maskawa matrix elements squared add u to 1 and do not suress the b quark roduction. In our calculation we neglect this suression which otentially exists in the intermediate Higgs boson mass range. Finally the scale Q 0 of the QCD evolution requires some attention. In the leading-log aroximation, which we are using, its value for Q Q 0 is formally irrelevant (changing Q0 gives next-to-leading-log corrections). At nite Q the choice deends on the hysical situation in the rocess. In e- scattering we are interested in the electroweak bosons, 'as few o shell as ossible' which ractically means the mass negative and close to zero. Therefore, as concerns the masses, the dierence between hotons and weak bosons vanishes and in all cases we should take Q 0 = QCD. The contribution to the total cross-section for the rocess e =e HX coming from the 'resolved' bosons (Fig. 1 b,c) reads B = X i;j;; Z 1 dx x f e B (x) Z 1 dy =x y f B i (y)f P j xy ^ ij (13) where = M H =s with M H being the Higgs boson mass and s the total c.m. energy squared. The function f e B is the boson B (of olarization ) density inside electron, f B i is the quark/antiquark/gluon (of olarization ) density inside the boson B (of olarization ) and fj P the antiquark/quark/gluon (of olarization ) density inside the roton. The sum extends over artons (i; j = q; q; G), their olarization and the boson olarization. The olarization{indeendent artonic cross-section ^ GG = 144 s jnj G FM H (14) s for gluon{gluon (Fig. 1b) and ^ qq = GFm q 3 s for quark{antiquark annihilation (Fig.1c). Here GF is the Fermi couling, m q the quark mass and N a function of the quark and Higgs boson masses [11]. The equivalent boson densities deend on the exchanged boson and its olarization: f e (x) = 4 w + w (1 x) 1 x ln xs + M M (15) ; (16) 4

6 ++Z Z ++Z Z [b] 10 5 s = 314 GeV [b] 10 3 s =1:6TeV MH [GeV] MH [GeV] Figure : Contribution from the 'resolved' electroweak bosons to the cross-section for the Higgs boson roduction in e- scattering at: a) s = 314 GeV and b) s =1:6 TeV as function of the Higgs boson mass. f e Z (x) = 4 f e (x) = 4 z + z (1 x) 1 1+(1 x) 1 x x ln xs + M Z M Z ln (1 x)s xme ; (17) ; (18) where 1 w+ = sin ; w =0;z+= tan 1 1 sin ;z = tan (19) and me is the electron mass. The arton densities f B i fulll several relations [8], for examle in the case of : f d+ = f + u ; (0) f d = f + u+ ; (1) f + d+ = f + d+ = f d = f u = f u = f + u+ ; () f + d = f + d+ = f d + = f u+ = f u+ = f + u ; (3) f + G = f G+ ; (4) f + G+ = f G : (5) In the examles shown below we use their exlicit asymtotic form following from the numerical solutions of the Eqs.(11). Only in the case of the hoton we are able to see whether the asymtotic solutions lead to dierent results than the more realistic arametrisations 5

7 [b] 10 5 quarks + gluons quarks gluons 10 6 s = 314 GeV MH [GeV] Figure 3: The 'resolved' contribution to the cross-section for the Higgs boson roduction in e- scattering at s = 314 GeV as function of the Higgs mass. The gluonic and quark arts lotted searately. of its structure. e have checked that the arametrisation of Ref.[1] (LAC3) gives the cross-section for the e- Higgs boson roduction u to 30% larger in the considered energy and Higgs boson mass range. The arton densities inside the roton fi P (x) are taken from the arametrisation of Ref. [13] (MRS3). The results for scattering energies s = 314 and 1600 GeV are shown in Figs. and 3. One sees that the 'resolved' contribution is about a factor of 4 smaller than that of the 'resolved' at lower energies s = 314 GeV and aroaches one half at s = 1:6 TeV (Fig.). The Z contribution is the smallest for all considered energies and Higgs boson masses. In all cases the quark{antiquark diagram (Fig. 1c) is larger than the gluonic one (Fig. 1b), mainly due to resence of the b quark (Fig 3.). One should kee in mind that the dominant term in the Higgs roduction cross-section, the - fusion (Fig. 1a) [4, 5] exceeds the 'resolved' boson contribution by at least an order of magnitude. The conclusion is rather obvious: the QCD structure of the gauge bosons, used in e- scattering, does not hel in the hunt for the Higgs boson. 4 Summary In the aer we have considered the inuence of the QCD structure of the electroweak gauge bosons on the e- roduction of the Higgs boson. e have found that using the asymtotic 6

8 form of the 'resolved' and Z, the contribution to the cross-section of the structure is of the same order as that of the hoton, the Z term being slightly smaller. In general however the considered new diagrams cannot comete with the dominant channel i.e. the - fusion. ehave also checked the Higgs boson roduction via 'resolved' bosons in e + e + scattering. As exected, the cross-section is suressed additionally, as comared to the - and Z-Z fusion, by a factor of which multilies the arton densities and consequently is negligible. One general lesson follows from the above studies. The structure function contributes to the considered rocesses aroximately with the same strength as the structure of the hoton. This means that one should look for its aearance in the reactions where the 'resolved' hoton is known to dominate. 5 Acknowledgments This work has been erformed during our visit to DESY, Hamburg. e would like to thank the DESY Theory Grou for hositality and the Volkswagen Foundation for nancial suort. References [1]. S lominski and J. Szwed, Phys. Lett. B 33 (1994) 47.. S lominski and J. Szwed, in High Energy Sin Physics, Proc. of X Int. Sym. on high Energy Sin Physics, Nagoya, Jaan, 199; ed. T. Hasegawa et al. (Universal Academy, Tokyo, 1993); []. S lominski and J. Szwed, Phys. Rev. D5 (1995). [3] E. itten, Nucl. Phys. B10, 189 (1977); C.H. Llewellyn Smith, Phys. Lett. 79B, 83 (1978); R.J. Deitt et al., Phys. Rev. D19, 046 (1979); T.F. alsh and P. Zerwas, Phys. Lett. 36 B (1973) 195; R.L. Kingsley, Nucl. Phys. B 60 (1973) 45. [4] Z. Hioki et al., Progr. Theor. Phys 69 (1983) 1484; D.A. Dicus and S.D. illenbrock, Phys. Rev. D 3 (1985) 164. [5] G. Altarelli, B. Mele and F. Pitolli, Nucl. Phys. B 87 (1987) 05. [6]. S lominski and J. Szwed, Acta Physica Polonica B (1991) 859. [7] G. Altarelli and G. Parisi, Nucl. Phys. B16 (1977) 98. [8]. S lominski and J. Szwed, unublished. [9] C. eizsacker and E.J. illiams, Z. Phys. 88, ). [10] G.L. Kane,.. Reko and.b. Rolnick, Phys. Lett., 148B, 367 (1984). [11] R.N. Cahn and S. Dawson, Phys. Lett. 136 B (1984) 196. [1] H. Abramowicz, K. Charchula and A. Levy, Phys. Lett. B 69 (1991) 458. [13] A.D. Martin,.J. Stirling and R.G. Roberts, Phys. Rev. D