Production of Z-Higgs boson pairs at photon linear colliders

Experiments at future linear e+e colliders, such as the next linear collider (NLC), will be able to investigate in detail the interactions of gauge bosons, fermions, and scalars. In particular, one of the prime targets is the study of the interactions of the Higgs boson, for which the pp mode of the collider seems especially suitable [1—3]. By using the old concept of Compton laser backscattering [4], it is feasible to obtain very energetic photons from an electron beam: The scattering of a laser with few eV against an electron beam can give rise to a scattered photon beam carrying almost all the parent electron energy with similar luminosity [5]. This mechanism can be used at the NLC [6] which has a projected center of mass energy of 500—1000 GeV with a yearly integrated luminosity around 10 fb . At the NLC operating in the pq mode, Higgs bosons can be produced via one-loop triangle diagrams [1], or in association with a W-boson pair (pp m W+W H) [2] or a top-quark pair (pp ~ ttH) [3]. Our aim in this note is to study the associated production of Higgs and Z bosons in pp collisions, pp m ZH, which occurs at the one-loop level within the scope of

Experiments at future linear e+e colliders, such as the next linear collider (NLC), will be able to investi- gate in detail the interactions of gauge bosons, fermions, and scalars.In particular, one of the prime targets is the study of the interactions of the Higgs boson, for which the pp mode of the collider seems especially suitable [1 -3].
By using the old concept of Compton laser backscatter- ing [4], it is feasible to obtain very energetic photons from an electron beam: The scattering of a laser with few eV against an electron beam can give rise to a scattered photon beam carrying almost all the parent electron energy with similar luminosity [5].This mechanism can be used at the NLC [6] which has a projected center of mass en- ergy of 500 -1000 GeV with a yearly integrated luminos- ity around 10 fb .At the NLC operating in the pq mode, Higgs bosons can be produced via one-loop trian- gle diagrams [1], or in association with a W-boson pair (pp m W+W H) [2] or a top-quark pair (pp ~ttH) [3].
Our aim in this note is to study the associated produc- tion of Higgs and Z bosons in pp collisions, pp m ZH, which occurs at the one-loop level within the scope of  standard model.There are several other interesting pro- cesses that take place at photon colliders at the one-loop level, such as photon-photon scattering [7], the produc- tion of Z pairs [8], pZ pairs [9], and Higgs boson pairs [10].Our calculation complements the literature for the evaluation of one-loop processes in pp collisions.
In the standard model, the process pp m ZH occurs, u priori, via lepton, quark, and R' boson loops.Neverthe- less, because of the C-conserving couplings of the bosonic sector, the contribution of the W loops vanishes since the initial (final) state is C even (odd).Therefore this reac- tion takes place only through the fermionic triangle and box one-loop diagrams involving the axial couplings of the Z.This implies that the helicity amplitude (T~~) for this process can be readily obtained &om the known result (T e) for the reaction ggi ZH [11,12] through the replacement n, T~ee""(s,t, u) b : 2N, Qfcr, T"~"~(s, t, u), where ltl = 3 is the number of colors, and Qf is the charge of the fermion running in the loop.Ai and A2 are the helicities of the photons while A3 is the helicity of the Z boson.In our calculations we used the expression given in Ref. [11] for the amplitude Tee.
In the helicity basis, there are 12 possible helicity con- Ggurations; however, due to CI' invariance and Bose symmetry, only five of them give rise to independent con- tributions.Denoting by op, p, p, the contribution to the In Fig. 1, we plot the five independent contributions as a function of the center-of-mass energy of the pp sys- tem.The triangle loops contribute only to the J, = 0 amplitudes (+ + 0 and --0), while the box diagrams contribute to all of them.In spite of the interference between the triangle and the box contributions being de-  structive [ll], the largest polarized cross section comes &om the + + 0 helicity configuration.
Figure 2 shows the behavior of the unpolarized elemen- tary cross section, IrQr + N, I"pQ"+N, Is Qs, --0, where If is the weak isospin of the fermion f Therefo.re the cross section increases as the mass splitting inside a generation increases.In consequence, as we could expect, for a fixed value of the Higgs boson mass, the cross section at high energies is larger for a heavier top quark.More- over, the elementary cross section exhibits peaks around the threshold for the production of the fermionsthat is, for the center-of-mass energies around twice the fermion masses.
In order to evaluate the total cross section for the ZH production in a pp collider, we must fold the photon lu- minosity with the subprocess elementary cross section, 1.e. ) for the subprocess pp ~ZH as a function of the center- of-mass energy of the pp system for two difFerent values of the top quark mass.Since the Z boson couples axi- ally with the fermions in the loop, the contribution of a degenerated family to this process vanishes.In fact, the invariant amplitude in this limit is proportional to We assumed that the backscattered photon beam is not polarized and employed the spectrum of backscattered photons Fr, (z, y) given in Ref. [5] with z = 4.8 in order to maximize the available energy of the photons and to avoid unwanted e+e pair production, which leads to a reduction of the pp luminosity.
In Fig. 3 we plot the results for the total cross section GeV.
FIG. 3. Total cross section cr(p7 ~ZH) as a function of the Higgs boson mass (M~) for Js = 500 and 1000 GeV and mt~~--140 and 200 GeV (four lower curves).For the sake of comparison we also plotted the cross section of the process 77 ~H for ~s = 500 GeV and 1 TeV (upper curves) at i/s = 500 and 1000 GeV.From this figure it is clear that the cross section grows as the value of mt ~and/or i/s increases.This behavior can be easily related to the subprocess elementary cross section given in Fig. 2 and to the available phase space for ZH production.There- fore, within the &amework of the standard model, this process will give rise only to very few events for a yearly integrated luminosity of 10 fb, even at very high ener- gies.For the sake of comparison, we also plot the cross section for the lower order process pp -+ H [1] which is a factor 10 -1000 times larger than the cross section for the ZH production.In principle, the process ZH could be used as a possible signature for invisibly decaying Higgs bosons in pp collisions [13] since in this mode the pp m H production mechanism would lead to no visible signature.However, because of the low event rate, it is not possi- ble to look for invisibly decaying Higgs bosons since the signal will be immersed in a large pp ~ZZ background, whose cross section [8] is about 300 (1000) times larger than the ZH one, for mH = mz for ~s = 500 GeV ( 1TeV) and mt & --140 GeV.The larger size of the ZZ cross section is due to the contribution &om R' loops and, as expected, the fermion-loop contributions to the ZZ and ZH processes are of the same order of magnitude (see the dotted curve in Fig. 3(b) of the first reference in [8]) In order to access the effect of new charged particles that might exist, we also analyzed this process taking into account a fourth sequential generation of fermions.For most values of the allowed parameter space, this rnodification leads to a slight increase in the total cross section that is of the order of 10%.This is due to the fact that the elementary cross section is significantly modified only for the center-of-mass energies above the threshold for «he production of the new fermions and the limited available phase space in this energy regime.An interesting scenario that might increase dramatically the event rate for the ZH production is the enlargement of the Higgs sector, e.g. , two doublet models.In this case, there will be contributions &om bosonic TV loops for the associate production of a Z and a pseudoscalar Higgs boson and it is expected, as in the Z pair production [8], that this will dominate over the fermionic one.

(
+s) is the center-of-mass energy of the e+e

FIG. 1 .
FIG. 1. Contributions to the elementary cross section o'(pp ~ZH) from each helicity amplitude as a function of the center-of-mass energy E» assuming M~--80 and 140 O.J.P.E. is very grateful to the Institute of Elemen- tary Particle Physics Research of the Physics Department, University of Wisconsin -Madison, where part of this work was done, for its kind hospitality.This work was supported by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, by the U.S. Department of En- ergy under contract No. DE-AC02-76ER00881, by the Texas National Research Laboratory Commission un- der Grant No. RGFY93-221, by the National Science Foundation under Contract INT 916182, by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq/Brazil), and by Fundagao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP/Brazil).