Identifying the Higgs Boson in Electron--Photon Collisions

We analyze the production and detection of the Higgs boson in the next generation of linear $e^+e^-$ colliders operating in the $e\gamma$ mode. In particular, we study the production mechanism $e + \gamma \rightarrow e \gamma \gamma \rightarrow e + H$, where one photon is generated via the laser backscattering mechanism, while the other is radiated via the usual bremsstrahlung process. We show that this is the most important mechanism for Higgs boson production in a $500$ GeV $e\gamma$ collider for $M_H\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$>$}140$ GeV. We also study the signals and backgrounds for detection of the Higgs in the different decay channels, $b \bar b$, $W^+W^-$, and $ZZ$, and suggest kinematical cuts to improve the signature of an intermediate mass Higgs boson.

The most crucial missing element of the Standard Model is the Higgs boson. Its couplings with all other particles are predicted by the model and once measured can shed some light on the spontaneous symmetry breakdown mechanism. In particular, the one-loop Hγγ coupling receives contributions from all charged particles that acquire their masses from the Higgs mechanism, and the study of this coupling can provide us with fundamental information about the particle mass spectrum. In this work we analyze the capability of an eγ collider to produce and study the Higgs boson properties, in particular its coupling to photons.
An important feature of the next generation of linear e + e − colliders (NLC) is that they should also be able to operate in the eγ or γγ modes. The conversion of electrons into photons can occur via the laser backscattering mechanism [1]. In this case the energy and luminosity of the photon beam would reach almost the same values of the parent electron beam. This makes the NLC a very versatile machine which will be able to use energetic electrons and/or photons as initial states.
In the NLC operating in the e + e − mode the most promising mechanisms to produce the Standard Model Higgs are the Bjorken process, e + +e − → Z → Z +H, and the vector boson fusion mechanism, e + + e − → W + W − → ν +ν + H [2], where the Higgs boson coupling with W 's and Z's could be very well determined. However, it is virtually impossible to study the coupling of the Higgs to γγ pairs due to the small branching ratio of Higgs into a photon pair. Higher order electroweak processes for the Higgs boson production, such as e + + e − → V V H (V = W, Z) [3], could in principle give more information on the Higgs boson couplings, but unfortunately their total cross sections are rather small.
The Standard Model Higgs boson can also be produced at the NLC operating in the γγ mode, as suggested in Ref. [4]. This mode is particularly interesting since in principle it allows a detailed study of the coupling Hγγ. However, as it was pointed out in Ref. [5], resolved photon processes can impose a severe drawback for the Higgs detection in the bb channel. Another possibility of Higgs production is the associated production with the top quark through the process γγ → ttH [6], which is suited for the analyses of the ttH coupling.
However, for a 500 GeV collider the total cross section for this process is below 0.5 fb for M H > 60 GeV.
In this letter we concentrate on the possibility of identifying the Higgs boson with the NLC operating in eγ mode. We stress that this set up provides us with a rich source of γγ interactions when the hard backscattered photon interacts with photons radiated by the electrons in the other beam. This way the Higgs boson can be produced in the process which takes place via the Hγγ coupling. We show that for a 500 GeV collider, this is the most important mechanism for the production of a Higgs with M H > 140 GeV even when compared with the previously suggested [7,8] associated production γ + e → W + ν e + H.
We study the bb, W + W − , and ZZ signatures of the Higgs and compare it with the possible backgrounds coming from direct and resolved photon processes, and from double vector boson production in eγ collisions. We show how convenient kinematical cuts are able to improve in a significant way the signal over background ratio for the intermediate mass Higgs that decays mainly through the heavy quark channel.
The scattering of an energetic electron by a soft photon from a laser allows the transformation of an electron beam into a photon beam whose spectrum is [9] with where σ c is the Compton cross section, and ξ ≃ 4Eω 0 /m 2 , with m and E being the electron mass and energy. In our calculation we have chosen the laser energy, ω 0 , in order to maximize the backscattered photon energy without spoiling the luminosity through e + e − pair creation by the interaction between the laser and the backscattered photon. This can be accomplished by taking ξ = 2(1 + √ 2) ≃ 4.8. With this choice, the photon spectrum exhibits a peak close to its maximum which occurs at x max = ξ/(1 + ξ) ≃ 0.83.
Another source of photons is bremsstrahlung from the electrons in the other beam. The spectrum of bremsstrahlung photons can be described by the usual Weizsäcker-Williams In the narrow width approximation, the cross section for the process in Eq. 1 can be expressed in terms of the two photon distributions and the width Γ(H → γγ) as where τ H = M 2 H /s and √ s is the center of mass energy of the original e + e − collider. Since we are assuming that all the electron beam is converted into photons and we have performed the convolution with the photon distributions, the corresponding number of events will be given by It can lead to more than 100 Higgs events per year for a Higgs mass up to 320-400 GeV depending on the top quark mass, assuming a integrated luminosity L e + e − = 100 fb −1 .
The cross section for an specific Higgs decay channel is obtained in the narrow width approximation by the product of the production cross section (Eq. 4) and the corresponding decay branching ratio, which can be found elsewhere [2]. In Fig. 1.b we show the cross section for the processes e + γ → eγγ → e + H → ebb(V V * ), with V = W ± , Z. The Higgs boson signal is dominated by different channels depending on its mass, and therefore the possibility of detecting the Higgs strongly depends on the mass value.
The most promising signal over background ratio is attained when the Higgs boson decays into the ZZ channel, which is important for M H ∼ > 180 GeV. Unlike in the γγ mode of the collider [4] where this channel is free of irreducible background at tree level, in the eγ mode there is a possible source of background via the process e + γ → e + Z + Z, with the final electron going in the beam pipe. In Fig. 2 we compare the total cross section of the Higgs signal measured in fb with the invariant mass distribution (measured in fb/10 GeV) of the background [10]. In the computation of the background we assumed an angular size for the beam pipe of θ e < 5 • . From Fig. 2.a we see that for 500 GeV machine, and assuming an invariant mass resolution of the order of 20 GeV, the Higgs signal overcomes the background in almost all the M H range without need of any further cut. The signal to background ratio in this channel becomes better at higher center of mass energies as illustrated in Fig. 2.b.
In the case of the W + W − channel the situation becomes worse. The background from e+γ → e+W + +W − is large since it receives the main contribution from the effective photon process e + γ → eγγ → e + W + + W − , where, as in the Higgs signal, the electron escapes undetected. Since in the γγ center of mass frame the signal is isotropic while the background is forward-backward peaked [4], it is possible to improve the signal to background ratio by imposing a cut on the W scattering angle in that system. We chose | cos θ W | < 0.85. As seen in Fig For a lighter Higgs boson, M H < 150 GeV, we should rely on the bb decay channel. In this case there are large backgrounds coming from the direct photon process, γ + γ → b +b, and also from the once resolved photon ones, γ + γ(g) → b +b [5], where the photon interacts via its gluonic content. Moreover, there are also large reducible backgrounds due to the production of charmed quarks, which can fake b-quarks as they possess a production cross section which exceeds the b-pair background by up to one order of magnitude. Again we use the S-wave nature of the Higgs resonance to improve the signal to background ratio by requiring that the scattering angle of the b's (c's) with respect to the beam axis is large enough | cos θ| < 0.85 in the bb rest frame. Imposing this cut in all the following, we compare in Fig. 4.a the total cross section of the Higgs signal H → bb, measured in fb, with the invariant mass distributions (measured in fb/10 GeV) of the various backgrounds.
Since there is a considerable uncertainty regarding the gluon content of the photon, we used two different sets of gluon distribution functions inside the photon to characterize our lack of information: the parameterization by Drees and Grassie [11] (DG), which provides for a relatively soft gluon distribution, and the LAC3 parameterization of Ref. [12], which gives a considerably harder gluon distribution. tend to follow the initial backscattered photon. Resolved backgrounds, however, present a flat distribution since they receive two contributions which are kinematically separated [13]: in resolved processes where the bremsstrahlung photon is probed, the jets follow the initial backscattered photon and populate the positive rapidity region, while in those where laser backscattered photon is resolved the jets follow the direction of the bremsstrahlung photon and have negative values of (y 1 + y 2 ). As a consequence the resolved background can be reduced by a factor of 50% approximately by imposing that (y 1 + y 2 ) > 0. We should remark that this kind of kinematical cut would be worthless in γγ collisions when both photons come from the laser backscattering mechanism. In this latter case, both the signal and the resolved background are expected to have approximately the same behavior over all the rapidity range [5].
The final results for bb channel are shown in Fig. 5, where an invariant mass resolution of 20 GeV is assumed for the backgrounds (for a discussion on this point see Ref. [5]). A 90% efficiency for both b identification and c rejection would lead to a 3-6 σ effect for the Higgs boson mass in the range 75 < M H < 155 GeV, assuming an integrated luminosity of 100 fb −1 for the NLC with √ s = 500 GeV. In order to improve the significance level of the signal and its potential to study the coupling Hγγ, we can consider two possibilities: first we can reduce the direct background (and increase the signal) by polarizing both the laser backscattered photon and the electron [4]. Second, the hadronic calorimeter should be able to give a good coverage close to the beam pipe in order to detect the jet associated with the remnants of the resolved photon, allowing to veto the background coming from the gluonic content of the photon.
In conclusion, we demonstrate that the process e + γ → eγγ → e + H is able to yield a  (b) (y 1 +y 2 ) distribution in the laboratory frame for the bb pairs. The Higgs signal and the different backgrounds are shown for the invariant mass of 130 GeV for the bb pair, using the same cuts and notation as in (a).

FIG. 5.
Cross section for the Higgs signal and backgrounds (same notation as Fig. 4). For the backgrounds an invariant mass resolution m H ± 10 GeV is assumed. In all cases we require | cos θ| Q < 0.85 in the QQ rest frame and |y 1 + y 2 | > 0 in the laboratory frame.