Doubly charged Higgs from e–γ scattering in the 3-3-1 Model

Abstract

We studied the production and signatures of doubly charged Higgs bosons in the process γe ⁻→H ⁻⁻ E ⁺, where E ⁺ is a heavy lepton, at the e ⁻ e ⁺ International Linear Collider (ILC) and CERN Linear Collider (CLIC). The intermediate photons are given by the Weizsäcker–Williams and laser-backscattering distributions. We found that significant signatures are obtained by bremsstrahlung and backward Compton scattering of laser. A clear signal can be obtained for doubly charged Higgs bosons, doubly charged gauge bosons and heavy leptons.

Appendix

The spectrum of bremsstrahlung photons can be described by the well-known Weizsäcker–Willians distribution [20, 21]

$$f_{\gamma/e}^{WW} (x) = \frac{\alpha}{2\pi} \frac{1+ (1- x)^{2}}{x} \ln \frac{s}{4 m_{e}^{2}} , $$

where x is the longitudinal momentum fraction of the electron carried off by the photon, s is the center-of-mass energy of the e ⁻ e ⁺ pair and m _e is the electron mass. This spectrum is peaked at small x, i.e. most of its photons are soft.

Hard photons can be obtained by laser-backscattering, which converts an e beam into a γ one, that is, the scattering of an energetic electron by a soft photon from a laser allows the transformation of an electron beam into a photon beam. Here the intense photon beams is generated by backward Compton scattering of soft photons from a laser of a few eV energy. The energy spectrum of the backscattered laser photons is [22]

where σ _c is the total Compton cross section. For the photons going in the direction of the initial electron, the fraction x represents the ratio between the scattered photon and the initial electron energy (x=ω/E). In writing the last equation, we defined

$$D(\xi) = \biggl(1- \frac{4}{\xi} -\frac{8}{\xi^{2}} \biggr) \ln(1+ \xi) + \frac{1}{2} +\frac{8}{\xi} -\frac{1}{2(1+ \xi)^{2}} , $$

with

$$\xi\equiv\frac{4E \omega_{0}}{m^{2}} \cos^{2} \frac{\alpha_{0}}{2} \simeq \frac{2 \sqrt{s} \omega_{0}}{m^{2}} . $$

m and E are the electron mass and energy, respectively, ω ₀ is the laser photon energy, and (α ₀∝0) is the electron–laser collision angle. It is easy to verify that the maximum value possible of x in this process is

$$x_m = \frac{\omega_m}{E} = \frac{\xi}{1+\xi} . $$

From the energy spectrum of the backscattered laser photons we can see that the fraction of photons with energy close to the maximum value grows with E and ω ₀. Usually, the choice of ω ₀ is such that it is not possible for the backscattered photon to interact with the laser and create e ⁻+e ⁺ pairs, otherwise the conversion of electrons to photons would be dramatically reduced. In our numerical calculations, we assumed ω ₀≃1.26 eV, which is below the threshold of e ⁻+e ⁺ pair creation (ω _m ω ₀<m ²). Thus for the ILC beams ($\sqrt{s} = 1000~\mbox{GeV}$), we have ξ≃9.7, D(ξ)≃2.5, and x _m ≃0.9. Therefore the laser-backscattering option offers the prospect of intense beams of real photons with an energy up to about 90 % of the e ^± beam.