Photo-production of the Higgs boson at the LHeC

In this paper, we study the photo-production of Higgs boson at the LHeC. The process can be used as a complementary precision measurement for Higgs to di-photon partial decay width $\Gamma({h\to\gamma\gamma})$, and it has a clean final state without additional colored particles in the central rapidity region other than the decay products of the Higgs. However, there are some non-photon-fusion processes with final states of this feature, for example, Higgs gluon fusion production from $\gamma g$ scattering. These processes may be indistinguishable from and thus contaminate the photo-production in the detector. We compute the scattering amplitudes for all these processes and estimate their cross sections through Monte Carlo phase space integration. Different photon-PDF sets lead to rather different photo-production cross sections, while give very close results for contaminating processes. We also study the phenomenology of the photo-production at the LHeC via various Higgs decay channels. The signal significance in the standard model can be close to or over $2\sigma$ for $E_{e}=60~\text{GeV}$ or $E_{e}=120~\text{GeV}$ respectively. However, the photo-production and other contaminating processes are hard to distinguish at the detector level, and are hence combined into one signal, to which the photo-production only contributes less than 10\%. Therefore, even though the significance of this signal reaches an observable level, it does not imply that the Higgs photo-production can be observed with the assumed experimental conditions in our analysis.