Photo-production of the Higgs boson at the LHeC

As one category of vector boson fusion, photo-production is one important production mechanism at $e$-$p$ colliders. A future $e$-$p$ collider -- Large Hadron-electron Collider (LHeC) has been discussed as a "Higgs factory" candidate where the Higgs boson produced via weak boson fusion (WBF) at the LHeC plays an important role in precision measurement of Yukawa couplings. On the other hand, a measurement of photo-production of the Higgs boson, if possible, might be complementary to the measurement of Higgs to di-photon partial decay width $\Gamma({h\to\gamma\gamma})$. In this paper, we study the possibility of measuring this production process at the LHeC with the help of the photon PDFs published in recent years. This process has a clean final state without additional colored particles in the detectable region other than the decay products of the Higgs. We compute the cross sections of all related processes and find that the production rate is at the same order as the neutral current WBF production of Higgs boson with missing forward jets. However, a detailed phenomenological study of various Higgs decay channels shows that even in the most promising semi-leptonic $WW$ channel, the feasibility of identifying such photo-production is negative due to an irreducible photo-production of $W^{+}W^{-}$.