Electroweak corrections to Higgs boson production via W W fusion at the future LHeC

Precision measurement of quark Yukawa couplings is a crucial aspect of Higgs property study. Proposed as a future upgrade of the Large Hadron Collider (LHC), the Large Hadron electron Collider (LHeC) provides opportunities to probe quark Yukawa couplings with a high precision because of relatively low rate from QCD background as compared with that of the Higgs processes at the LHC. For this purpose, it is important to have a precision prediction of the Higgs production rate at the LHeC. The leading production channel of the Higgs boson at the LHeC is via weak boson fusion (WBF) which has the unique kinematic feature of forward tagging jets. Since there is no color exchange between the forward-backward objects in WBF processes, electroweak radiative corrections become particularly important. In this paper, we focus on the electroweak radiative corrections at next-to-leading order for Higgs boson production in the WBF channel at the LHeC. In the two renormalization schemes we use, the loop corrections are respectively at the level of 9% and 18% relative to the leading order result, and the next-to-leading calculation in both schemes agree up to a truncation error expected from the perturbative method. The size of the EW correction exceeds that from QCD radiations and is shown to be important for the study of Higgs phenomenology.