  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.
