Probing the Higgs trilinear self-coupling through Higgs+jet production

We present the calculation of the next-to-leading order (NLO) electroweak (EW) corrections proportional to the Higgs trilinear self-coupling ($\lambda_{HHH}$) for Higgs boson plus one jet production at the Large Hadron Collider (LHC). We use the method of large top quark mass expansion to tackle the most challenging two-loop virtual amplitude, and apply the Pad\'{e} approximation to extend the region of convergence of the expansion. We find that the NLO EW corrections is $0.66\%$ for the total cross section. For the invariant mass distribution and Higgs boson transverse momentum distribution, the NLO corrections are almost flat with their values similar in size. Our results can be used to set extra constraints on $\lambda_{HHH}$ at the LHC.