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Probing the trilinear Higgs boson self-coupling via single Higgs production at the LHeC

The determination of the Higgs self coupling is one of the key ingredients for understanding the mechanism behind the electroweak symmetry breaking. An indirect method for constraining the Higgs trilinear self coupling via single Higgs production at next-to-leading order (NLO) has been proposed in order to avoid the drawbacks of studies with double Higgs production. In this paper we study the Higgs self interaction through the vector boson fusion (VBF) process $e^{-} p \to ν_{e} h j$ at the future LHeC. At NLO level, we compute analytically the scattering amplitudes for relevant processes, in particular those induced by the Higgs self interaction. A Monte Carlo simulation and a statistical analysis utilizing the analytic results are then carried out for Higgs production through VBF and decay to $b\bar{b}$, which yield for the trilinear Higgs self-coupling rescaling parameter $κ_λ$ the limit [-0.57, 2.98] with $2~\text{ab}^{-1}$ integrated luminosity. If we assume about 10% of the signal survives the event selection cuts, and include all the background, the constraint will be broadened to [-2.11, 4.63].