Constraints on the trilinear Higgs coupling from vector boson fusion and associated Higgs production at the LHC

We examine the constraints on the trilinear Higgs coupling $\lambda$ that originate from associated ($Vh$) and vector boson fusion (VBF) Higgs production in $pp$ collisions in the context of the Standard Model effective field theory. The 1-loop contributions to $pp \to V h$ and $pp \to jj h$ that stem from insertions of the dimension-6 operator $O_6 = - \lambda \left (H^\dagger H \right )^3$ are calculated and combined with the ${\cal O} (\lambda)$ corrections to the partial decay widths of the Higgs boson. Employing next-to-next-to-leading order QCD predictions, we analyse the sensitivity of current and forthcoming measurements of the signal strengths in $Vh$ and VBF Higgs production to changes in $\lambda$. We show that future LHC runs may be able to probe modifications of $\lambda$ with a sensitivity similar to the one that is expected to arise from determinations of double-Higgs production. The sensitivity of differential $Vh$ and VBF Higgs distributions to a modified $h^3$ coupling is also studied.