Dimension-six operators in Higgs boson pair production via vector-boson fusion at the LHC

The effective Lagrangian formalism provides a way to study the new physics effects at the electroweak scale. We study the Higgs pair production via the vector-boson fusion (VBF) at the Large Hadron Collider within the framework of the effective field theory. The effects from the dimension-six operators involved in the VBF Higgs pair production, particularly $\mathcal{O}_{\Phi,2}$ and $\mathcal{O}_{\Phi,3}$ which are relevant to the triple Higgs self-coupling, on the integrated cross section and various kinematic distributions are investigated. We find that the distributions of Higgs pair invariant mass, Higgs transverse momentum and rapidity are significantly altered by the operators $\mathcal{O}_{\Phi,2}$ and $\mathcal{O}_{\Phi,3}$. These features are helpful in disentangling the contributions from the operators $\mathcal{O}_{\Phi,2}$ and $\mathcal{O}_{\Phi,3}$ in triple Higgs self-coupling. We also provide the 5$\sigma$ discovery and 3$\sigma$ exclusion limits for the coefficients of $\mathcal{O}_{\Phi,2}$ and $\mathcal{O}_{\Phi,3}$ by measuring the VBF Higgs pair production process including the sequential $H \rightarrow b\bar{b}$ decays at the $14~ {\rm TeV}$ LHC.