Higgs boson pair production in the D=6 extension of the SM

We derive the constraints that can be imposed on the dimension-6 effective theory extension of the Standard Model, using gluon-fusion-initiated Higgs boson pair production at the LHC. We use a realistic analysis focussing on the $hh \rightarrow (b\bar{b}) ( \tau^+ \tau^- )$ final state, including initial-state radiations and non-perturbative effects. We include conservative estimates of the theoretical uncertainties on the signal rate predictions as well as the statistical uncertainties. We first consider a theory containing only modifications of the trilinear coupling through an $c_6 \lambda\, H^6/ \Lambda^2$ Lagrangian term, and then examine the full parameter space of the effective theory, incorporating current bounds obtained through single Higgs boson measurements. We also consider a simplified scenario, where we only allow a sub-set of parameters to vary and set the others to zero. We find that the currently unbounded parameter, $c_6$, could be constrained to lie within $-0.9 \lesssim c_6 \lesssim 1.7$ at 1$\sigma$ confidence, at the end of the high-luminosity run of the LHC (14 TeV), independently of the values of the other dimension-6 coefficients. In the simplified scenario this bound is found to be $|c_6| \lesssim 1.3$. This study constitutes a first step towards the inclusion of multi-Higgs production in a full fit to the dimension-6 effective field theory framework.