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 radiation and non-perturbative effects. We include the statistical uncertainties on the signal rates as well as conservative estimates of the theoretical uncertainties. We first consider a theory containing only modifications of the trilinear coupling, through a $c_6 \lambda\, H^6/ v^2$ 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 an alternative scenario, where we vary a smaller sub-set of parameters. Allowing, finally, the values of the other coefficients to vary within \textit{projected} experimental ranges, we find that the currently unbounded parameter, $c_6$, could be constrained to lie within $|c_6| \lesssim 0.6$ at 1$\sigma$ confidence, at the end of the high-luminosity run of the LHC (14~TeV) in the full model, and to $-0.6 \lesssim c_6 \lesssim 0.5$ in the alternative model. This study constitutes a first step towards the inclusion of multi-Higgs boson production in a full fit to the dimension-6 effective field theory framework.