Analytical parametrization and shape classification of anomalous HH production in the EFT approach

In this document we study the effect of anomalous Higgs boson couplings on non-resonant pair production of Higgs bosons ($HH$) at the LHC. We explore the space of the five parameters $\kappa_{\lambda}$, $\kappa_{t}$, $c_2$, $c_g$, and $c_{2g}$ in terms of the corresponding kinematics of the final state, and describe a partition of the space into a limited number of regions featuring similar phenomenology in the kinematics of $HH$ final state. We call clusters the sets of points belonging to the same region; to each cluster corresponds a representative point which we call a benchmark. We discuss a possible technique to estimate the sensitivity of an experimental search to the kinematical differences between the phenomenology of the benchmark points and the rest of the parameter space contained in the corresponding cluster. We also provide an analytical parametrization of the cross-section modifications that the variation of anomalous couplings produces with respect to standard model $HH$ production along with a recipe to translate the results into other parameter-space bases. Finally, we provide a preliminary analysis of variations in the topology of the final state within each region based on recent LHC results.