One-loop corrections for WW to HH in Higgs EFT with the electroweak chiral Lagrangian

Abstract

In this work, we present the computation of the one-loop electroweak radiative corrections to the scattering process WW → HH within the context of the Higgs Effective Field Theory (HEFT). We assume that the fermionic interactions are like in the Standard Model, whereas the beyond Standard Model interactions in the bosonic sector are given by the electroweak chiral Lagrangian (EChL). The computation of the one-loop amplitude and the renormalization program is performed in terms of the involved one-particle-irreducible (1PI) functions and using Rζ covariant gauges. The renormalization of 1PI functions at arbitrary external momenta is a more ambitious program than just renormalizing the amplitude with on-shell external legs, and it has the advantage that they can be used in several scattering amplitudes. In fact, we use here some of the 1PI functions already computed in our previous work (devoted to WZ → WZ). We will complement them here with the computation of the new 1PI functions required for WW → HH. From this renormalization procedure, we will also derive the full set of renormalized coefficients of the EChL that are relevant for this scattering process. In the last part, we will present the numerical results for the EChL predictions of the one-loop level cross section, σ(WW → HH)|1-loop, as a function of the center-of-mass energy, showing the relative size of the one-loop radiative corrections with respect to the tree-level prediction in terms of the EChL coefficients. The results of the one-loop corrections to WW → HH for the SM case will be also presented, for comparison with the EChL case, following the same computational method - i.e., by means of the renormalization of 1PI functions