Interference effects in Higgs production through Vector Boson Fusion in the Standard Model and its singlet extension

Interference effects play an important role in Electroweak Physics. They are responsible for the restoration of unitarity at large energies. When, as is often the case, higher order corrections are only available for some particular subamplitude, interferences need to be carefully computed in order to obtain the best theoretical prediction. It has been recently pointed out in gluon fusion that whenever more than one neutral, CP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{C}\mathcal{P} $$\end{document} even, scalars are present in the spectrum large cancellations can occur. We extend these studies to Vector Boson Scattering, examining interference effects in the Higgs sector in the Standard Model and its one Higgs Singlet extension. Already in the SM there is a significant difference between the results obtained considering only s-channel Higgs exchange and those obtained from the full set of scalar exchange diagrams. In the 1HSM these effects are modulated by the interference between the two neutral Higgses. The full interference between the heavy Higgs diagrams and the rest of the amplitude, which is the sum of light Higgs exchange diagrams and of those diagrams in which no Higgs appear, is very small for values of the mixing angle compatible with the experimental constraints.