Introducing tools to test Higgs interactions via $WW$ scattering I: one-loop calculations and renormalization in the HEFT

TL;DR

This paper develops one-loop calculations and renormalization techniques within the Higgs Effective Field Theory to ensure unitarity and causality in $WW$ scattering processes, aiding the search for physics beyond the Standard Model.

Contribution

It provides comprehensive one-loop computations, counterterm determination, and analysis of gauge effects in Higgs EFT, facilitating more accurate studies of Higgs interactions.

Findings

Full one-loop calculations for $WW$ scattering processes.

Determination of counterterms in the on-shell scheme.

Analysis of gauge effects on resonance properties.

Abstract

Effective field theories are useful tools to search for physics beyond the Standard Model (SM). However, effective theories can lead to non-unitary behavior with fastly growing amplitudes. This unphysical behavior may lead to large sensitivity to SM deviations, making necessary a unitarization of the amplitudes prior to a comparison with experiment. In the present work, we focus on all the processes entering the two-Higgs production by longitudinal $WW$ scattering: we perform a full one-loop calculation of all relevant processes, we determine the necessary counterterms in the on-shell scheme, and we study how the full inclusion of the gauge degrees of freedom modifies the previously computed masses and widths of the dynamical resonances arising from the unitarization process in the vector-isovector channel. Altogether, we are able to provide the technical tools that are needed to study the low-energy couplings in the Higgs effective theory under the requirements of unitarity and causality.