Two--loop heavy Higgs correction to Higgs decay into vector bosons

TL;DR

The paper computes the leading heavy-Higgs ($m_H$) contributions to the Higgs decays into vector bosons at two loops using the equivalence theorem in the Landau gauge. It develops an on-shell renormalization framework for the scalar sector, and employs a computer-aided approach to evaluate two-loop diagrams, including analytic master-integral results and numerical $g$/$f$ function evaluations for finite momenta. The key finding is that the two-loop corrections grow as $m_H^4$ and, near $m_H \approx 930$ GeV, become as large as the one-loop corrections, signaling the breakdown of perturbation theory in this renormalization scheme. This has important implications for the reliability of electroweak predictions in the heavy-Higgs regime and for related phenomena such as WW scattering at TeV scales.

Abstract

The leading $m_H$ radiative correction to the Higgs decay width into a pair of weak vector bosons is calculated at the two--loop level, using the equivalence theorem in Landau gauge. The result indicates the breakdown of perturbation theory if the Higgs boson is heavier than $\sim 930$ GeV, in spite of the smallness of the one--loop radiative correction.