Analyticity, renormalization, and evolution of the soft-quark function

TL;DR

This paper calculates the renormalization and evolution of the soft-quark function relevant for Higgs decay processes, confirming a prior conjecture and analyzing its analyticity structure using light-cone perturbation theory.

Contribution

It provides the first explicit computation of the soft-quark function's renormalization and evolution at order alpha_s, confirming previous theoretical conjectures.

Findings

Confirmed the conjectured form of renormalization and evolution at order alpha_s.

Analyzed the analyticity structure of the soft-quark function.

Enhanced understanding of the soft-quark function in Higgs decay factorization.

Abstract

We compute the renormalization and evolution of the soft-quark function that appears in the factorization theorem for Higgs-boson decays to two photons through a $b$-quark loop. Our computation confirms a conjecture by Liu, Mecaj, Neubert, Wang, and Fleming for the form of the renormalization and evolution of the soft-quark function in order $\alpha_s$. We also work out the analyticity structure of the soft-quark function by making use of light-cone perturbation theory.