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

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.

40 pages, 12 figures, as usual plus additional diagrams calculated, typos corrected, text improved, references added