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 αs , We also work out the analyticity structure of the soft-quark function by making use of light-cone perturbation theory.