Two-loop radiative jet function for exclusive B-meson and Higgs decays

Abstract

Abstract The rare radiative B-meson decay B − → γ ℓ − v ¯ $$ {B}^{-}\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ and the radiative Higgs-boson decay h → γγ mediated by light-quark loops both receive large logarithmic corrections in QCD, which can be resummed using factorization theorems derived in soft-collinear effective theory. In these factorization theorems the same radiative jet function appears, which is a central object in the study of factorization beyond the leading order in scale ratios. We calculate this function at two-loop order both in momentum space and in a dual space, where its renormalization-group evolution takes on a simpler form. We also derive the two-loop anomalous dimension of the jet function and present the exact solution to its evolution equation at two-loop order. Another important outcome of our analysis is the explicit form of the two-loop anomalous dimension of the B-meson light-cone distribution amplitude in momentum space.

Keywords

• Effective Field Theories
• Renormalization Group
• Perturbative QCD
• Resummation