Two-Loop Radiative Jet Function for Exclusive $B$-Meson and Higgs Decays

Abstract

The rare radiative $B$-meson decay $B^{-}\to \gamma {\ell }^{-}\bar{\nu }$ and the radiative Higgs-boson decay $h\to \gamma \gamma$ 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.

arXiv comment1 figure, 19 pages plus appendices; v2: significantly extended version containing new results for the 2-loop anomalous dimensions of the jet function and the B-meson light-cone distribution amplitude in momentum space (section 2.4), and analytic solutions of the RG equations at 2-loop order (section 2.5), references added; v3: extended discussion in Sections 2.1 and 4, version published in JHEP

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