Abstract
The rare radiative B-meson decay {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.
Highlights
We have presented a detailed study of the radiative jet function J(p2) defined in (1.2), which plays a central role in the theory of factorization at subleading power in scale ratios
This object appears in factorization theorems for important exclusive processes such as the rare B-meson decay B− → γ −νand the contributions to the radiative Higgs-boson decay h → γγ mediated by light-quark loops
We have further derived the anomalous dimensions for the jet functions in momentum and the dual space, including for the first time the so-far unknown twoloop contributions not controlled by the cusp anomalous dimension
Summary
At one-loop order, we find that the bare jet function in d = 4 − 2 spacetime dimensions reads. While at one-loop order one could renormalize the jet function by means of a local counterterm, the correct renormalization factor has a more complicated non-local form.. Independent of the renormalization scale [19] In this process, the known RG equations for the B-meson light-cone distribution amplitude (LCDA) [22] and some other quantities have been used. For the space-like case an analogous expression holds, where p 2 is integrated over the interval Treating both cases at the same time, we write the renormalization condition in the form. At one-loop order the plus distribution has no effect when the renormalized jet function is derived from (2.5). One of the main goals of this paper is to calculate the two-loop corrections to this formula
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