Two-loop radiative jet function for exclusive B-meson and Higgs decays
Ze Long Liu, Matthias Neubert
Abstract
A bstract The rare radiative B -meson decay $$ {B}^{-}\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> 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.