Renormalisation group evolution of the shape function g17 in $$ \overline{B}\to {X}_s\gamma $$ and $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ at subleading power
Year: 2025
Type: article
Abstract: A bstract We derive and solve the renormalisation-group (RG) equation of the shape function g 17 ( ω, ω 1 ; μ ), which appears at subleading power in the factorisation of the inclusive decays $$ \overline{B}\to {X}_s\gamma $$ B ¯ → X s γ and $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ B ¯ → X s ℓ + ℓ − . Our results provide the first ingredient for a next-to-leading order analysis of the respective resolved-photon $$ {Q}_1^c-{Q}_{7\gamma } $$ Q 1 c − Q 7 γ interference contribution, whose current uncertainties are among the largest ones in both inclusive penguin modes. As a by-product of our study, we find that the analytic properties of the soft anomalous dimension as well as the jet functions in a factorisation theorem allow for a simplified renormalisation of operators in Heavy-Quark Effective Theory that are composed of fields smeared along distinct light-cone directions. Their hadronic matrix elements become relevant in various inclusive and exclusive B -decays beyond leading power in the heavy-quark and large-energy expansion. Using these insights, we derive and solve a simpler “reduced” RG equation of an amplitude-level soft function that describes the long-distance QCD dynamics for penguin contributions to exclusive $$ {\overline{B}}_{d,s}\to \gamma \gamma $$ B ¯ d , s → γγ decays, and which has recently been discussed in the literature.
Source: Journal of High Energy Physics
Authors: Riccardo Bartocci, Philipp Böer, Tobias Hurth
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409393241