NLO analysis of the subleading-power $Q_1-Q_{7γ}$ interference in $\bar{B}\to X_sγ$ at large photon energies

TL;DR

The paper advances the program of achieving NLO accuracy for the subleading-power $Q_1^q$–$Q_{7γ}$ interference in $\bar B \to X_s γ$ at large photon energies by first renormalizing the subleading shape function $g_{17}(ω,ω_1;μ)$: computing its one-loop anomalous dimension and solving its RG equation, which factorizes into two independent evolutions for the $n$- and $\bar n$-sector. It provides explicit evolution kernels $U_n^{(17)}$ and $U_{\bar n}^{(17)}$ that resum logarithms between the soft and hard-collinear scales, and discusses the related amplitude-level three-particle $B$-meson LCDA $Φ_G(ω,ω_1;μ)$, whose reduced anomalous dimension preserves decoupling of the light-cone sectors despite its two-variable non-locality. A missing piece for the full NLO result is the two-loop jet function with an internal charm loop, with the massless case already prepared for cross-checks; work toward the finite charm-mass generalization is in progress. Altogether, these results aim to reduce scale ambiguities and charm-mass dependencies in the dominant non-local, power-suppressed contribution to the photon-energy spectrum in $\bar B \to X_s γ$, thereby sharpening SM predictions and NP sensitivity.

Abstract

We report on progress towards including next-to-leading order (NLO) radiative corrections to the subleading-power factorization formula for the $Q_1^{q}-Q_{7γ}$ interference contribution in $\bar{B}\to X_sγ$ at large photon energies, $m_b - 2E_γ= \mathcal{O}(Λ_{\rm QCD})$. The novel ingredients for a NLO analysis are the one-loop anomalous dimension of the subleading shape function $g_{17}(ω,ω_1;μ)$, which was recently computed by us, and the two-loop corrections to the jet function with an internal charm loop. Here we summarize the renormalization of $g_{17}(ω,ω_1;μ)$, and further discuss that our insights allow for a simplified renormalization of a specific generalization of a three-particle $B$-meson light-cone distribution amplitude, but with non-aligned light-like separations of the fields.

Figures (1)

• Figure 1: One-loop diagrams contributing to the UV singularities of the HQET operator $\mathcal{O}_{17}(t,r)$. The effective vertex denoted by the $\otimes$ symbol represents the non-local structure of fields and Wilson lines in \ref{['eq:Q17']}.