Update of the nonlocal sub-leading ${O}_1$-${O}_7$ contribution to $\bar B \to X_s γ$ at LO

TL;DR

This paper computes the complete nonlocal, sub-leading resolved contribution to the inclusive radiative decay $\bar{B} \to X_s \gamma$ arising from the interference of ${\cal O}_1^c$ and ${\cal O}_{7\gamma}$ at leading order, explicitly including the previously subtracted Voloshin term. The authors implement a SCET-based factorisation framework and model the nonperturbative shape function $h_{17}$ via a Hermite basis to quantify the complete convolution with perturbative jet functions, while accounting for correlations between the shape-function and Voloshin uncertainties. Their numerical analysis, performed over a structured parameter grid and including LO scale variation, yields a large LO uncertainty: ${\cal F}^{\rm Complete}_{17} = (7.8 \pm 5.2)\%$, with a range ${\cal F}^{\rm Complete}_{17} \in [2.6, 13]\%$ when scales are varied. This highlights the significant theoretical uncertainty at LO and motivates the ongoing ${\cal O}(\alpha_s)$ calculation to achieve RG-improved predictions and reduced scale dependence for this important contribution to $\bar{B} \to X_s \ gamma$.

Abstract

In all previous calculations of the non-local sub-leading contribution to the inclusive penguin decay $\bar B \to X_s γ$ due to the interference of the electroweak operators ${O}_1^c$ - ${O}_{7γ}$ the local Voloshin term was subtracted. In view of the ongoing analysis at order $α_s$, we present a calculation of the complete non-local contribution which takes into account the high correlation between the uncertainties of the local Voloshin and the non-local term of the previous analyses.