The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO: light-fermion and large-$N_{\rm c}$ corrections

TL;DR

This paper presents a comprehensive calculation of the photon-energy spectrum in the inclusive decay $B o X_s\gamma$ at N$^3$LO, including various corrections and mass schemes, enhancing theoretical precision.

Contribution

It provides the first N$^3$LO calculation of the spectrum with complete light-fermion, two-loop fermion, and large-$N_c$ corrections, improving decay rate predictions.

Findings

Calculated the spectrum at N$^3$LO with full corrections.

Analyzed decay rates with and without photon energy cuts.

Compared different bottom-quark mass schemes for better perturbative behavior.

Abstract

We calculate the photon-energy spectrum of the inclusive radiative decay $B\to X_s\gamma$, induced by the electromagnetic dipole operator $O_7$, to next-to-next-to-next-to-leading order and consider the complete corrections for light fermions, for the contributions with two closed massive fermion loops, and for the limit of large QCD colour factors $N_{\rm c}$ in the remaining part. We discuss the total decay rate both without and with a cut on the photon energy. In addition to the on-shell renormalization of the bottom-quark mass, we also consider the kinetic mass and the MSR mass schemes. The latter two lead to an improved perturbative behaviour of the decay rate.