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

Matteo Fael; Fabian Lange; Kay Schönwald; Matthias Steinhauser

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arXiv · 2603.15751

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

Matteo Fael·Fabian Lange·Kay Schönwald·Matthias Steinhauser

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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.

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Matteo Fael, Fabian Lange, Kay Schönwald, Matthias Steinhauser. 2026-03-16. The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO: light-fermion and large-$N_{\rm c}$ corrections. https://arxiv.org/abs/2603.15751

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