Three-loop $b\to s\gamma$ vertex with current-current operators

TL;DR

This paper calculates three-loop corrections to the $b o s\gamma$ decay process from current-current operators, providing both numerical and analytic results to improve theoretical precision in heavy quark decay predictions.

Contribution

It presents the first analytic results for the next-to-leading order contribution to the three-loop $b o s\gamma$ vertex corrections from current-current operators.

Findings

Provides expansions in $m_c/m_b$ with numerical coefficients for various schemes.

Offers analytic results for the next-to-leading order contribution.

Enhances the theoretical framework for NNLO interference calculations.

Abstract

We compute three-loop vertex corrections to $b\to s\gamma$ induced by current-current operators. The results are presented as expansions in $m_c/m_b$ with numerical coefficients which allow to cover all relevant values for the heavy quark masses in different renormalization schemes. Moreover we provide for the first time analytic results for the next-to-leading order contribution. Our results present an important building block to the next-to-next-to-leading order interference contributions of the current-current operators $Q_1$ and $Q_2$ with the electric dipole operator $Q_7$.