Addendum: Towards next-to-next-to-leading-log accuracy for the width difference in the $\mathbf{B_s-\bar{B}_s}$ system: fermionic contributions to order $\mathbf{(m_c/m_b)^0}$ and $\mathbf{(m_c/m_b)^1}$

TL;DR

This paper computes three-loop integrals to precisely determine fermionic contributions to the B_s-ar{B}_s width difference at next-to-next-to-leading order in QCD, including full charm quark mass dependence.

Contribution

It provides the first analytic calculation of fermionic contributions to the Wilson coefficients at NNLO with complete charm mass dependence.

Findings

Analytic expressions for three-loop master integrals.

Fermionic contributions to Wilson coefficients at NNLO.

Full charm mass dependence included in results.

Abstract

We calculate the three-loop master integrals of Ref. [1] [arXiv:1709.02160] in analytic form. This allows us to present the fermionic contributions to the $\Delta B=2$ Wilson coefficients of the $B$-$\bar B$ decay matrix in next-to-next-to-leading order of QCD with full analytic dependence on the mass of the charm quark in the fermionic loops.