Addendum: Towards next-to-next-to-leading-log accuracy for the width difference in the ${\mathbf{B}}_{\mathbf{s}}-{\bar{\mathbf{B}}}_{\mathbf{s}}$ system: fermionic contributions to order $({\mathbf{m}}_{\mathbf{c}}/{\mathbf{m}}_{\mathbf{b}}{)}^0$ and $({\mathbf{m}}_{\mathbf{c}}/{\mathbf{m}}_{\mathbf{b}}{)}^1$

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.

Comments: 5 pages