Update on technical aspects of $B$ meson mixing at NNLO

This report summarises important technical challenges and their solutions in the calculation of the next-to-next-to-leading order QCD corrections to the width difference $\mathrm{\Delta }{\mathrm{\Gamma }}_s$ in the $B_s-{\bar{B}}_s$ system. We focus on the treatment of spinor structures with products of up to 22 $\gamma$ matrices by means of projection and tensor integrals. Moreover, we present an approach for the semi-numeric computation of master integrals.