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

Abstract

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 $\Delta {\Gamma }_s$ in the $B_s-{\overline{B}}_s$ 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.

Comments: Contribution to the Proceedings of Loops and Legs in Quantum Field Theory 2024 (LL2024)