Towards two- and three-loop QCD corrections to the width difference in $B_s-\bar{B}_s$ mixing

TL;DR

This paper advances the theoretical calculation of the width difference in $B_s$ meson mixing by computing two- and three-loop QCD corrections at NNLO, aiming to reduce uncertainties in the prediction.

Contribution

It provides the first steps towards a complete NNLO analytic calculation of Wilson coefficients for $B_s$ mixing, addressing key technical challenges.

Findings

Progress towards full NNLO analytic results for Wilson coefficients.

Discussion of technical and conceptual difficulties in NNLO calculations.

Outlook on the availability of improved theoretical predictions for $ riangle \Gamma_s$.

Abstract

In this work we address the issue of large perturbative uncertainties in the theory prediction for $\Delta \Gamma_s$, the width difference in the $B^0_s - \bar{B}^0_s$ mixing process. To this aim we complete important steps towards the full analytic result for the previously unknown Wilson coefficients from the matching between $|\Delta B|=1$ and $|\Delta B|=2$ effective Hamiltonians at next-to-next-leading order (NNLO) in the strong coupling constant. We provide a thorough discussion of technical and conceptual difficulties behind this computation and give an outlook regarding the availability of the new NNLO theory prediction for $\Delta \Gamma_s$.