Improving the theoretical prediction for the B<inf>s</inf> - B̄ <inf>s</inf> width difference: Matrix elements of next-to-leading order Δ B = 2 operators

We present lattice QCD results for the matrix elements of $R_2$ and other dimension-7, $\Delta B = 2$ operators relevant for calculations of $\Delta \Gamma_s$, the $B_s-\bar{B}_s$ width difference. We have computed correlation functions using 5 ensembles of the MILC Collaboration's 2+1+1-flavour gauge field configurations, spanning 3 lattice spacings and light sea quarks masses down to the physical point. The HISQ action is used for the valence strange quarks, and the NRQCD action is used for the bottom quarks. Once our analysis is complete, the theoretical uncertainty in the Standard Model prediction for $\Delta \Gamma_s$ will be substantially reduced.This work was funded in part by STFC grants ST/L000385/1 and ST/L000466/1. CJM is supported in part by the US Department of Energy through Grant Number DE-FG02-00ER41132. Results described here were obtained using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service as part of the DiRAC facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the Universities of Cambridge and Glasgow. This equipment was funded by BIS National E-infrastructure capital grant (ST/K001590/1), STFC capital grants ST/H008861/1 and ST/H00887X/1, and STFC DiRAC Operations grants ST/K00333X/1, ST/M007073/1, and ST/P002315/1. MW is grateful for an IPPP Associateship held while this work was undertaken and for discussions with A Lenz