Lattice QCD Matrix Elements for the B_{s}^{0}-B[over ¯]_{s}^{0} Width Difference beyond Leading Order.

Christine T H Davies,Christopher J Monahan,Junko Shigemitsu,Matthew Wingate,G Peter Lepage,Judd Harrison

doi:10.1103/physrevlett.124.082001

Abstract

Predicting the B_{s}^{0}-B[over ¯]_{s}^{0} width difference ΔΓ_{s} relies on the heavy quark expansion and on hadronic matrix elements of ΔB=2 operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators R_{2,3} and linear combinations R[over ˜]_{2,3} using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC Collaboration ensembles of gauge field configurations with 2+1+1 flavors of sea quarks with the HISQ discretization, including lattices with physically light up or down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first standard model determination of ΔΓ_{s} using lattice QCD results for all hadronic matrix elements through O(1/m_{b}). The main result of our calculations yields the 1/m_{b} contribution ΔΓ_{1/m_{b}}=-0.022(10) ps^{-1}. Adding this to the leading order contribution, the standard model prediction is ΔΓ_{s}=0.092(14) ps^{-1}.

Highlights

Predicting the B0s − B 0s width difference ΔΓs relies on the heavy quark expansion and on hadronic matrix elements of ΔB 1⁄4 2 operators
A few observables are, to a high level of precision, sensitive only to short-distance physics. Predictions for these are reliably calculable because the dominant contribution comes from top-quark loops; there is no significant contribution from intermediate-state hadronic physics
Unlike the mass difference, which comes from the real part of the mixing amplitude, the width difference comes from the imaginary part which, by the optical theorem, describes the decays to real final states, primarily b → ccs decays

Summary

Published by the American Physical Society

Predicting the SM width difference ΔΓs requires the determination of matrix elements of a nonlocal product of effective operators HeΔfFf 1⁄41, with charm and up quarks in the virtual loops. [8,9] for sum rule calculations) The precision of these determinations has become good enough that matrix elements of higher-dimension operators are needed in order to reduce the SM uncertainty in ΔΓs. The goal here is to replace order-of-magnitude estimates based on the vacuum saturation approximation with first principles calculations including a quantitative analysis of errors In this first step, we neglect OðαsÞ corrections to the dimension-7 operators. The lattice actions used are the same as in our recent study of the dimension-6 operator matrix elements [6]. In order to implement the derivative operator, the calculation of the associated three-point correlation functions will require new strange quark propagators, beyond those used in Ref.

We must estimate the uncertainty due to not knowing the

BRk k

Our results permit the first lattice determination of