Lattice QCD matrix elements for the $B_s^0-{\bar{B}}_s^0$ width difference beyond leading order

Abstract

Predicting the $B_s^0-{\bar{B}}_s^0$ width difference $\Delta {\Gamma }_s$ relies on the heavy quark expansion and on hadronic matrix elements of $\Delta B=2$ operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators $R_{2,3}$ and linear combinations ${\tilde{R}}_{2,3}$ using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC ensembles of gauge field configuations with $2+1+1$ flavors of sea quarks with the HISQ discretization, including lattices with physically light up/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 $\Delta {\Gamma }_s$ using lattice QCD results for all hadronic matrix elements through $\mathcal{O}(1/m_b)$. The main result of our calculations yields the $1/m_b$ contribution $\Delta {\Gamma }_{1/m_b}=-0.022(10){\mathrm{ps}}^{-1}$. Adding this to the leading order contribution, the Standard Model prediction is $\Delta {\Gamma }_s=0.092(14){\mathrm{ps}}^{-1}$.

6 pages

References in corpus (34)

• Improved Nonrelativistic QCD for Heavy Quark Physics
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Theoretical update of Bs-Bs-bar mixing
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Constrained Curve Fitting
• Scaling studies of QCD with the dynamical HISQ action
• Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• $B_{(s)}^0$-mixing matrix elements from lattice QCD for the Standard Model and beyond
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• B-meson decay constants from improved lattice NRQCD and physical u, d, s and c sea quarks
• Width Difference in the $B_s-\overline{B_s}$ System
• The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea
• Neutral B-meson mixing from full lattice QCD at the physical point
• B-meson decay constants: a more complete picture from full lattice QCD
• Bs mixing observables and Vtd/Vts from sum rules
• Precise determination of the lattice spacing in full lattice QCD
• $B_s\to K\ell \nu$ form factors from lattice QCD
• The B^+ B_d^0 Lifetime Difference Beyond Leading Logarithms
• B-physics from Nf=2 tmQCD: the Standard Model and beyond
• The B_s and D_s decay constants in 3 flavor lattice QCD
• Dimension-six matrix elements for meson mixing and lifetimes from sum rules
• Gradient flow and scale setting on MILC HISQ ensembles
• Neutral $B$ meson mixings and $B$ meson decay constants with static heavy and domain-wall light quarks
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• $B_s^0-\overline{B_s^0}$ Mixing Parameters from Unquenched Lattice QCD
• Towards next-to-next-to-leading-log accuracy for the width difference in the $B_s-{\bar{B}}_s$ system: fermionic contributions to order $(m_c/m_b{)}^0$ and $(m_c/m_b{)}^1$
• Numerical updates of lifetimes and mixing parameters of B mesons
• Fast Fits for Lattice QCD Correlators
• Scaling and Further Tests of Heavy Meson Decay Constant Determinations from Nonrelativistic QCD
• Matching lattice and continuum four-fermion operators with nonrelativistic QCD and highly improved staggered quarks
• Improving the theoretical prediction for the $B_s-{\bar{B}}_s$ width difference: matrix elements of next-to-leading order $\Delta B=2$ operators

Cited by in corpus (8)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• Measurement of the $CP$-violating phase ${\varphi }_s$ in $B_s^0\to J/\psi \varphi$ decays in ATLAS at 13 TeV
• Revisiting Inclusive Decay Widths of Charmed Mesons
• Penguin contribution to width difference and CP asymmetry in $B_q$-${\bar{B}}_q$ mixing at order ${\alpha }_s^2{N}_f$
• Renormalisation scale setting for D-mixing
• The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Quark flavor physics and lattice QCD