# Lattice QCD Matrix Elements for the ${B}_{s}^{0}-{\overline{B}}_{s}^{0}$ Width Difference beyond Leading Order

## Abstract

Predicting the B$$^0_s$$–¯B$$^0_s$$ width difference ΔΓs 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_{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 ΔΓ1/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}.

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)

- Contributing Org.:
- HPQCD Collaboration

- OSTI Identifier:
- 1601722

- Alternate Identifier(s):
- OSTI ID: 1602422

- Report Number(s):
- JLAB-THY-19-3052; DOE/OR/23177-4778; INT-PUB-19-044

Journal ID: ISSN 0031-9007; PRLTAO; 082001

- Grant/Contract Number:
- FG02-00ER41132; AC05-06OR23177

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 8; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Flavor changing neutral currents; Hadron mixing; Heavy quark effective theory; Lattice QCD

### Citation Formats

```
Davies, Christine T. H., Harrison, Judd, Lepage, G. Peter, Monahan, Christopher J., Shigemitsu, Junko, Wingate, Matthew, and HPQCD Collaboration. Lattice QCD Matrix Elements for the B s 0 − B ¯ s 0 Width Difference beyond Leading Order. United States: N. p., 2020.
Web. https://doi.org/10.1103/PhysRevLett.124.082001.
```

```
Davies, Christine T. H., Harrison, Judd, Lepage, G. Peter, Monahan, Christopher J., Shigemitsu, Junko, Wingate, Matthew, & HPQCD Collaboration. Lattice QCD Matrix Elements for the B s 0 − B ¯ s 0 Width Difference beyond Leading Order. United States. https://doi.org/10.1103/PhysRevLett.124.082001
```

```
Davies, Christine T. H., Harrison, Judd, Lepage, G. Peter, Monahan, Christopher J., Shigemitsu, Junko, Wingate, Matthew, and HPQCD Collaboration. Wed .
"Lattice QCD Matrix Elements for the B s 0 − B ¯ s 0 Width Difference beyond Leading Order". United States. https://doi.org/10.1103/PhysRevLett.124.082001.
```

```
@article{osti_1601722,
```

title = {Lattice QCD Matrix Elements for the B s 0 − B ¯ s 0 Width Difference beyond Leading Order},

author = {Davies, Christine T. H. and Harrison, Judd and Lepage, G. Peter and Monahan, Christopher J. and Shigemitsu, Junko and Wingate, Matthew and HPQCD Collaboration},

abstractNote = {Predicting the B$^0_s$–¯B$^0_s$ width difference ΔΓs 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 R2,3 and linear combinations ˜R2,3 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 ΔΓs using lattice QCD results for all hadronic matrix elements through O(1/mb). The main result of our calculations yields the 1/mb contribution ΔΓ1/mb = –0.022(10) ps–1. Adding this to the leading order contribution, the standard model prediction is ΔΓs = 0.092(14) ps–1.},

doi = {10.1103/PhysRevLett.124.082001},

journal = {Physical Review Letters},

number = 8,

volume = 124,

place = {United States},

year = {2020},

month = {2}

}

https://doi.org/10.1103/PhysRevLett.124.082001

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