# Isovector charges of the nucleon from $2+1+1$ -flavor lattice QCD

## Abstract

We present high statistics results for the isovector charges $${g}_{A}^{u{-}d}$$, $${g}_{S}^{u{-}d}$$ and $${g}_{T}^{u{-}d}$$ of the nucleon. Calculations were carried out on eleven ensembles of gauge configurations generated by the MILC collaboration using highly improved staggered quarks action with $2+1+1$ dynamical flavors. These ensembles span four lattice spacings $$a{\approx}0.06$$, 0.09, 0.12 and 0.15 fm and light-quark masses corresponding to $${M}_{{\pi}}{\approx}135$$, 225 and 315 MeV. Excited-state contamination in the nucleon three-point correlation functions is controlled by including up to three-states in the spectral decomposition. Remaining systematic uncertainties associated with lattice discretization, lattice volume and light-quark masses are controlled using a simultaneous fit in these three variables. Our final estimates of the isovector charges in the $$\overline{\mathrm{MS}}$$ scheme at 2 GeV are $${g}_{A}^{u{-}d}=1.218(25)(30)$$, $${g}_{S}^{u{-}d}=1.022(80)(60)$$ and $${g}_{T}^{u{-}d}=0.989(32)(10)$$. The first error includes statistical and all systematic uncertainties except that due to the extrapolation ansatz, which is given by the second error estimate. We provide a detailed comparison with the recent result of $${g}_{A}^{u{-}d}=1.271(13)$$ by the CalLat collaboration and argue that our error estimate is more realistic. Combining our estimate for $${g}_{S}^{u{-}d}$$ with the difference of light quark masses $$({m}_{d}{-}{m}_{u}{)}^{\mathrm{QCD}}=2.572(66)\text{ }\text{ }\mathrm{MeV}$$ given by the MILC/Fermilab/TUMQCD collaboration for $2+1+1$-flavor theory, we obtain $$({M}_{N}{-}{M}_{P}{)}^{\mathrm{QCD}}=2.63(27)\text{ }\text{ }\mathrm{MeV}$$. We update the low-energy constraints on novel scalar and tensor interactions, $${{\epsilon}}_{S}$$ and $${{\epsilon}}_{T}$$, at the TeV scale by combining our new estimates for $${g}_{S}^{u{-}d}$$ and $${g}_{T}^{u{-}d}$$ with precision low-energy nuclear experiments, and find them comparable to those from the ATLAS and the CMS experiments at the LHC.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Dept.
- Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy. Dept. of Computational Mathematics, Science and Engineering

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Brookhaven National Lab. (BNL), Upton, NY (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Michigan State Univ., East Lansing, MI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); LANL Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)

- Contributing Org.:
- Precision Neutron Decay Matrix Elements (PNDME) Collaboration

- OSTI Identifier:
- 1465231

- Alternate Identifier(s):
- OSTI ID: 1466649; OSTI ID: 1479939

- Report Number(s):
- BNL-208001-2018-JAAM; LA-UR-18-25335

Journal ID: ISSN 2470-0010

- Grant/Contract Number:
- SC0012704; AC02-05CH11231; AC05-00OR22725; AC52-06NA25396; PHY 1653405

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice field theory; Atomic, Nuclear and Particle Physics

### Citation Formats

```
Gupta, Rajan, Jang, Yong-Chull, Yoon, Boram, Lin, Huey-Wen, Cirigliano, Vincenzo, and Bhattacharya, Tanmoy. Isovector charges of the nucleon from 2+1+1 -flavor lattice QCD. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.034503.
```

```
Gupta, Rajan, Jang, Yong-Chull, Yoon, Boram, Lin, Huey-Wen, Cirigliano, Vincenzo, & Bhattacharya, Tanmoy. Isovector charges of the nucleon from 2+1+1 -flavor lattice QCD. United States. doi:10.1103/PhysRevD.98.034503.
```

```
Gupta, Rajan, Jang, Yong-Chull, Yoon, Boram, Lin, Huey-Wen, Cirigliano, Vincenzo, and Bhattacharya, Tanmoy. Fri .
"Isovector charges of the nucleon from 2+1+1 -flavor lattice QCD". United States. doi:10.1103/PhysRevD.98.034503.
```

```
@article{osti_1465231,
```

title = {Isovector charges of the nucleon from 2+1+1 -flavor lattice QCD},

author = {Gupta, Rajan and Jang, Yong-Chull and Yoon, Boram and Lin, Huey-Wen and Cirigliano, Vincenzo and Bhattacharya, Tanmoy},

abstractNote = {We present high statistics results for the isovector charges ${g}_{A}^{u{-}d}$, ${g}_{S}^{u{-}d}$ and ${g}_{T}^{u{-}d}$ of the nucleon. Calculations were carried out on eleven ensembles of gauge configurations generated by the MILC collaboration using highly improved staggered quarks action with $2+1+1$ dynamical flavors. These ensembles span four lattice spacings $a{\approx}0.06$, 0.09, 0.12 and 0.15 fm and light-quark masses corresponding to ${M}_{{\pi}}{\approx}135$, 225 and 315 MeV. Excited-state contamination in the nucleon three-point correlation functions is controlled by including up to three-states in the spectral decomposition. Remaining systematic uncertainties associated with lattice discretization, lattice volume and light-quark masses are controlled using a simultaneous fit in these three variables. Our final estimates of the isovector charges in the $\overline{\mathrm{MS}}$ scheme at 2 GeV are ${g}_{A}^{u{-}d}=1.218(25)(30)$, ${g}_{S}^{u{-}d}=1.022(80)(60)$ and ${g}_{T}^{u{-}d}=0.989(32)(10)$. The first error includes statistical and all systematic uncertainties except that due to the extrapolation ansatz, which is given by the second error estimate. We provide a detailed comparison with the recent result of ${g}_{A}^{u{-}d}=1.271(13)$ by the CalLat collaboration and argue that our error estimate is more realistic. Combining our estimate for ${g}_{S}^{u{-}d}$ with the difference of light quark masses $({m}_{d}{-}{m}_{u}{)}^{\mathrm{QCD}}=2.572(66)\text{ }\text{ }\mathrm{MeV}$ given by the MILC/Fermilab/TUMQCD collaboration for $2+1+1$-flavor theory, we obtain $({M}_{N}{-}{M}_{P}{)}^{\mathrm{QCD}}=2.63(27)\text{ }\text{ }\mathrm{MeV}$. We update the low-energy constraints on novel scalar and tensor interactions, ${{\epsilon}}_{S}$ and ${{\epsilon}}_{T}$, at the TeV scale by combining our new estimates for ${g}_{S}^{u{-}d}$ and ${g}_{T}^{u{-}d}$ with precision low-energy nuclear experiments, and find them comparable to those from the ATLAS and the CMS experiments at the LHC.},

doi = {10.1103/PhysRevD.98.034503},

journal = {Physical Review D},

number = 3,

volume = 98,

place = {United States},

year = {2018},

month = {8}

}

DOI: 10.1103/PhysRevD.98.034503

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