# Weak neutral current axial form factor using $$ \left(\overline{\nu}\right)\nu $$-nucleon scattering and lattice QCD inputs

## Abstract

We present a determination of the neutral current weak axial charge $G$ $$^{Z}_{A}$$(0) = –0.654(3) _{stat}(5) _{sys} using the strange quark axial charge $G$ $$^{s}_{A}$$(0) calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region 0.24 ≲ Q ^{2} ≲ 0.71 GeV ^{2} to determine the neutral current weak axial form factor $G$ $$^{Z}_{A}$$(Q ^{2}) in the range of 0 ≲ Q ^{2} ≤ 1 GeV ^{2}. This yields a phenomenological value of $G$ $$^{Z}_{A}$$(0) = –0.687(89)stat(40)sys. The value of $G$ $$^{Z}_{A}$$(0) constrained by the lattice QCD calculation of $G$ $$^{s}_{A}$$(0), when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G$ $$^{Z}_{A}$$(Q ^{2}) for Q ^{2} > 0. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near Q ^{2} = 0 and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G$ $$^{Z}_{A}$$(Q ^{2}) obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.

- Authors:

- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Univ. of Kentucky, Lexington, KY (United States)

- 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) (SC-26)

- OSTI Identifier:
- 1595282

- Report Number(s):
- JLAB-THY-18-2792; DOE/OR/23177-4525; arXiv:1809.03509

Journal ID: ISSN 1029-8479

- Grant/Contract Number:
- AC05-06OR23177; SC0013065; AC05-00OR22725; ACI-1053575

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Neutrino Physics

### Citation Formats

```
Sufian, Raza Sabbir, Liu, Keh-Fei, and Richards, David G. Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs. United States: N. p., 2020.
Web. doi:10.1007/JHEP01(2020)136.
```

```
Sufian, Raza Sabbir, Liu, Keh-Fei, & Richards, David G. Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs. United States. doi:10.1007/JHEP01(2020)136.
```

```
Sufian, Raza Sabbir, Liu, Keh-Fei, and Richards, David G. Tue .
"Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs". United States. doi:10.1007/JHEP01(2020)136. https://www.osti.gov/servlets/purl/1595282.
```

```
@article{osti_1595282,
```

title = {Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs},

author = {Sufian, Raza Sabbir and Liu, Keh-Fei and Richards, David G.},

abstractNote = {We present a determination of the neutral current weak axial charge $G$ $^{Z}_{A}$(0) = –0.654(3)stat(5)sys using the strange quark axial charge $G$ $^{s}_{A}$(0) calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region 0.24 ≲ Q2 ≲ 0.71 GeV2 to determine the neutral current weak axial form factor $G$ $^{Z}_{A}$(Q2) in the range of 0 ≲ Q2 ≤ 1 GeV2. This yields a phenomenological value of $G$ $^{Z}_{A}$(0) = –0.687(89)stat(40)sys. The value of $G$ $^{Z}_{A}$(0) constrained by the lattice QCD calculation of $G$ $^{s}_{A}$(0), when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G$ $^{Z}_{A}$(Q2) for Q2 > 0. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near Q2 = 0 and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G$ $^{Z}_{A}$(Q2) obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.},

doi = {10.1007/JHEP01(2020)136},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2020,

place = {United States},

year = {2020},

month = {1}

}

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