Progress on Constraining the Strange Quark Contribution to the Nucleon Spin

TL;DR

The paper tackles constraining the strange quark contribution to the nucleon spin by fitting both neutral-current elastic neutrino data and parity-violating electron scattering data to extract the strange vector and axial form factors $G_E^s(Q^2)$, $G_M^s(Q^2)$, and $G_A^s(Q^2)$. It employs two parameterizations for $G_A^s(Q^2)$ (a modified-dipole form and a $z$-expansion) and simple forms for the vector form factors, performing six global fits with three nuclear models (RFG, SuSA, SF) to include MiniBooNE data on a hydrocarbon target. The results tighten the low-$Q^2$ constraints on $G_A^s(Q^2)$ significantly, while $G_E^s(Q^2)$ and $G_M^s(Q^2)$ remain near zero; however, a precise determination of $\Delta s = G_A^s(Q^2=0)$ is not yet achieved, highlighting the need for exclusive NCES measurements and improved treatment of two-body currents. The work provides a framework for combining diverse data sets to probe strangeness in the nucleon and points to MicroBooNE-era data as a crucial next step.

Abstract

We report on a global fit of neutral-current elastic (NCE) neutrino-scattering data and parity-violating electron-scattering (PVES) data with the goal of determining the strange quark contribution to the vector and axial form factors of the proton. Knowledge of the strangeness contribution to the axial form factor, $G_A^s(Q^2)$, at low $Q^2$ will reveal the strange quark contribution to the nucleon spin, as $G_A^s(Q^2=0)=Δs$. Previous fits [1,2] of this form included data from a variety of PVES experiments (PVA4, HAPPEx, G0, SAMPLE) and the NCE neutrino and anti-neutrino data from BNL E734. These fits did not constrain $G_A^s(Q^2)$ at low $Q^2$ very well because there was no NCE data for $Q^2<0.45$ GeV$^2$. Our new fit includes for the first time MiniBooNE NCE data from both neutrino and anti-neutrino scattering; this experiment used a hydrocarbon target and so a model of the neutrino interaction with the carbon nucleus was required. Three different nuclear models have been employed; a relativistic Fermi gas (RFG) model, the SuperScaling Approximation (SuSA) model, and a spectral function (SF) model [3]. We find a tremendous improvement in the constraint of $G_A^s(Q^2)$ at low $Q^2$ compared to previous work, although more data is needed from NCE measurements that focus on exclusive single-proton final states, for example from MicroBooNE [4]. This work has been published in Physical Review D [5]. [1] S.F. Pate, D. McKee, V. Papavassiliou, Phys. Rev. C78, 015207 (2008) [2] S.F. Pate, D. Trujillo, EPJ Web of Conferences 66, 06018 (2014) [3] C. Giusti and M.V. Ivanov, J. Phys. G: Nucl. Part. Phys. 47 024001 (2020) [4] L. Ren, NuFact 2021, PoS, 402, 205 (2022), 10.22323/1.402.0205 [5] S.F. Pate et al., Phys. Rev. D 109, 093001, 2024

Figures (2)

• Figure 1: Independent determinations of the strangeness form factors of the nucleon using subsets of existing experimental data: Liu et al. (green squares) Liu:2007yi; Androić et al. (blue triangles) Androic:2009zu; Baunack et al. (red squares) Baunack:2009gy; Pate et al. (open circles use HAPPEx and E734 data, and closed circles use G0-Forward and E734 data) Pate:2008va. This selection of results is representative and not intended to be exhaustive.
• Figure 2: An illustration of the effect of the introduction of the MiniBooNE neutral current data into our global fit. The data points are the same as in Fig. \ref{['fig:old_points']}. The black solid line is the central value for the modified-dipole fit not using the MiniBooNE data. The red solid line includes the MiniBooNE data using the spectral function nuclear model. The dashed lines represent the 70% confidence limit for each fit. As mentioned in the text, the vector form factors fit is only slightly affected by the introduction of the MiniBooNE data, while the constraints on the axial form factor are greatly improved.