Nucleon axial form factors in generalized nonlocal chiral effective theory

TL;DR

The paper develops a generalized SU(2) nonlocal chiral effective theory to regulate pion loop corrections while preserving chiral symmetry, and applies it to nucleon axial structure. It introduces a nonlocal pion field with regulator H(a) and gauge links, leading to a regulator-dependent tree-level contribution to axial form factors and UV-finite loop corrections. By fitting next-to-leading and next-to-next-to-leading order LECs to lattice QCD data, the authors obtain smaller nonlocal LECs than in local approaches and achieve good agreement with lattice results for G_A(Q^2) up to Q^2 ≈ 1 GeV^2, as well as reasonable description of G_P(Q^2) in a similar range; they extract g_A, ⟨r_A^2⟩, and g_P with quantified uncertainties. The work demonstrates that nonlocal regularization can robustly describe nucleon axial observables and provides a framework for incorporating finite-size effects into chiral EFT while maintaining symmetry constraints.

Abstract

In this work, we first investigate the chiral transformation properties of the nonlocal pion field operator and construct a generalized nonlocal chiral Lagrangian that is invariant under $\mathrm{SU}(2)$ chiral symmetry transformations. As a simple application, we then calculate the leading and next-leading order pion one loop corrections to the nucleon axial form factors within nonlocal chiral perturbation theory. Then, we fit the next leading order and next-next leading order low energy coupling constants (LECs) to lattice QCD data. The fitted results show that the nonlocal LECs are comparatively smaller than their local counterparts. Finally, using these LECs, we compute the $Q^{2}$ dependence of the nucleon axial form factors. The numerical results indicate that the nonlocal nucleon axial form factors are consistent with lattice QCD data in a wide $\rm Q^{2}$ range, up to $\rm Q^{2} = 1~\mathrm{GeV}^{2}$

Figures (6)

• Figure 1: Leading and next- to-leading order pion one loop corrections to the nucleon self energy, dashed and solid lines denote the pion and nucleon fields, respectively.
• Figure 2: Pion one loop corrections to the nucleon axial form factors are shown, where the crossed circle, the crossed square and crossed ellipse represent the leading, next-to-leading and next-next-to leading order axial vector currents, the circled plus is next leading order additional gauge link axial vector current, and the cross with a dashed line is the pion pole dominant diagram.
• Figure 3: The nucleon mass as a function of pion mass is shown, the red and blue error bars are the lattice data, the green and pink error bands represent the theoretical uncertainty that originating from uncertainty of $c_1$, $c_2$, $c_{3}$.
• Figure 4: Nucleon axial charge $g^{R}_{A}$ (left panel ) and squared axial charge radii $\left\langle {r_A^2 } \right\rangle$ (right panel ) as a function of pion mass, where the red and blue error bars are the lattice data fromJager:2013khaHorsley:2013ayvEdwards:2005ymGupta:2017dwj, the green and pink error bands represent the theoretical uncertainty that arising from uncertainty of $c_4$ , $d_{16}$, $d_{22}$.
• Figure 5: The $Q^{2}$-dependence of the nucleon axial form factors $G_{A}(Q^{2})$ and $G_{P}(Q^{2})$ is compared with lattice QCD data from Refs. Gupta:2017dwjAlexandrou:2020okkCapitani:2017qpcAlexandrou:2023qbgJang:2023zts. In the figures, the error bars denote the statistical uncertainties of the lattice QCD results, while the green error bands represent the theoretical uncertainties arising from the low‑energy constants (LECs) and the regulator cutoff $\Lambda$.