Dirac and Pauli form factors from lattice QCD

TL;DR

This work computes nucleon electromagnetic form factors from lattice QCD with two dynamical flavors, across four lattice spacings, varying volumes, and $m_c\pi$ down to ~180 MeV, applying Kelly-inspired $Q^2$ parametrizations to extract $F_1$, $F_2$, and derived radii and moments. The analysis shows that the $Q^2$-dependence is largely governed by vector-meson exchange, while the low-$Q^2$ radii and the isovector anomalous magnetic moment remain below experimental values, with signs of chiral non-analytic behavior emerging at light masses. Chiral extrapolations using several EFT schemes reveal tensions and limited applicability near the physical point, underscoring the challenge of connecting lattice results to phenomenology and the importance of lighter pions, larger volumes, and improved momentum-resolution (e.g., twisted boundary conditions). The study highlights systematic uncertainties from excited states, discretization, and finite-volume effects, and calls for resonance-inclusive EFTs to more accurately capture the observed $m_c\pi$ and $Q^2$ dependences. Overall, the results establish both the potential and the current limitations of lattice QCD for precise nucleon form-factor phenomenology and point to concrete directions for future progress.

Abstract

We present a comprehensive analysis of the electromagnetic form factors of the nucleon from a lattice simulation with two flavors of dynamical O(a)-improved Wilson fermions. A key feature of our calculation is that we make use of an extensive ensemble of lattice gauge field configurations with four different lattice spacings, multiple volumes, and pion masses down to m_π~ 180 MeV. We find that by employing Kelly-inspired parametrizations for the Q^2-dependence of the form factors, we are able to obtain stable fits over our complete ensemble. Dirac and Pauli radii and the anomalous magnetic moments of the nucleon are extracted and results at light quark masses provide evidence for chiral non-analytic behavior in these fundamental observables.

Figures (36)

• Figure 1: Dirac form factor $F_1(Q^2)$ in the isovector channel. All ensembles are included, and darker colors correspond to lighter pion masses. The gray shaded band represents the parametrization by Alberico et al. Alberico:2008sz of the experimental data.
• Figure 2: Pauli form factor $F_2(Q^2)$ in the isovector channel. All ensembles are included, and darker colors correspond to lighter pion masses. The gray shaded band represents the parametrization of Ref. Alberico:2008sz of the experimental data.
• Figure 3: Dirac form factor $F_1(Q^2)$ in the isosinglet ($u+d$) channel. All ensembles are included, and darker colors correspond to lighter pion masses. The gray shaded band represents the parametrization by Alberico et al. Alberico:2008sz of the experimental data.
• Figure 4: Pauli form factor $F_2(Q^2)$ in the isosinglet ($u+d$) channel. All ensembles are included, and darker colors correspond to lighter pion masses. The gray shaded band represents the parametrization of Ref. Alberico:2008sz of the experimental data.
• Figure 5: The ratio $F^d_1/F^u_1$ of down to up quark contributions to the Dirac form factor. All ensembles are included. The darker colors correspond to lighter pion masses. The gray shaded band represents the parametrization of Ref. Alberico:2008sz of the experimental data.