Nucleon electromagnetic form factors on the lattice and in chiral effective field theory

TL;DR

This work computes nucleon electromagnetic form factors from quenched lattice QCD with ${O(a)}$-improved Wilson fermions, examining the quark-mass and momentum-transfer dependencies and comparing with chiral effective field theory (ChEFT) in the Small Scale Expansion. By fitting lattice data to dipole forms, the authors extract dipole masses and radii, and then confront the results with ${ m O}(oldsymbol{\e^3})$ SSE expressions for $F_1^v$, $F_2^v$, and the isovector radii, applying a normalization to account for the nucleon-mass shift with quark mass. The combined fits show that the isovector magnetic moment and Pauli radius are reasonably described by SSE with a small core term, while the isovector Dirac radius cannot be matched without sizable core contributions, highlighting limitations of the ${O}(oldsymbol{\e^3})$ EFT at the quark masses studied. The isoscalar sector remains uncertain due to disconnected contributions and larger lattice errors, and the study emphasizes the need for dynamical fermions and lighter quark masses to validate EFT extrapolations and connect to experiment.

Abstract

We compute the electromagnetic form factors of the nucleon in quenched lattice QCD, using non-perturbatively improved Wilson fermions, and compare the results with phenomenology and chiral effective field theory.

Figures (15)

• Figure 1: Nucleon mass squared versus pion mass squared from the data in Table \ref{['tab:param']}. The dotted curve shows our phenomenological chiral extrapolation (Eq. (\ref{['extra']})) for $\beta=6.4$. The full curve corresponds to the chiral extrapolation derived from chiral perturbation theory (Eq. (\ref{['nuclmass']})) with the parameters given in Appendix A.
• Figure 2: The ratios $R_3^{\mathrm {pol}}$ (left) and $R_4^{\mathrm {unpol}}$ (right) plotted versus $\tau$ for $\beta = 6.2$, $\kappa = 0.1344$. Here $\vec{p} = \vec{0}$ and $\vec{q}$ is the fourth momentum in the list (\ref{['qlist']}). The vertical dashed lines indicate the fit range for the extraction of the plateau value.
• Figure 3: Dipole fits of $G_e^v$ data (top) and $G_m^v$ data (bottom) at $\beta=6.4$ and $m_\pi = 0.648 \, \text{GeV}$.
• Figure 4: Isovector dipole masses together with linear fits. The extrapolated value at the physical pion mass is marked by a cross. The solid circle indicates the phenomenological value computed from the radii given in Ref. mergell.
• Figure 5: Isovector magnetic moment together with a linear fit. The extrapolated value at the physical pion mass is marked by a cross. The solid circle indicates the experimental value.