The nucleon electromagnetic form factors from Lattice QCD

TL;DR

This study computes the isovector nucleon electromagnetic form factors $G_E(Q^2)$ and $G_M(Q^2)$ using Wilson fermions in both quenched and two-flavor unquenched lattice QCD, enabling access to low and intermediate momentum transfers and direct comparison with experiment. By employing a fixed-sink, overconstrained analysis on large lattices, the authors extract the full $Q^2$-dependence, dipole masses, and radii, and perform linear chiral extrapolations in $m_\pi^2$ to reach the chiral limit, complemented by one-loop chiral EFT fits for the magnetic sector. The results show modest unquenching effects and that $G_M$ approaches experimental values after extrapolation, while $G_E$ remains higher than data, revealing limitations from lattice spacing and chiral reach. The work provides precise lattice benchmarks for nucleon form factors and underscores the need for finer lattices and lighter quark masses to reconcile all observables with experiment.

Abstract

We evaluate the isovector nucleon electromagnetic form factors in quenched and full QCD on the lattice using Wilson fermions. In the quenched theory we use a lattice of spatial size 3 fm at beta=6.0 enabling us to reach low momentum transfers and a lowest pion mass of about 400 MeV. In the full theory we use a lattice of spatial size 1.9 fm at beta=5.6 and lowest pion mass of about 380 MeV enabling comparison with the results obtained in the quenched theory. We compare our lattice results to the isovector part of the experimentally measured form factors.

Figures (20)

• Figure 1: The rho effective mass as a function of the time separation on a $16^3\times 32$ quenched lattice at $\beta=6.0$ and $\kappa=0.153$ using Dirichlet boundary conditions in the temporal direction. In the upper graph, filled triangles show results obtained with local source and sink, crosses with Wuppertal smeared source and local sink and open triangles (asterisks) with Wuppertal smeared source using hypercubic (APE) smearing for the gauge links used in the construction of the hopping matrix $H({\bf x},{\bf z};U(t))$. The lower graph shows with crosses results obtained using Wuppertal smeared source and sink and with open triangles (asterisks) results with Wuppertal smeared source and sink where hypercubic (APE) smearing is applied to the spatial links entering the hopping matrix.
• Figure 2: The nucleon effective mass as a function of the time separation on a $16^3\times 32$ quenched lattice at $\beta=6.0$ and $\kappa=0.153$. The notation is the same as that of Fig. \ref{['fig:meff rho']}.
• Figure 3: The isovector electric form factor, $G_E$, extracted by interpolation from the measured proton and neutron electric form factors.
• Figure 4: The isovector magnetic form factor, $G_M$, extracted by interpolation from the measured proton and neutron magnetic form factors.
• Figure 5: The ratio of isovector form factors $G_E$ over $G_M$ as compared to the corresponding ratio of proton form factors from recent polarization experiments Jeff.