Nucleon electromagnetic form factors in twisted mass lattice QCD

TL;DR

This paper computes the nucleon electromagnetic form factors using two-flavor twisted mass lattice QCD. It systematically studies finite-volume and discretization (cut-off) effects by simulating at two volumes (L=2.1,2.8 fm) and three lattice spacings (a≈0.089,0.070,0.056 fm), and performs chiral and continuum extrapolations to the physical pion mass. The authors extract isovector electric and magnetic form factors, along with derived quantities like the anomalous magnetic moment and radii, using smeared interpolating fields and ratio methods that avoid disconnected diagrams. Through HBχPT with explicit Delta degrees of freedom, they show that the continuum-extrapolated results approach experimental trends at low Q^2, though some tensions remain (notably for the Pauli radius and the Q^2 fall-off). The work validates the TMF framework and informs systematic uncertainties in lattice determinations of nucleon structure.

Abstract

We present results on the nucleon electromagnetic form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length L=2.1 fm and L=2.8 fm. Cut-off effects are investigated using three different values of the lattice spacings, namely a=0.089 fm, a=0.070 and a=0.056 fm. The nucleon magnetic moment, Dirac and Pauli radii are obtained in the continuum limit and chirally extrapolated to the physical pion mass allowing for a comparison with experiment.

Figures (15)

• Figure 1: Connected nucleon three-point function.
• Figure 2: The nucleon isovector form factors $G_E^{p-n}$ and $G_M^{p-n}$ at $m_\pi\sim 300$ MeV for a lattice of size $24^3\times 48$ (filled red circles) and $32^3\times 64$ (filled blue squares). The dashed lines correspond to a dipole parametrization of Eq. (\ref{['dipole']}) with the dipole mass $m_E$ and $m_M$ taken to be the $\rho-$meson mass $m_\rho$ determined on the $24^3\time 48$ lattice. The dotted lines are dipole fits to the lattice data. The value of the magnetic form factor at $Q^2=0$ is fitted to the lattice data.
• Figure 3: The nucleon isovector electric (upper) and magnetic (lower) form factors $G_E^{p-n}(Q^2)$ and $G_M^{p-n}(Q^2)$ at $m_\pi\sim 470$ MeV at $\beta=3.9$ (filled red circles), $4.05$ (filled green triangles) and $4.2$ (magenta stars) versus $Q^2$. The open symbols and crosses denoted the values at $Q^2=0$ at $\beta=3.9, 4.05,$ and $4.2$ respectively, extracted by fitting the data to a dipole form.
• Figure 4: The nucleon isovector electric (upper) and magnetic (lower) form factors $G_E^{p-n}(Q^2)$ and $G_M^{p-n}(Q^2)$ at $m_\pi\sim 260$ MeV at $\beta=3.9$ (filled red circles) and $4.2$ (magenta stars) versus $Q^2$. The open symbols and crosses denoted the values at $Q^2=0$ at $\beta=3.9$ and $4.2$ respectively, extracted by fitting the data to a dipole form.
• Figure 5: The nucleon form factors $G_E^{p-n}(Q^2)$ and $G_M^{p-n}(Q^2)$ at $\beta=3.9$ for $m_\pi = 468$ MeV (crosses), $m_\pi = 432$ MeV (filled red circles) and $m_\pi = 303$ MeV (filled blue triangles) versus $Q^2$. The dashed lines are the result of a dipole fit to the lattice data.The solid line is J. Kelly's parametrization to the experimental data Kelly:2004hm.