Nucleon electromagnetic form factors with a nonlocal chiral effective Lagrangian

The relativistic version of finite-range regularization is proposed. The covariant regulator is generated from the nonlocal Lagrangian. This nonlocal interaction is gauge invariant and is applied to study the nucleon electromagnetic form factors at momentum transfer up to $2{\mathrm{GeV}}^2$. Both octet and decuplet intermediate states are included in the one-loop calculation. Using a dipole regulator with $\mathrm{\Lambda }$ around 0.85 GeV, the obtained form factors, electromagnetic radii, as well as the ratios of the form factors are all comparable with the experimental data. This successful application of chiral effective Lagrangian to relatively large momentum transfer makes it possible to further investigation of hadron quantities at high $Q^2$.

Figure 1

One-loop Feynman diagrams for the nucleon electromagnetic form factors. The solid, double-solid, dashed, and wave lines are for the octet baryons, decuplet baryons, pseudoscalar mesons, and photons, respectively. The rectangle and black dot represent magnetic and additional interacting vertex.

Figure 2

The proton magnetic form factor versus momentum transfer $Q^2$ with $\mathrm{\Lambda }=0.85\mathrm{GeV}$. The solid line is for the empirical result. The dotted, dot-dashed, and dashed lines are for the tree, loop, and total contribution, respectively.

Figure 3

Same as Fig. 2 but for the proton electric form factor.

Figure 4

The magnetic form factor of neutron versus momentum transfer $Q^2$ with $\mathrm{\Lambda }=0.85\mathrm{GeV}$. The solid line is for the empirical result. The dotted, dot-dashed, and dashed lines are for the tree, loop, and total contribution, respectively.

Figure 5

The electric form factor of neutron versus momentum transfer $Q^2$ with $\mathrm{\Lambda }=0.85\mathrm{GeV}$. The experimental date are from [43].

Figure 6

Radio of proton electric to normalized magnetic form factor versus momentum transfer $Q^2$. The experimental result is from [44].

Figure 7

Radio of neutron electric to normalized magnetic form factor versus momentum transfer $Q^2$. The experimental result is from [45].

Figure 8

The interacting vertex in the calculation of nucleon form factors. Only the $\pi$ case is shown as an example. The rectangle and black dot represent the magnetic and additional interacting vertex.