Chiral extrapolation of nucleon magnetic form factors

The extrapolation of nucleon magnetic form factors calculated within lattice QCD is investigated within a framework based upon heavy baryon chiral effective-field theory. All one-loop graphs are considered at arbitrary momentum transfer and all octet and decuplet baryons are included in the intermediate states. Finite range regularization is applied to improve the convergence in the quark-mass expansion. At each value of the momentum transfer ($Q^2$), a separate extrapolation to the physical pion mass is carried out as a function of $m_{\pi }$ alone. Because of the large values of $Q^2$ involved, the role of the pion form factor in the standard pion-loop integrals is also investigated. The resulting values of the form factors at the physical pion mass are compared with experimental data as a function of $Q^2$ and demonstrate the utility and accuracy of the chiral extrapolation methods presented herein.

Figure 1

The one-loop Feynman diagrams for the nucleon magnetic moments. The solid, thick solid, dash and dotted lines are for the octet baryons, decuplet baryons, pseudoscalar mesons, and photons, respectively.

Figure 2

The proton magnetic moment [10] versus squared pion mass. The lines with label a and $\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{f}+\mathrm{g}$ correspond to the contributions of Fig. 1a and the sum of the other diagrams, respectively.

Figure 3

The neutron magnetic moment [10] versus squared pion mass. The lines with label a and $\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{f}+\mathrm{g}$ correspond to the contributions of Fig. 1a and the sum of the other diagrams, respectively.

Figure 4

The proton and neutron magnetic moments versus the regulator scale $\Lambda$.

Figure 5

The proton magnetic form factor [10] at $Q^2=0.23{\mathrm{GeV}}^2$ versus the squared pion mass. The lines with label a and $\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{f}+\mathrm{g}$ correspond to the contributions of Fig. 1a and the sum of the other diagrams, respectively.

Figure 6

The neutron magnetic form factor [10] at $Q^2=0.23{\mathrm{GeV}}^2$ versus squared pion mass. The lines with label a and $\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{f}+\mathrm{g}$ correspond to the contributions of Fig. 1a and the sum of the other diagrams, respectively.

Figure 7

The proton magnetic form factors [11] at $Q^2=0.557$, 1.08, 1.14 and $2.28{\mathrm{GeV}}^2$ versus pion mass.

Figure 8

The neutron magnetic form factors [11] at $Q^2=0.557$, 1.08, 1.14 and $2.28{\mathrm{GeV}}^2$ versus pion mass.

Figure 9

The proton magnetic form factor [10] at $Q^2=0.23{\mathrm{GeV}}^2$ versus pion mass. The dashed and solid lines are for the results with and without the pion form factor, respectively.

Figure 10

The proton and neutron magnetic form factors at physical pion mass versus the momentum transfer, $Q^2$. The hollow and solid square points are for the fits with and without the inclusion of the form factor of the pion, respectively.