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

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

Figure 1

Nucleon mass squared versus pion mass squared from the data in Table 1. The dotted curve shows our phenomenological chiral extrapolation (Eq. (10)) for $\beta =6.4$. The full curve corresponds to the chiral extrapolation derived from chiral perturbation theory (Eq. (A1)) with the parameters given in Appendix.

Figure 2

The ratios $R_3^{\mathrm{p}\mathrm{o}\mathrm{l}}$ (left) and $R_4^{\mathrm{u}\mathrm{n}\mathrm{p}\mathrm{o}\mathrm{l}}$ (right) plotted versus $\tau$ for $\beta =6.2$, $\kappa =0.1344$. Here $\overrightarrow{p}=\overrightarrow{0}$ and $\overrightarrow{q}$ is the fourth momentum in the list (29). 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 $m_{\pi }=0.648\mathrm{G}\mathrm{e}\mathrm{V}$.

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. [30].

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.

Figure 6

The ratio ${\mu }^p{G}_e^p/G_m^p$ from the chirally extrapolated dipole fits of the proton form factors (curve) compared with the experimental data from Refs. [2] (squares) and [3] (circles). The error band (indicated by the hatched area) has been computed from the errors of the extrapolated dipole masses. For the experimental numbers only the statistical errors are shown.

Figure 7

One-loop diagrams in SSE contributing to the electromagnetic form factors. The wiggly line represents an external vector field.

Figure 8

Comparison of the dispersion-theoretical description of the isovector nucleon form factors with the SSE curves and the dipole approximations following from the SSE.

Figure 9

Our results for the isovector (normalized) magnetic moments compared with the SSE extrapolation curve of Ref. [24]. The solid circle represents the experimental value of ${\mu }_v$.

Figure 10

Isovector radii compared with fit curves. For the fit parameters see Table 7. The dashed line corresponds to the fit without core term. The solid circles represent the experimental values.

Figure 11

Isovector (normalized) anomalous magnetic moments compared with (combined) fit. For the fit parameters see Table 7. The dashed line corresponds to the fit without core term. The solid circle represents the experimental value of ${\kappa }_v$.

Figure 12

Isoscalar (normalized) anomalous magnetic moments compared with SSE fit. The solid circle represents the experimental value of ${\kappa }_s$. The cross with the attached error bar shows the value at $m_{\pi }^{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}$.

Figure 13

Anomalous magnetic moments of proton and neutron (normalized) with chiral extrapolation curves. The solid circles represent the experimental values.

Figure 14

The ratio ${\kappa }_p/{\kappa }_n$ (identical to the ratio of the normalized anomalous magnetic moments) with chiral extrapolation curve. The dotted line shows the value $-1.0$ predicted by the nonrelativistic quark model. The solid circle represents the experimental value.

Figure 15

Diagrams in $\mathcal{O}({ϵ}^3)$ SSE contributing to the nucleon mass.