Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining chiral effective field theory (chi EFT) and dispersion analysis. The spectral functions on the two-pion cut at t > 4M(pi)(2) are constructed using the elastic unitarity relation and an N/D representation. chi EFT is used to calculate the real functions J(+/-)(1) (t) = f(+/-)(1) (t)/F pi (t) (ratios of the complex pi pi -> N (N) over bar partial-wave amplitudes and the timelike pion FF), which are free of pi pi rescattering. Rescattering effects are included through the empirical timelike pion FF vertical bar F pi(t)vertical bar(2). The method allows us to compute the isovector EM spectral functions up to t similar to 1 GeV2 with controlled accuracy (leading order, next-to-leading order, and partial next-to-next-to-leading order). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at t = 0 (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives, which are not affected by higher-order chiral corrections and are obtained almost parameter-free in our approach, and explain their collective behavior. We estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-Q(2) FF data is achieved up to similar to 0.5 GeV2 for G(E), and up to similar to 0.2 GeV2 for G(M). Our results can be used to guide the analysis of low-Q(2) elastic scattering data and the extraction of the proton charge radius.