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

Abstract

We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining chiral effective field theory (χEFT) and dispersion analysis. The spectral functions on the two-pion cut at t>4Mπ2 are constructed using the elastic unitarity relation and an N/D representation. χEFT is used to calculate the real functions J±1(t)=f±1(t)/Fπ(t) (ratios of the complex ππ→NN partial-wave amplitudes and the timelike pion FF), which are free of ππ rescattering. Rescattering effects are included through the empirical timelike pion FF |Fπ(t)|2. The method allows us to compute the isovector EM spectral functions up to t∼1GeV2 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-Q2 FF data is achieved up to ∼0.5GeV2 for GE, and up to ∼0.2GeV2 for GM. Our results can be used to guide the analysis of low-Q2 elastic scattering data and the extraction of the proton charge radius.