Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory

Abstract

Background: The transverse densities ρ1,2(b) describe the distributions of electric charge and magnetic moment at fixed light-front time and connect the nucleon's elastic form factors with its partonic structure. The dispersive representation of the form factors F1,2(t) expresses the densities in terms of exchanges of hadronic states in the t-channel and permits their analysis using hadronic physics methods.Purpose: Compute the densities at peripheral distances b = O(M −1 π ), where they are generated predominantly by the two-pion states in the dispersive representation. Quantify the uncertainties.Methods: Dispersively improved chiral effective field theory (DIχEFT) is used to calculate the isovector spectral functions Im F1,2(t) on the two-pion cut. The method includes ππ interactions (ρ resonance) through elastic unitarity and provides realistic spectral functions up to t ≈ 1 GeV 2 . Higher-mass states are parametrized by effective poles and constrained by sum rules (charges, radii, superconvergence relations). The densities ρ1,2(b) are obtained from their dispersive representation. Uncertainties are quantified by varying the spectral functions. The method respects analyticity and ensures the correct b → ∞ asymptotic behavior of the densities.Results: Accurate densities are obtained at all distances b 0.5 fm, with correct behavior down to b → 0. The region of distances is quantified where transverse nucleon structure is governed by the two-pion state. The light-front current distributions in the polarized nucleon are computed and discussed.Conclusions: Peripheral nucleon structure can be computed from first principles using DIχEFT. The method can be extended to generalized parton distributions and other nucleon form factors.