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

Abstract

Background: The transverse densities ${\rho }_{1,2}(b)$ 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 $F_{1,2}(t)$ 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 $b=\mathcal{O}(M_{\pi }^{-1})$, where they are generated predominantly by the two-pion states in the dispersive representation. Quantify the uncertainties. Methods: Dispersively improved chiral effective field theory (DI$\chi$EFT) is used to calculate the isovector spectral functions $\text{Im}{F}_{1,2}(t)$ on the two-pion cut. The method includes $\pi \pi$ interactions ($\rho$ resonance) through elastic unitarity and provides realistic spectral functions up to $t\approx$ 1 GeV${}^2$. Higher-mass states are parametrized by effective poles and constrained by sum rules (charges, radii, superconvergence relations). The densities ${\rho }_{1,2}(b)$ are obtained from their dispersive representation. Uncertainties are quantified by varying the spectral functions. The method respects analyticity and ensures the correct $b\to \infty$ asymptotic behavior of the densities. Results: Accurate densities are obtained at all distances $b\gtrsim 0.5$ fm, with correct behavior down to $b\to 0$. 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 DI$\chi$EFT. The method can be extended to generalized parton distributions and other nucleon form factors.

20 pages, 12 figures, 1 table

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