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

TL;DR

This paper uses dispersively improved chiral effective field theory to accurately compute the transverse charge and current densities in the nucleon at peripheral distances, linking hadronic physics with nucleon structure.

Contribution

It introduces a first-principles method to calculate nucleon transverse densities using DIχEFT, including realistic spectral functions and uncertainty quantification.

Findings

Accurate densities obtained for distances greater than 0.5 fm.

Correct asymptotic behavior of densities at small distances.

Quantified the region where two-pion states dominate nucleon structure.

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 $\textrm{Im}\, F_{1, 2}(t)$ 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 $b \rightarrow \infty$ asymptotic behavior of the densities. Results: Accurate densities are obtained at all distances $b \gtrsim 0.5$ fm, with correct behavior down to $b \rightarrow 0$. 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.