Empirical Determination of the Pion Mass Distribution

TL;DR

This paper uses existing experimental data to create model-independent representations of the pion's internal structure, leading to a data-driven prediction of its mass distribution form factor and insights into pion structure.

Contribution

It introduces a novel data-driven approach to determine the pion mass distribution form factor using model-independent GPD representations from experimental data.

Findings

The ratio of radii from mass distribution and electromagnetic form factors is 0.79(3).

The pion mass distribution form factor is harder than the electromagnetic form factor.

Predictions provide constraints for theoretical models of pion structure.

Abstract

Existing pion+nucleus Drell-Yan and electron+pion scattering data are used to develop ensembles of model-independent representations of the pion generalised parton distribution (GPD). Therewith, one arrives at a data-driven prediction for the pion mass distribution form factor, $\theta_2$. Compared with the pion elastic electromagnetic form factor, $\theta_2$ is harder: the ratio of the radii derived from these two form factors is $r_\pi^{\theta_2}/r_\pi = 0.79(3)$. Our data-driven predictions for the pion GPD, related form factors and distributions should serve as valuable constraints on theories of pion structure.