Empirical Determination of the Pion Mass Distribution

Existing pion+nucleus Drell-Yan and electron+pion scattering data are used to develop ensembles of model-independent representations of the pion generalized parton distribution (GPD). Therewith, one arrives at a data-driven prediction for the pion mass distribution form factor, ${\theta }_2^{\pi }$. Compared with the pion elastic electromagnetic form factor, ${\theta }_2^{\pi }$ 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.