Hadron tomography by generalized distribution amplitudes in pion-pair production process γ* γ → π0 π0 and gravitational form factors for pion

Abstract

Hadron tomography can be investigated by three-dimensional structure functions such as generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions, and generalized distribution amplitudes (GDAs). Here, we extract the GDAs, which are s-t crossed quantities of the GPDs, from cross-section measurements of hadron-pair production process γ* γ → π0 π0 at KEKB. This work is the first attempt to obtain the GDAs from the actual experimental data. The GDAs are expressed by a number of parameters and they are determined from the data of γ* γ → π0 π0 by including intermediate scalar- and tensor-meson contributions to the cross section. Our results indicate that the dependence of parton-momentum fraction z in the GDAs is close to the asymptotic one. The timelike gravitational form factors 1 and 2 are obtained from our GDAs, and they are converted to the spacelike ones by the dispersion relation.From the spacelike 1 and 2, gravitational densities of the pion are calculated. Then, we obtained the mass (energy) radius and the mechanical (pressure and shear force) radius from 2 and 1, respectively. They are calculated as r2 mass =0.32 0.39 fm, whereas the mechanical radius is larger r2 mech =0.82 0.88 fm. This is the first report on the gravitational radius of a hadron from actual experimental measurements. It is interesting to find the possibility that the gravitational mass and mechanical radii could be different from the experimental charge radius r2 charge =0.672 0.008 fm for the charged pion.