Hadron tomography by generalized distribution amplitudes in the pion-pair production process. γ*γ → π0π0 and gravitational form factors for pion

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 gamma*gamma -> pi(0)pi(0) 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 gamma*gamma -> pi(0)pi(0) 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 Theta(1) and Theta(2) are obtained from our GDAs, and they are converted to the spacelike ones by the dispersion relation. From the spacelike Theta(1) and Theta(2), gravitational densities of the pion are calculated. Then, we obtained the mass (energy) radius and the mechanical (pressure and shear force) radius from Theta(2) and Theta(1), respectively. They are calculated as root < r(2)>(mass) = 0.56-0.69 fm, whereas the mechanical radius is larger root < r(2)>(mech) = 1.45-1.56 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 root < r(2)>(charge) = 0.672 +/- 0.008 fm for the charged pion. For drawing a clear conclusion on the GDAs of hadrons, accurate experimental data are needed, and it should be possible, for example, by future measurements of super-KEKB and international linear collider. Accurate measurements will not only provide important information on hadron tomography but also possibly shed light on gravitational physics in the quark and gluon level.