Hadron tomography and its application to gravitational radii of hadrons

TL;DR

This paper investigates the internal structure of hadrons using gravitational form factors derived from generalized distribution amplitudes, revealing insights into their mass, pressure, and shear distributions at the quark-gluon level.

Contribution

The study determines pion GDAs from experimental data and calculates gravitational form factors, connecting hadron structure to gravitational physics at the microscopic scale.

Findings

Calculated gravitational radii of the pion.

Compared gravitational and charge radii.

Demonstrated link between hadron structure and gravitational physics.

Abstract

Hadron tomography has been investigated by three-dimensional structure functions, such as generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs). The GDAs are $s$-$t$ crossed quantities of the GPDs, and both functions probe gravitational form factors for hadrons. We determined the pion GDAs by analyzing Belle data on the differential cross section for the two-photon process $\gamma^* \gamma \to \pi^0 \pi^0$. From the determined GDAs, we calculated timelike gravitational form factors of the pion and they were converted to the spacelike form factors by using the dispersion relation. These gravitational form factors $\Theta_1$ and $\Theta_2$ indicate mechanical (pressure, shear force) and gravitational-mass (or energy) distributions, respectively. Then, gravitational radii are calculated for the pion from the form factors, and they are compared with the pion charge radius. We explain that the new field of gravitational physics can be developed in the microscopic level of quarks and gluons.