Tomography and gravitational radii for hadrons by three-dimensional structure functions

TL;DR

This paper presents the first experimental extraction of gravitational form factors and radii of pions using three-dimensional structure functions derived from recent KEKB measurements, linking hadron tomography with gravitational physics.

Contribution

It introduces a novel method to determine gravitational form factors of hadrons from experimental data on generalized distribution amplitudes, opening new avenues in hadron structure studies.

Findings

Determined pion gravitational form factors and radii from experimental data.

Showed that GDAs encode information on energy-momentum tensor form factors.

Proposed a new approach connecting microscopic hadron structure with gravitational physics.

Abstract

Three-dimensional tomography of hadrons can be investigated by generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions (TMDs), and generalized distribution amplitudes (GDAs). The GDA studies had been only theoretical for a long time because there was no experimental measurement until recently, whereas the GPDs and TMDs have been investigated extensively by deeply virtual Compton scattering and semi-inclusive deep inelastic scattering. Here, we report our studies to determine pion GDAs from recent KEKB measurements on the differential cross section of $\gamma^* \gamma \to \pi^0 \pi^0$. Since an exotic-hadron pair can be produced in the final state, the GDAs can be used also for probing internal structure of exotic hadron candidates in future. The other important feature of the GDAs is that the GDAs contain information on form factors of the energy-momentum tensor for quarks and gluons, so that gravitational form factors and radii can be calculated from the determined GDAs. We show the mass (energy) and the mechanical (pressure, shear force) form factors and radii for the pion. Our analysis should be the first attempt for obtaining gravitational form factors and radii of hadrons by analysis of actual experimental measurements. We believe that a new field of gravitational physics is created from the microscopic level in terms of elementary quarks and gluons.