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Generalized distribution amplitudes (GDAs) are one type of three-dimensionalstructure functions, and they are related to the generalized distributionfunctions (GPDs) by the $s$-$t$ crossing of the Mandelstam variables. The GDAstudies provide information on three-dimensional tomography of hadrons. TheGDAs can be investigated by the two-photon process $\gamma^* \gamma \to h\barh$, and the GPDs are studied by the deeply virtual Compton scattering $\gamma^*h \to \gamma h$. The GDA studies had been pure theoretical topics, although theGPDs have been experimentally investigated, because there was no availableexperimental measurement. Recently, the Belle collaboration reported theirmeasurements on the $\gamma^* \gamma \to \pi^0 \pi^0$ differential crosssection, so that it became possible to find the GDAs from their measurements.Here, we report our analysis of the Belle data for determining the pion GDAs.From the GDAs, the timelike gravitational form factors $\Theta_1 (s)$ and$\Theta_2 (s)$ can be calculated, which are mechanical (pressure, shear force)and mass (energy) form factors, respectively. They are converted to thespacelike form factors by using the dispersion relation, and then gravitationalradii are evaluated for the pion. The mass and mechanical radii are obtainedfrom $\Theta_2$ and $\Theta_1$ as $\sqrt {\langle r^2 \rangle_{\text{mass}}}=0.56 \sim 0.69$ fm and $\sqrt {\langle r^2 \rangle_{\text{mech}}} =1.45 \sim1.56$ fm, whereas the experimental charge radius is $\sqrt {\langle r^2\rangle_{\text{charge}}} =0.672 \pm 0.008$ fm for the charged pion. Futuredevelopments are expected in this new field to explore gravitational physics inthe quark and gluon level.

3D structure of hadrons by generalized distribution amplitudes and gravitational form factors