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 -> pi0 pi0 [1]. 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.

In addition to our recent GDA studies, related topics are discussed. The GDA studies should be valuable for probing internal structure of hadrons, especially for exotic hadron candidates which cannot be used as fixed targets for GPD measurements [2]. Internal structure of exotic hadron candidates could be also investigated by using the constituent counting rule in perturbative QCD [3]. I comment that there is a future possibility to investigate the GPDs at J-PARC for nucleon tomography [4].

[1] S. Kumano, Qin-Tao Song, and O. V. Teryaev, Phys. Rev. D97 (2018) 014020.
[2] S. Kumano and H. Kawamura, Phys.Rev. D89 (2014) 054007.
[3] H. Kawamura, S. Kumano, T. Sekihara, Phys. Rev. 88 (2013) 034010;
   W.-C. Chang, S. Kumano, and T. Sekihara, Phys. Rev. D 93 (2016) 034006.
[4] S. Kumano, M. Strikman, and K. Sudoh, Phys. Rev. D80 (2009) 074003;
   T. Sawada, Wen-Chen Chang, S. Kumano, Jen-Chieh Peng, S. Sawada, and K. Tanaka,
   Phys. Rev. D 93 (2016) 114034.