Di-$\pi^0$ Production and Generalized Distribution Amplitudes at Future Electron-Ion Colliders

Generalized distribution amplitudes (GDAs) offer valuable insights into the three-dimensional structure of hadrons, delineating the amplitudes associated with the transition from a quark-antiquark pair to a hadron pair. Currently, hadron GDAs can be probed in electron-positron collisions, with experimental feasibility demonstrated at facilities such as Belle and BESIII. In this study, we put forth the proposition that hadron GDAs can also be investigated in electron-hadron collisions at forthcoming Electron-Ion Colliders (EICs), specifically through the subprocess $\gamma^*\gamma \to h_1 h_2$. In this framework, a quasi-real photon, emitted by the ion, exhibits a photon flux proportional to the square of the ion's electric charge. Consequently, we anticipate that the cross sections in EICs will be substantially larger than those in electron-positron collisions. We present numerical calculations pertaining to di-$\pi^0$ production employing the equivalent photon approximation (EPA). Our findings suggest that, within the same kinematic region, electron-proton ($e$-$p$) collisions at the EIC could yield an event rate comparable to that of Belle II, while electron-gold ($e$-Au) collisions are expected to generate an even greater number of events. This enhanced event rate facilitates a high-precision examination of di-$\pi^0$ GDAs at the EIC.