Di-$$\pi ^0$$ production and generalized distribution amplitudes at future electron-ion colliders

Abstract 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 $$\gamma ^*\gamma \rightarrow h_1 h_2.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>γ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>γ</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:msub> <mml:mi>h</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> 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- $$\pi ^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> 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- $$\pi ^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> GDAs at the EIC.