Accessing gluon GTMD Fᵍ1,4 via the sin (2φ ) azimuthal asymmetry of exclusive π ⁰ production in ep collisions

The longitudinal single-target spin asymmetry in exclusive π ⁰ π 0 production in ep collisions is a sensitive probe of the imaginary part of the gluon generalized transverse momentum dependent distribution F1,4ᵍ F 1 , 4 g . It appears as a characteristic sin (2φ ) sin ( 2 ϕ ) azimuthal correlation between the transverse momenta of the scattered electron and the recoil proton, generated by Coulomb–nuclear interference; consequently, the Primakoff process should be included. We compute the relevant gluon distributions in a light-front spectator model of the proton that explicitly incorporates gluonic degrees of freedom. This work presents the first model calculation of the imaginary part of F1,4ᵍ F 1 , 4 g and delivers predictions for the resulting asymmetries in kinematics relevant to the planned Electron–Ion Colliders (EIC and EicC), providing theoretical predictions for upcoming measurements.