Accessing gluon GTMD $F^g_{1,4}$ via the $\langle\sin(2\phi)\rangle$ azimuthal asymmetry of exclusive $\pi^0$ production in $ep$ collisions

Abstract

The longitudinal single-target spin asymmetry in exclusive $\pi^0$ production in $ep$ collisions is a sensitive probe of the imaginary part of the gluon generalized transverse momentum dependent distribution $F_{1,4}^g$. It appears as a characteristic $\sin(2\phi)$ 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 $F_{1,4}^g$ 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.