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

production in ep collisions is a sensitive probe of the imaginary part of the gluon generalized transverse momentum dependent distribution

$$F_{1,4}^g$$ F 1 , 4 g

. It appears as a characteristic

$$\sin (2\phi )$$ 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

$$F_{1,4}^g$$ 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.