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 $$\pi ^0$$ <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 in ep collisions is a sensitive probe of the imaginary part of the gluon generalized transverse momentum dependent distribution $$F_{1,4}^g$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:mi>g</mml:mi> </mml:msubsup> </mml:math> . It appears as a characteristic $$\sin (2\phi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>sin</mml:mo> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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 $$F_{1,4}^g$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:mi>g</mml:mi> </mml:msubsup> </mml:math> 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.