Associate production J/ψ plus γ at the Large Hadron Collider and Electron-Ion Collider

Charmonium production associated with a photon in coherent hadron-hadron interactions at high-energy colliders is a suitable observable to test the partonic density function in the proton and in nuclei. We employ nonrelativistic quantum chromodynamics to investigate the transverse momentum distribution and total cross sections of J/psi + gamma production at the Large Hadron Collider (LHC) and the electron-ion collider (EIC). Our results show that discrimination can be made to test the parameters for the matrix elements operators, which varies by a factor of 3. A higher transverse momentum region is more sensitive for pPb collisions at the LHC, although the EIC kinematic region is also favorable at low transverse momentum.