Heavy quarkonia in QGP medium in an arbitrary magnetic field

We compute the heavy quarkonium complex potential in an arbitrary magnetic field strength generated in the relativistic heavy-ion collision. First, the one-loop gluon polarization tensor is obtained in the presence of an external, constant, and homogeneous magnetic field using the Schwinger proper time formalism in Euclidean space. The gluon propagator is computed from the gluon polarization tensor, and it is used to calculate the dielectric permittivity in the presence of the magnetic field in the static limit. The modified dielectric permittivity is then used to compute the heavy quarkonium complex potential. We find that the heavy quarkonium complex potential is anisotropic in nature, which depends on the angle between the quark-antiquark ($Q\bar{Q}$) dipole axis and the direction of the magnetic field. We discuss the effect of the magnetic field strength and the angular orientation of the dipole on the heavy quarkonium potential. We discuss how the magnetic field influences the thermal widths of quarkonium states. Further, we also discuss the limitation of the strong-field approximation as done in literature in the light of heavy-ion observables, as the effect of the magnetic field is very nominal to the quarkonium potential.