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Medium-Induced Quarkonium Dissociation at Finite Chemical Potential and Weak Magnetic Field

We investigate the in-medium modification and dissociation of heavy quarkonium in a hot QCD medium at finite quark chemical potential and in the weak magnetic-field regime. Starting from the one-loop resummed gluon propagator in the imaginary-time formalism, and incorporating non-perturbative effects through a phenomenological correction to the HTL description, we compute the real and imaginary parts of the dielectric permittivity. This, in turn, leads to a complex heavy-quark potential: the real part is used to determine binding energies by solving the nonrelativistic Schrödinger equation, while the imaginary part generates thermal decay widths, dominated by Landau damping. Within the explored parameter range, temperature has the greatest control over Debye screening, potential modification, and quarkonium stability, whereas finite density and weak magnetic fields introduce comparatively smaller quantitative changes. As the temperature increases, binding energies decrease and thermal widths grow, giving rise to the expected hierarchy between ground and excited states and a sequential suppression pattern in the dissociation temperatures. Overall, our results indicate that while finite chemical potential and weak magnetic fields can shift quarkonium properties in a measurable way, thermal effects remain the primary driver of dissociation, with direct relevance for heavy-ion collision phenomenology.