$J/\psi$ and $\eta_c$ in asymmetric hot magnetized nuclear matter

We investigate the mass-shift of vector channel $J/\psi$ and pseudoscalar channel $\eta_c$ in strongly magnetized asymmetric nuclear medium at finite temperature using the conjunction of chiral $SU(3)$ model with the QCD sum rules. The magnetic field dependence of scalar gluon condensate $\left\langle \frac{\alpha_{s}}{\pi} G^a_{\mu\nu} {G^a}^{\mu\nu} \right\rangle$ as well as the twist-2 gluon condensate $\left\langle \frac{\alpha_{s}}{\pi} G^a_{\mu\sigma} {{G^a}_\nu}^{\sigma} \right\rangle$ calculated from chiral SU($3$) model, are implemented in QCD sum rules to calculate the magnetic field dependence of $J/\psi$ and $\eta_c$ meson masses. The effects of constant external magnetic field at finite density and temperature of the medium are found to be appreciable in symmetric and asymmetric nuclear matter. The results of the present investigation may be helpful to understand the experimental observables arising from the Compressed Baryonic Matter (CBM) produced in asymmetric non-central heavy ion collision experiments.