$J/psi$ and $eta_{c}$ in strongly magnetized nuclear matter -- a QCD sum rule approach.

The mass modifications of the charmonium states $J/psi$ and $eta_c$ in strongly magnetized nuclear matter are calculated using a QCD sum rule approach. The shifts in the masses of these states arise due to the medium modifications of the scalar and twist-2 gluon condensates. The gluon condensates are calculated within a chiral effective model, from the medium modifications of a scalar dilaton field, which is incorporated in the hadronic model to simulate the broken scale invariance of QCD. The effects of the magnetic field, isospin asymmetry and density on the masses of these charmonium states have been investigated. In the presence of the magnetic field, there are contributions from the Landau levels for the proton, the charged baryon. The anomalous magnetic moments of the nucleons have been taken into consideration in the present work, and the contributions of these effects are compared to the case when the anomalous magnetic moments are not taken into account.