Charmonium ground states in presence of strong magnetic fields

The in-medium masses of the lowest S-wave charmonium states (vector meson, $J/\psi$ and pseudoscalar meson, $\eta_c$) and P-wave charmonium states (scalar, $\chi_{c0}$ and axialvector $\chi_{c1}$) are investigated in magnetized nuclear matter, within the framework of QCD sum rule approach. These are computed from the medium modifications of the scalar as well as twist--2 gluon condensates, obtained from the medium modifications of a scalar dilaton field, within a chiral effective model. The effects of the magnetic field, isospin asymmetry and density on the masses of these charmonium states have been investigated. The modifications of the masses of the P-wave charmonium states ($\chi_{c0}$ and $\chi_{c1}$) are observed to be much larger as compared to those of the S-wave states, $J/\psi$ and $\eta_c$ within the QCD sum rule approach. The effects of the coupling of the spin with the magnetic field are also investigated in the present work, which result in the mixing of the spin zero charmonium state with the longitudinal component of the vector meson. This leads to an increase (drop) in mass of the longitudinal $J/\psi$ ($\eta_c$) for the S-wave states. The effects of the spin-magnetic field interactions are observed to be dominant at high magnetic fields.