  The masses and decay widths of charmonium states are studied in the presence
of strong magnetic fields. The mixing between the pseudoscalar and vector
charmonium states at rest is observed to lead to appreciable negative
(positive) shifts in the masses of the pseudoscalar (longitudinal component of
the vector) charmonium states in vacuum/hadronic medium in the presence of high
magnetic fields. The pseudoscalar and vector charmonium masses in the hadronic
medium, calculated in an effective chiral model from the medium changes of a
scalar dilaton field, have additional significant modifications due to the
mixing effects. The masses of the $D$ and $\bar D$ mesons in the magnetized
hadronic matter are calculated within the chiral effective model. The partial
decay widths of the vector charmonium state to $D\bar D$ are computed using a
field theoretical model for composite hadrons with quark/antiquark
constituents, and are compared to the decay widths calculated using an
effective hadronic Lagrangian. The effects of the mixing are observed to lead
to significant contributions to the masses of the pseusoscalar and vector
charmonium states, and an appreciable increase in the decay width $\psi(3770)
\rightarrow D\bar D$ at large values of the magnetic fields. These studies of
the charmonium states in strong magnetic fields should have observable
consequences on the dilepton spectra, as well as on the production of the open
charm mesons and the charmonium states in ultra relativistic heavy ion
collision experiments.
