  The mass modifications of the open charm ($D$ and $D^*$) mesons, and their
effects on the decay widths $D^*\rightarrow D\pi$ as well as of the charmonium
state, $\Psi(3770)$ to open charm mesons ($\Psi(3770)\rightarrow D\bar D$), are
investigated in the presence of strong magnetic fields. These are studied
accounting for the mixing of the pseudoscalar ($P$) and vector ($V$) mesons
($D-D^*$, $\eta_c'-\Psi(3770)$ mixings), with the mixing parameter, $g_{PV}$ of
a phenomenological three-point ($PV\gamma$) vertex interaction determined from
the observed radiative decay width of $V\rightarrow P\gamma$. For charged
$D-D^*$ mixing, this parameter is dependent on the magnetic field, because of
the Landau level contributions to the vacuum masses of these mesons. The masses
of the charged $D$ and $D^*$ mesons modified due to $PV$ mixing, in addition,
have contributions from the lowest Landau levels in the presence of a strong
magnetic field. The effects of the magnetic field on the decay widths are
studied using a field theoretic model of composite hadrons with quark (and
antiquark) consittuents. The parameter for the charged $D-D^*$ mixing is
observed to increase appreciably with increase in the magnetic field. This
leads to dominant modifications to their masses, and hence the decay widths of
charged $D^*\rightarrow D\pi$ as well as $\Psi(3770)\rightarrow D^+D^-$ at
large values of the magnetic field. The modifications of the masses and decay
widths of the open and hidden charm mesons in the presence of strong magnetic
fields should have observable consequences on the production of the open charm
($D$ and $D^*$) mesons as well as of the charmonium states resulting from
non-central ultrarelativistic heavy ion collision experiments.
