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We investigate the medium modifications of the masses of pseudoscalar opencharm ($D$ and $\bar D$) mesons and the charmonium state ($\psi(3770)$) inmagnetized hot isospin asymmetric strange hadronic medium within a chiraleffective model. The partial decay widths of $\psi(3770)$ to $D\bar D$ mesonsare computed from the medium modifications of the in-medium masses of thesemesons, using (I) the $^3P_0$ model and (II) a field theoretical (FT) model ofcomposite hadrons with quark (and antiquark) constituents. The productioncross-sections of $\psi(3770)$, arising from scattering of the $D$ and $\bar D$mesons are obtained from the in-medium masses and the decay widths of thecharmonium state. The effects of the magnetic field are considered due to theDirac sea (DS) of the baryons, the mixing of the pseudoscalar ($S$=0) andvector ($S$=1) meson (PV mixing), the Landau level contributions for thecharged hadrons. The anomalous magnetic moments (AMMs) of the baryons are alsotaken into account in the present study. For $\rho_B=\rho_0$, the inclusion ofhyperons in the medium is observed to lead to magnetic catalysis (MC), contraryto inverse magnetic catalysis (IMC) observed for magnetized nuclear matter. Theproduction cross-section of $\psi(3770)$ in the hot magnetized strange hadronicmatter is observed to have a distinct double peak structure arising from the PVmixing. This is because of the fact that the mass of the longitudinal componentof the charmonium state is modified by PV mixing, whereas, the masses of thetransverse components remain unaffected. These can have observable consequenceson the dilepton spectra as well as on the production of the charm mesons inultra-relativistic peripheral heavy ion collision experiments, where theproduced magnetic field is huge.

Charmonium production in hot magnetized hyperonic matter -- effects of baryonic Dirac sea and PV mixing