In-medium decay widths of hidden and open charm vector mesons in a field theoretic model for composite hadrons

We calculate the decay widths of the charmonium states, $J/\psi$, $\psi (3686)$ and $\psi(3770)$, to $D\bar D$ pairs, as well as the decay width of $D^* \rightarrow D\pi$, in isospin asymmetric strange hadronic matter, using a field theoretical model for composite hadrons with quark constituents. For this purpose we use the quark antiquark pair creation term of the free Dirac Hamiltonian written in terms of the constituent quark field operators, and use explicit charmonium, $D$, $\bar {D}$, $D^*$ and $\pi$ states to evaluate the matrix elements for the charmonium as well as $D^*$ decay amplitudes. The medium modifications of the partial decay widths of charmonium to $D\bar D$ pair, arising from the mass modifications of the $D(\bar D)$ and the charmonium states calculated in a chiral effective model, are also included. The effects of the isospin asymmetry, the strangeness fraction of the hadronic matter on the masses of the charmonium states and $D(\bar D)$ mesons and hence on the decay widths, have also been studied. The decay width of $D^* \rightarrow D \pi$ in the hadronic matter has also been calculated within the composite quark model in the present work, accounting for the medium modifications of the $D$ and $D^*$ masses. The density modifications of the charmonium states and $D(D^*)$ mesons, which are observed to be appreciable at high densities, will be of relevance in the compressed baryonic matter (CBM) experiments at the future facility of FAIR, GSI, where charmed hadrons will be produced by annihilation of antiprotons on nuclei. The interactions of the charmonium states and $D(D^*)$ with the nuclear medium could lead to the possiblility of the formation of exotic bound states of the nuclei with the (excited) charmonium states as well as with $D(D^*)$ mesons.