Medium modifications of Heavy Quarkonia masses in a generalized Linear Sigma Model

We study the mass shifts of the charmonium ($\bar{c}c$) states ($J/\psi$, $\psi(2S)$, $\psi(1D)$, $\chi_{c0}$, $\chi_{c1}$ and $\chi_{c2}$) as well as the bottomonium ($\bar{b}b$) states ($\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon_2(1D)$, $\chi_{b0}$, $\chi_{b1}$ and $\chi_{b2}$) in isospin asymmetric nuclear matter. These are investigated using a generalized linear sigma model. The broken scale invariance of QCD is incorporated in the chiral $SU(2)\times SU(2)$ Lagrangian through an effective potential involving logarithmic terms of a scalar (glueball) dilaton field $\chi$. The mass shifts of the quarkonium states are obtained through the medium modifications of the dilaton field which simulates the scalar gluon condensate of QCD. We observe an appreciable mass drop in the states of heavy quarkonia under this study. The in-medium masses at finite densities thus obtained should modify the in-medium partial decay widths of heavy quarkonia to open heavy flavor mesons. These density effects can be probed in in the high energy nuclear collisions at the future facility at GSI (at Germany) and JINR (at Russia) in the experiments producing highly dense baryonic matter.