Production cross-sections and Radiative Decay widths of Heavy Quarkonia in magnetized matter

We study the production cross-sections and radiative decay widths of heavy quarkonia (charmonia and bottomonia) in magnetized nuclear matter. The production cross-sections of the $\psi(3770)$ and $\Upsilon(4S)$, from the $D\bar D$ and $B\bar B$ scatterings respectively, are studied from the medium modifications of the masses and partial decay widths to open charm (bottom) mesons, of these heavy flavor mesons. Within a chiral effective model, the masses of the vector and pseudoscalar charmonium (bottomonium) states are calculated from the medium modification of a dilaton field, $\chi$, which mimics the gluon condensates of QCD. In the presence of a magnetic field, there is mixing of the pseudoscalar (P) meson and the longitudinal component of the vector (V) meson (PV mixing), which leads to appreciable modifications of their masses. The radiative decay widths of the vector (V) heavy quarkonia to the pseudoscalar (P) mesons ($J/\psi\rightarrow \eta_c(1S) \gamma$, $\psi(2S)\rightarrow \eta_c(2S) \gamma$ and $\psi(1D)\rightarrow \eta_c(2S) \gamma$ for the charm sector and $\Upsilon(NS)\rightarrow \eta_b(NS)\gamma$, $N$=1,2,3,4, for the bottom sector) in the magnetized asymmetric nuclear matter are also investigated in the present work. The difference in the mass of the transverse component from the longitudinal component of the vector meson, arising due to PV mixing, is observed as a double peak structure in the invariant mass spectrum of the production cross-section of $\psi(3770)$. The modifications of the production cross-sections as well as the radiative decay widths of the heavy quarkonia in the magnetized matter should have observable consequences on the production of these heavy flavour mesons resulting from ultra-relativistic peripheral heavy ion collision experiments, where the created magnetic field can be extremely large.