Charmonia and Bottomonia in asymmetric magnetized hot nuclear matter

Abstract: We investigate the mass-shift of $P$-wave charmonium (${\chi_c}0$, ${\chi_c}_1$) and $S$ and $P$-wave bottomonium ($\eta_b$, $\Upsilon$, ${\chi_b}_0$ and ${\chi_b}_1$) states in magnetized hot asymmetric nuclear matter using the unification of QCD sum rules (QCDSR) and chiral $SU(3)$ model. Within QCDSR, we use two approaches, $i.e.$, moment sum rule and Borel sum rule. The magnetic field induced scalar gluon condensate $\left\langle \frac{\alpha{s}}{\pi} G^a_{\mu\nu} {G^a}^{\mu\nu} \right\rangle$ and the twist-2 gluon operator $\left\langle \frac{\alpha_{s}}{\pi} G^a_{\mu\sigma} {{G^a}_\nu}^{\sigma} \right\rangle $ calculated in chiral $SU(3$) model are utilised in QCD sum rules to calculate the in-medium mass-shift of above mesons. The attractive mass-shift of these mesons is observed which is more sensitive to magnetic field in high density regime for charmonium, but less for bottomonium. These results may be helpful to understand the decay of higher quarkonium states to the lower quarkonium states in asymmetric heavy ion collision experiments.