# Charmonia and Bottomonia in asymmetric magnetized hot nuclear matter

## TL;DR

This paper studies how magnetic fields and nuclear matter conditions affect the masses of certain charmonium and bottomonium states using QCD sum rules and chiral models, revealing attractive mass shifts relevant for heavy ion collisions.

## Contribution

It combines QCD sum rules with chiral SU(3) models to analyze meson mass shifts in magnetized hot asymmetric nuclear matter, a novel integrated approach.

## Key findings

- Mass shifts are attractive for both charmonium and bottomonium.
- Mass shifts are more sensitive to magnetic fields in high-density regimes for charmonium.
- Results aid understanding of quarkonium decay in asymmetric heavy ion collisions.

## 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.