Quarkonium in non-zero isospin chemical potential environment at $T \simeq 0$

Abstract

We study how the isospin asymmetry affects quarkonium states in QCD at near zero temperature. Using lattice Non-Relativistic QCD formalism, we calculate bottom quark correlators in the gauge field ensembles generated with $N_f = 2 + 1$ flavors of dynamical staggered quarks whose dynamics include the isospin chemical potential effect and then construct $S-$ and $P-$ wave quarkonium state correlators. From these quarkonium correlators, we consider the ratios of quarkonium correlators at non-zero isospin chemical potential to that at $\mu_I a = 0.000$. Here, the gauge field ensemble with $\mu_I a = 0.000, 0.048, 0.053, 0.059, 0.066, 0.080, 0.092$ and $0.106$ on a $32^3 \times 48$ lattice with non-zero isospin current strength $\lambda a = 0.0010, 0.0018,$ and $0.0036$, where $m_\pi = 135$ MeV and $a = 0.1535$ fm from \cite{Brandt:2022hwy}, are used. Preliminary results suggest that for $\mu_I a = 0.106$, the Upsilon mass gets heavier than the Upsilon mass in the vacuum and that below $\mu_I a = 0.106$ the isospin asymmetry effect on the Upsilon mass is not monotonic.