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 $μ_I a = 0.000$. Here, the gauge field ensemble with $μ_I a = 0.000, 0.048, 0.053, 0.059, 0.066, 0.080, 0.092$ and $0.106$ on a $32^3 \times 48$ lattice with non-zero isospin current strength $λa = 0.0010, 0.0018,$ and $0.0036$, where $m_π= 135$ MeV and $a = 0.1535$ fm from \cite{Brandt:2022hwy}, are used. Preliminary results suggest that for $μ_I a = 0.106$, the Upsilon mass gets heavier than the Upsilon mass in the vacuum and that below $μ_I a = 0.106$ the isospin asymmetry effect on the Upsilon mass is not monotonic.

Figures (6)

• Figure 1: The change in the mass of $^1S_0$ and $^3S_1$ quarkonium states in the $SU(2)$ gauge theory vs. the baryon chemical potential (the left) Hands:2012yy. For QCD with an isospin asymmetry, the change in the mass of $\Upsilon$ state vs. the isospin charge density(the right) Detmold:2012pi.
• Figure 2: (the left figure) Upsilon propagator with $\hat{P} = 0$ and $\hat{P}^2 = 4 \sin^2 (\frac{2\pi}{L})$. (the right figure) $a E_{\eta_b}$ (lower line and lower data points and $a E_\Upsilon$ (upper line and upper data points) vs. lattice momentum, $\hat{P}^2$ for two different $(u,d)$ current sources, $\mu_I a = 0.0$ and $\mu_I a = 0.048$. The lines are with the fitted values from the dispersion relation.
• Figure 3: The ratio of the $\Upsilon$ correlators with $\lambda a = 0.0036$ for $\mu_I a = (0.000, 0.043, 0.053, 0.059, 0.066, 0.080, 0.092)$ and $0.106$ to the $\Upsilon$ correlator with $\mu_I a = 0$.
• Figure 4: The ratio of the $\Upsilon$ correlators with $\mu_I a = 0.048$ (the left), with $\mu_I a = 0.053$ (the center), with $\mu_I a = 0.059$ (the right) for three $\lambda a = (0.0010, 0.0018, 0.0036)$$(u,d)$ current sources.
• Figure 5: The ratio of the $\Upsilon$ correlators with $\mu_I a = 0.066$ (the left), with $\mu_I a = 0.080$ (the center), with $\mu_I a = 0.092$ (the right) for three $\lambda a = (0.0010, 0.0018, 0.0036)$$(u,d)$ current sources.