Quarkonium at non-zero isospin density

TL;DR

This study uses lattice QCD to analyze how quarkonium energies are affected by non-zero isospin density, revealing energy reductions and saturation linked to phase transitions in the medium.

Contribution

It provides the first lattice QCD calculation of quarkonium energy shifts in a non-zero isospin density medium and determines relevant scattering phase shifts.

Findings

Quarkonium energies decrease with increasing isospin density.

Energy shifts saturate near the pion gas to Bose-Einstein condensate transition.

Scattering lengths for $ ext{η}_b$-$ ext{π}$ and $ ext{Υ}$-$ ext{π}$ are estimated at physical pion mass.

Abstract

We calculate the energies of quarkonium bound states in the presence of a medium of nonzero isospin density using lattice QCD. The medium, created using a canonical (fixed isospin charge) approach, induces a reduction of the quarkonium energies. As the isospin density increases, the energy shifts first increase and then saturate. The saturation occurs at an isospin density close to that where previously a qualitative change in the behaviour of the energy density of the medium has been observed, which was conjectured to correspond to a transition from a pion gas to a Bose-Einstein condensed phase. The reduction of the quarkonium energies becomes more pronounced as the heavy-quark mass is decreased, similar to the behaviour seen in two-colour QCD at non-zero quark chemical potential. In the process of our analysis, the $\eta_b$-$\pi$ and $\Upsilon$-$\pi$ scattering phase shifts are determined at low momentum. An interpolation of the scattering lengths to the physical pion mass gives $a_{\eta_b,\pi} = 0.0025(8)(6)$ fm and $a_{\Upsilon,\pi} = 0.0030(9)(7)$ fm.