Kaon superfluidity in the early universe

TL;DR

This paper investigates the theoretical possibility of kaon superfluidity in the early universe, extending previous work on pion superfluidity, and concludes it is unlikely due to stability issues and quark density constraints.

Contribution

It explores the potential for kaon superfluidity in the early universe using a Ginzburg-Landau approach within the PNJL model, extending prior pion superfluidity studies.

Findings

Kaon superfluidity is less stable than pion superfluidity in the early universe.

Large s-quark densities required for kaon superfluidity are not feasible in early universe conditions.

Kaon superfluidity is unlikely to occur due to stability and density constraints.

Abstract

Previously, it was found that pion superfluidity could be realized in the QCD epoch of the early universe, when lepton flavor asymmetry $|l_{\rm e}+l_\mu|$ is large enough to generate a charge chemical potential $|\mu_{\rm Q}|$ larger than vacuum pion mass. By following the same logic, kaon superfluidity might also be possible when $|l_{\rm e}+l_\mu|$ is so large that $|\mu_{\rm Q}|$ becomes larger than vacuum kaon mass. Such a possibility is checked by adopting Ginzburg-Landau approximation within the three-flavor Polyakov--Nambu--Jona-Lasinio model. Consider the case with full chemical balance, though kaon superfluidity could be stable compared to the chiral phases with only $\sigma$ condensations, it would get killed by the more favored homogeneous pion superfluidity. If we introduce mismatch between $s$ and $d$ quarks, kaon superfluidity would require so large $s$ quark density that such a state is impossible in the early universe.