Exotic hybrid pseudopotentials at finite temperature and chemical potential

TL;DR

This paper uses gauge/gravity duality to analyze how exotic hybrid pseudopotentials, especially the $_u^-$ state, behave at finite temperature and chemical potential, revealing their sensitivity to these conditions and their melting behavior.

Contribution

It extends the defect-based hybrid meson model to finite chemical potential, comparing the behavior of $_g^+$ and $_u^-$ pseudopotentials under these conditions.

Findings

$_u^-$ pseudopotentials deviate from Coulomb-like behavior at short distances.

Temperature and chemical potential significantly decrease hybrid pseudopotentials and screen distances.

The $_u^-$ state melts more easily than the $_g^+$ ground state.

Abstract

Using gauge/gravity duality, we study the exotic hybrid pseudopotentials at finite temperature and chemical potential. The $\Sigma$ hybrid meson can be described by a model including an object called ``defect'' on a string linking the quark and antiquark. It was first proposed by Andreev and perfectly described the $\Sigma_u^-$ hybrid potential at zero temperature and chemical potential. In this paper, we would like to extend this model to finite chemical potential and compare the separate distance and pseudopotentials of $\Sigma_g^+ $ and $\Sigma_u^-$. Unlike $\Sigma_g^+$ ground state, the $\Sigma_u^-$ hybrid pseudopotentials no longer behave as Coulomb-like at short distances. In addition, temperature and chemical potential have a significant impact on the $\Sigma_u^-$ hybrid pseudopotentials. The screen distances and hybrid pseudopotentials of $\Sigma_u^-$ significantly decrease with the increase of temperature and chemical potential. At last, we draw the melting diagram of $\Sigma_g^+ $ and $\Sigma_u^-$ in the $T- \mu$ plane, and confirm that the quark-antiquark pair in $\Sigma_u^-$ excited state is easier to melt than in $\Sigma_g^+$ ground state.