Relation between quark-antiquark potential and quark-antiquark free energy in hadronic matter

TL;DR

This paper investigates how the quark-antiquark potential relates to the free energy in hadronic matter across different temperatures, providing insights into their equivalence and differences near the critical temperature.

Contribution

It clarifies the relationship between quark-antiquark potential and free energy at various temperatures, especially around the critical temperature, aiding in the study of hadron properties.

Findings

Potential equals free energy above critical temperature for heavy quarks.

Potential is larger than free energy for light quarks below critical temperature.

Free energy can be used as potential for studying hadron properties below critical temperature.

Abstract

In the high-temperature quark-gluon plasma and its subsequent hadronic matter created in a high-energy nucleus-nucleus collision, the quark-antiquark potential depends on the temperature. The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations. This requires one to study the relation between the quark-antiquark potential and the quark-antiquark free energy. When the system's temperature is above the critical temperature, the potential of a heavy quark and a heavy antiquark almost equals the free energy, but the potential of a light quark and a light antiquark, of a heavy quark and a light antiquark and of a light quark and a heavy antiquark is substantially larger than the free energy. When the system's temperature is below the critical temperature, the quark-antiquark free energy can be taken as the quark-antiquark potential. This allows one to apply the quark-antiquark free energy to study hadron properties and hadron-hadron reactions in hadronic matter.