String-based model with Hagedorn temperature of $T_H\sim 300~$MeV describes the spectrum of mesons and glueballs

TL;DR

This paper models the meson and glueball spectra in QCD using string-inspired exponential mass spectra characterized by a Hagedorn temperature around 300 MeV, aligning well with lattice QCD thermodynamics results.

Contribution

It introduces a string-based model with a Hagedorn temperature of about 300 MeV that accurately describes meson and glueball spectra and thermodynamics in QCD.

Findings

The Hagedorn temperature for mesons is around 300 MeV.

String models agree with lattice QCD results in the confined phase.

Glueball states exhibit a similar large Hagedorn temperature.

Abstract

We consider the thermodynamics of a color-confined phase of quantum chromodynamics (QCD) and pure gauge theory within a string-inspired model, corresponding to a physical spatial dimension, d = 3. We show that the physical mass spectrum of massive mesons--in both the strange and non-strange sectors separately--is reasonably well described and extended by the exponential mass spectrum of open strings, $\rho(m)$, characterized by a unique Hagedorn temperature, $T_H = \sqrt{3\sigma/2\pi}$, expressed by the string tension, $\sigma$. This $T_H$ is the value appropriate for d = 3 spatial dimensions, and is of order $T_H \sim 300~\rm MeV$ for typical values of the string tension. It is much larger than the values of $T_H$, which have been phenomenologically extracted so far to describe the meson spectrum. Glueball states in pure gauge theory, modeled by closed strings, exhibit a similarly large Hagedorn temperature, highlighting a universal feature of the exponential spectrum. We further analyze the thermodynamic properties of the equation of state at finite temperature and demonstrate that, in the confined phase, the string models agree with lattice QCD results. This lends further support to the recent interpretation of the QCD phase diagram that incorporates strings as relevant degrees of freedom.