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String-based model with Hagedorn temperature of TH∼300  MeV describes the spectrum of mesons and glueballs

Michał Marczenko1,2,*, Győző Kovács2,3,†, Larry McLerran4, and Krzysztof Redlich2,5

  • 1Incubator of Scientific Excellence—Centre for Simulations of Superdense Fluids, University of Wrocław, plac Maksa Borna 9, 50-204 Wrocław, Poland
  • 2Institute of Theoretical Physics, University of Wrocław, plac Maksa Borna 9, 50-204 Wrocław, Poland
  • 3Institute for Particle and Nuclear Physics, HUN-REN Wigner Research Centre for Physics, 1121 Budapest, Konkoly-Thege Miklós út 29-33, Hungary
  • 4Institute for Nuclear Theory, University of Washington, Box 351550, Seattle, Washington 98195, USA
  • 5Polish Academy of Sciences PAN, Podwale 75, 50-449 Wrocław, Poland

  • *Contact author: michal.marczenko@uwr.edu.pl
  • †Contact author: gyozo.kovacs@uwr.edu.pl
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Phys. Rev. D 112, 096010 – Published 7 November, 2025

DOI: https://doi.org/10.1103/cgyz-3956

Abstract

We consider the thermodynamics of a color-confined phase of quantum chromodynamics (QCD) and pure gauge theory within a string-inspired corresponding to a physical spatial dimension, d=3. We show that the physical mass spectrum of massive mesons—in both the strange and nonstrange sectors separately—is reasonably well described and extended by the exponential mass spectrum of open strings, ρ(m), characterized by a unique Hagedorn temperature TH=3σ/2π, expressed by the string tension σ. This TH is the value appropriate for d=3 spatial dimensions and is of the order of TH∼300  MeV for typical values of the string tension. It is much larger than the values of TH 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.

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Phys. Rev. D 112, 096010– Published 7 November, 2025
  • Received 8 September 2025
  • Accepted 21 October 2025
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