Limits on hadron spectrum from bulk medium properties

TL;DR

This paper investigates how lattice QCD measurements of bulk medium properties constrain the growth of the hadron spectrum, challenging the Hagedorn hypothesis unless significant repulsive interactions are included.

Contribution

It demonstrates that the observed thermodynamic properties limit the exponential growth of resonance states in the hadron spectrum, implying the need for repulsive interactions at high masses.

Findings

Rapid resonance growth is incompatible with lattice data without repulsion.

Hagedorn spectrum extension above 1.8 GeV affects thermodynamics near transition temperature.

Repulsive interactions are necessary to reconcile spectrum growth with lattice results.

Abstract

We bring up the fact that the bulk thermal properties of the hadron gas, as measured on the lattice, preclude a very fast rising of the number of resonance states in the QCD spectrum, as assumed by the Hagedorn hypothesis, unless a substantial repulsion between hadronic resonances is present. If the Hagedorn growth continued above masses ~1.8 GeV, then the thermodynamic functions would noticeably depart from the measured lattice values at temperatures above 140 MeV, just below the transition temperature to quark-gluon plasma.