Different Hagedorn temperatures for mesons and baryons from experimental mass spectra, compound hadrons, and combinatorial saturation

TL;DR

This study reveals that baryons have a lower Hagedorn temperature than mesons up to 1.8GeV, due to faster state growth, explained by a combinatorial model with an excitation energy limit causing a maximum hadron mass.

Contribution

It introduces a model where hadrons are compound objects of quanta, explaining the different Hagedorn temperatures and the saturation in hadron spectra.

Findings

Baryons have about 30% lower Hagedorn temperature than mesons.

The rapid growth of hadronic states is a combinatorial effect.

There is an upper limit on the excitation energy, leading to a maximum hadron mass.

Abstract

We analyze the light-flavor particle mass spectra and show that in the region up to ~1.8GeV the Hagedorn temperature for baryons is about 30% smaller than for mesons, reflecting the fact that the number of baryon states grows more rapidly with the mass. We also show that the spectra are well reproduced in a model where hadrons are compound objects of quanta, whose available number increases with mass. The rapid growth of number of hadronic states is a combinatorial effect. We also point out that an upper limit on the excitation energy of these quanta results in a maximum number of hadron states that can be formed. According to this combinatorial saturation, no more light-flavor hadron resonances exist above a certain mass.