Does the empirical meson spectrum support the Hagedorn conjecture?

TL;DR

This paper critically examines whether the observed meson spectrum supports the Hagedorn conjecture, concluding that current data and models do not provide strong evidence for an exponential Hagedorn spectrum in QCD.

Contribution

The paper argues that existing meson spectrum data and quark models do not convincingly support the Hagedorn conjecture and highlights limitations in current evidence and analysis methods.

Findings

Realistic quark models mimic meson spectrum growth without having Hagedorn spectra.

Available data cannot reliably determine the Hagedorn temperature.

Spectral behavior across channels conflicts with exponential growth expectations.

Abstract

It has long been conjectured that strong interactions give rise to a Hagedorn spectrum and theoretical arguments have been presented in support of Hagedorn spectrum in large $N_c$ QCD. This paper discusses the extent to which the meson spectrum should be viewed as evidence for a Hagedorn spectrum and argues that data do not provide a strong evidence for the Hagedorn conjecture. The conclusion is based on three reasons. It is shown that "realistic" quark models have a spectrum in which the number of mesons up to 2.3 GeV grows with mass in a very similar way to the spectrum of physical mesons up to 2.3 GeV. However, these models can be shown not to have Hagedorn spectra. It is also shown that the available data are insufficient to determine the Hagedorn temperature. The data can be described with comparable accuracy by various functional forms of the prefactor that yield radically different Hagedorn temperatures. An analysis of the behavior of the spectrum for the various parity-spin-charge conjugation-isospin channels also appears to be inconsistent with what one expects if the data were in the regime dominated by exponential behavior.