Conformal Invariance and Degrees of Freedom in the QCD String

TL;DR

This paper uses the growth pattern of meson states to constrain the degrees of freedom in the QCD string, finding a higher temperature than expected and supporting conformal invariance in hadronic spectra.

Contribution

It demonstrates that the observed meson spectrum constrains the effective QCD string's degrees of freedom and clarifies the relevant temperature, aligning with conformal invariance.

Findings

The relevant string temperature is higher than the traditional Hagedorn temperature.

The D_perp=2 scalar string model agrees well with experimental data.

Conformal and modular invariance are reflected in the hadronic spectrum.

Abstract

We demonstrate that the Hagedorn-like growth of the number of observed meson states can be used to constrain the degrees of freedom of the underlying effective QCD string. We find that the temperature relevant for such string theories is not given by the usual Hagedorn value $T_H\approx 160$ MeV, but is considerably higher. This resolves an apparent conflict with the results from a static quark-potential analysis, and suggests that conformal invariance and modular invariance are indeed reflected in the hadronic spectrum. We also find that the $D_\perp=2$ scalar string is in excellent agreement with data.