Nonlinear Regge trajectories and saturation of the Hagedorn spectrum

TL;DR

This paper links the saturation phenomena of Hagedorn's resonance distribution and Regge trajectories, suggesting both originate from quark deconfinement, with Regge slopes influencing the resonance density.

Contribution

It establishes a theoretical connection between saturation of Regge trajectories and the Hagedorn spectrum, highlighting the role of Regge slopes in resonance density.

Findings

Regge trajectory saturation relates to quark deconfinement.

The slope of Regge trajectories influences the Hagedorn resonance density.

Both phenomena share a common origin in QCD dynamics.

Abstract

We argue that two seemingly different phenomena, namely the well-known saturation of the Hagedorn exponential distribution and the less familiar saturation of Regge trajectories at resonance masses $m\approx$ 2-2.5 GeV are related and have the same origin: quark deconfinement. We show that the slope of the real part of non-linear Regge trajectories determines the prefactor $f(m)$ in Hagedorn's resonance mass density distribution $\rho(m)$. While the Hagedorn distribution comes from statistics, Regge trajectories contain dynamics.