Nonlinear Regge trajectories and saturation of the Hagedorn spectrum

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.