Nonlinear Regge trajectories and saturation of the Hagedorn spectrum

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.