Critical Behaviour in Statistical Qcd

• Hadrons have an intrinsic size, with a radius rh ≃ 1 fm, and hence a hadron needs a space of volume Vh ≃ (4π/3)r 3 h in order to exist. This suggests a limiting density nc of hadronic matter 1, with nc = 1/Vh ≃ 1.5 n0, where n0 ≃ 0.17 fm −3 denotes the density of normal nuclear matter. • Hadronic interactions provide abundant resonance production, and the resulting number ρ(m) of hadron species increases exponentially as function of the resonance mass m, ρ(m) ∼ exp(bm). Such a form for ρ(m) appeared first in the statistical bootstrap model, based on self-similar resonance formation or decay2. It was then also obtained in the more dynamical dual resonance approach3. In hadron thermodynamics, the exponential increase of the resonance degeneracy results in an upper limit for the temperature of hadronic matter2, Tc = 1/b ≃ 150− 200 MeV. • What happens beyond Tc? In QCD, hadrons are dimensionful color-neutral bound states of more basic pointlike colored quarks and gluons. Hadronic matter, consisting of colorless constituents of hadronic dimensions, can therefore turn at high temperatures and/or densities into a quark-gluon