A statistical approach to the QCD phase transition --A mystery in the critical temperature

Abstract

We study the QCD phase transition based on the statistical treatment with the bag-model picture of hadrons, and derive a phenomenological relation among the low-lying hadron masses, the hadron sizes and the critical temperature of the QCD phase transition. We apply this phenomenological relation to both full QCD and quenched QCD, and compare these results with the corresponding lattice QCD results. Whereas such a statistical approach works well in full QCD, it results in an extremely large estimate of the critical temperature in quenched QCD, which indicates a serious problem in understanding of the QCD phase transition. This large discrepancy traces back to the fact that enough number of glueballs are not yet thermally excited at the critical temperature T_c \simeq 280 MeV in quenched QCD due to the extremely small statistical factor as exp(-m_G/T_c) \simeq 0.00207. This fact itself has a quite general nature independent of the particular choice of the effective model framework. We are thus arrive at a mystery, namely, what is really the trigger of the deconfinement phase transition.