A Remark on the Large Difference between the Glueball Mass and T(C) in Quenched QCD

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The lattice QCD studies indicate that the critical temperature Tc ≃ 260-280 MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass m G ≃ 1500-1700 MeV, i.e., Tc ≪ m G. As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor as e-m G/Tc ≃ 0.00207 even near T ≃ Tc. We consider its physical implication, and argue the abnormal feature of the deconfinement phase transition in quenched QCD from the statistical viewpoint. To appreciate this, we demonstrate a statistical argument of the QCD phase transition using the recent lattice QCD data. From the phenomenological relation among Tc and the glueball mass, the deconfinement transition is found to take place in quenched QCD before a reasonable amount of glueballs is thermally excited. In this way, quenched QCD reveals a question ``what is the trigger of the deconfinement phase transition?''