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

The lattice QCD studies indicate that the critical temperature $T_c \simeq 260-280$ MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass $m_{\rm G} \simeq 1500-1700$ MeV, i.e., $ T_c \ll m_{\rm 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 $e^{-m_{\rm G}/T_c} \simeq 0.00207$ even near $T \simeq T_c$. 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 $T_c$ 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 ?''