A remark on the large difference between the glueball mass and $\mth{T_{c}}$ in quenched QCD

N. Ishii; H. Suganuma

doi:doi:10.1140/epja/i2002-10147-0

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2020 Impact factor 3.043

Hadrons and Nuclei

Eur. Phys. J. A 17, 77-82 (2003)
DOI: 10.1140/epja/i2002-10147-0

A remark on the large difference between the glueball mass and $\mth{T_{c}}$ in quenched QCD

N. Ishii¹ and H. Suganuma²

¹ Radiation Laboratory, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
² Faculty of Science, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro, Tokyo 152-8551, Japan

ishii@rarfaxp.riken.go.jp
suganuma@th.phys.titech.ac.jp

(Received: 18 November 2002 / Revised version: 16 January 2003 / Published online: 29 April 2003)

Abstract
The lattice QCD studies indicate that the critical temperature $T_{\rm c} \simeq 260\mbox{--}280$ MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass $m_{\rm G} \simeq 1500\mbox{--}1700$ MeV, i.e., $T_{\rm c} \ll m_{\rm G}$ . As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor $e^{-m_{\rm G}/T_{\rm c}} \simeq 0.00207$ even near $T \simeq T_{\rm c}$ . 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 between $T_{\rm c}$ 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 ?"

PACS
12.38.Mh - Quark-gluon plasma.
12.38.Gc - Lattice QCD calculations.
12.39.Ba - Bag model.
12.39.Mk - Glueball and nonstandard multi-quark/gluon states.

© Società Italiana di Fisica, Springer-Verlag 2003