Dual meson condensates in the Polyakov-loop extended linear sigma model

Abstract

Dual meson condensates as possible order parameters for deconfinement are investigated in a Polyakov-loop enhanced linear sigma model of QCD at both zero and finite isospin chemical potential ${\mu }_I$. We find that the rapid rise of the dual sigma condensate (corresponding to the dressed Polyakov-loop) with $T$ is driven by the chiral transition, no matter whether the Polyakov-loop dynamics is included or not. For ${\mu }_I>m_{\pi }/2$, the dual sigma condensate shows abnormal thermal behavior which even decreases with $T$ below the melting temperature $T_c^{I_3}$ of pion superfluidity; On the other hand, even the dual pion condensate always increases with $T$, its maximum slope locates exactly at $T_c^{I_3}$ rather than the deconfinement temperature $T_c^P$ determined by the Polyakov-loop. All these are qualitatively consistent with the previous results obtained in the Nambu-Jona-Lasinio type models. The dual vector meson condensate for ${\mu }_I>m_{\pi }/2$ is also calculated. This quantity is more sensitive to the chiral transition when taking into account the Dirac-sea contribution. Our study further suggests that it should be cautious to use dual observables to indicate the deconfinement transition, especially in QCD models.

arXiv comment9 pages,7 figures, discussions added, references added, typos corrected

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