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Effective Potential and Phase Diagram in the Strong-Coupling Lattice QCD with Next-to-Next-to-Leading Order and Polyakov Loop Effects

We investigate chiral and deconfinement transitions in the strong coupling lattice QCD for color SU(3). We combine the leading order Polyakov loop effective action of the strong coupling expansion and the next-to-next-to-leading order (1/g^4) fermionic effective action with one species of unrooted staggered fermion. Two approximation schemes are adopted to evaluate the Polyakov loop effects; a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The Polyakov loop is found to suppress the chiral condensate and to reduce the chiral transition temperature at mu = 0. The chiral transition temperature roughly reproduces the Monte Carlo results in the region beta = 2N_c /g^2 < 4.