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The extension of the Nambu-Jona-Lasino Model with six and eight quarkinteractions to include the Polyakov loop is analysed. Several interestingfeatures are determined to be an effect of the choice of the regularizationprocedure. The use of a Pauli-Villars covariant regularization enables acoherent and correct description of several quantities.

The Polyakov-Nambu-Jona-Lasinio model with six and eight quark interactions