Influence of the Polyakov loop on the chiral phase transition in the two flavor chiral quark model

The SU(2)_L×SU(2)_R chiral quark model consisting of the (σ,π→) meson multiplet and the constituent quarks propagating on the homogeneous background of a temporal gauge field is solved at finite temperature and quark baryon chemical potential μ_q using an expansion in the number of flavors N_f, both in the chiral limit and for the physical value of the pion mass. Keeping the fermion propagator at its tree level, several approximations to the pion propagator are investigated. These approximations correspond to different partial resummations of the perturbative series. Comparing their solution with a diagrammatically formulated resummation relying on a strict large-N_f expansion of the perturbative series, one concludes that only when the local part of the approximated pion propagator resums infinitely many orders in 1/N_f of fermionic contributions a sufficiently rapid crossover transition at μ_q=0 is achieved allowing for the existence of a tricritical point or a critical end point in the μ_q-T phase diagram. The renormalization and the possibility of determining the counterterms in the resummation provided by a strict large-N_f expansion are investigated.