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

Abstract

The SUð2Þ L Â SUð2Þ R chiral quark model consisting of the ð;Þ 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 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 q ¼ 0 is achieved allowing for the existence of a tricritical point or a critical end point in the q À 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.

Polyakov–Nambu–Jona-Lasinio phase diagrams and quarkyonic phase from order parameters

“…The second peak is uniquely coming from the Polyakov loop dynamics itself since in this temperature range, the quark condensate practically vanishes. This possibility of more than one peak in the temperature derivatives of the order parameters was already reported for the PNJL model [36], as well as in the linear sigma model coupled with the Polyakov loop [36][37][38]. We point out here that the construction of the phase diagram based on the choice of the coincident peaks in ∂ρ s /∂T and ∂Φ/∂T , leads to a situation where the region in which the chiral symmetry is broken (restored) and that one in which the quarks are confined (deconfined), are exactly the same.…”

Chiral transition in a magnetic field and at finite baryon density

“…The thermodynamics of the Polyakovextended quark-meson model (PQM) was studied in Refs. [14][15][16][17][18][19][20][21][22], and the PNJL model in Refs. [16,[23][24][25][26][27][28][29] Using the QM model, it is a common approximation to omit the quantum and thermal fluctuations of the * Electronic address: andersen@tf.phys.no † Electronic address: rashid.khan@ntnu.no bosonic degrees of freedom, i.e.…”

On the symmetry improved CJT formalism in the O(4) linear sigma model

“…Such an extension is straightforward but technically complicated. Finally, the O(4) linear sigma model with two quarks could be combined with the Polyakov loop which allows to investigate both the chiral and the deconfinement phase transition [40][41] [42], and recently in the two-particle irreducible (2PI) approximation, the QCD phase diagram has been already investigated in Ref [43]. Since here we have the gauge fields and the spontaneous breaking via the quark condensate, it would be more interesting to explore how the symmetry improved CJT formalism works in the Polykov-loop extended quark meson model with two or three flavors by directly comparing with the Lattice data or the other effective models.…”