We analyze the two flavor version of the Nambu-Jona-Lasinio model with a repulsive vector coupling (GV), at finite temperature and quark chemical potential, in the strong scalar coupling (Gs) regime. Considering GV = 0, we review how finite Nc effects are introduced by means of the Optimized Perturbation Theory (OPT) which adds a term to the thermodynamical potential. This 1/ Nc suppressed term is similar to the contribution obtained at the large-Nc limit when GV ≠ 0. Then, scanning over the quark current mass values, we compare these two different model approximations showing that both predict the appearance of two critical points when chiral symmetry is weakly broken. By mapping the first order transition region in the chemical potential-current mass plane, we show that, for low chemical potential values, the first order region shrinks as μ increases but the behavior gets reversed at higher values leading to the back-bending of the critical line. This result, which could help to conciliate some lattice results with model predictions, shows the important role played by finite Nc corrections which are neglected in the majority of the works devoted to the determination of the QCD phase diagram. Recently the OPT, with GV = 0, and the large-Nc approximation, with GV ≠ 0, were compared at zero temperature and finite density for one quark flavor only. The present work extends this comparison to finite temperatures, and two quark flavors, supporting the result that the OPT finite N
Cite this paper
R. Denke, J. Macias and M. Pinto, "Critical Line Back-Bending Induced either by Finite Nc
Corrections or by a Repulsive Vector Channel," Journal of Modern Physics
, Vol. 4 No. 12, 2013, pp. 1583-1590. doi: 10.4236/jmp.2013.412195
 P. de Forcrand and O. Philipsen, Journal of High Energy Physics, Vol. 0811, 2008.
 P. de Forcrand and O. Philipsen, Journal of High Energy Physics, Vol. 0701, 2007.
 P. de Forcrand, S. Kim and O. Philipsen, “A QCD Chiral Critical Point at Small Chemical Potential: Is It There or Not?” Proceedings of the 25th International Symposium on Lattice Field Theory, Regensburg, 30 July-4 August 2009.
 K. Fukushima, Physical Review D, Vol. 78, 2008, Article ID: 114019. http://dx.doi.org/10.1103/PhysRevD.78.114019
 V. Koch, “Exploring the QCD Phase Diagram: Fluctuations and Correlations,” Proceedings of the 5th International Workshop on Critical Point and Onset of Deconfinement, Long Island, 8-12 June 2009.
 E. S. Bowman and J. I. Kapusta, Physical Review C, Vol. 79, 2009, Article ID: 015202. http://dx.doi.org/10.1103/PhysRevC.79.015202
 L. Ferroni, V. Koch and M.B. Pinto, Physical Review C, Vol. 82, 2010, Article ID: 055205. http://dx.doi.org/10.1103/PhysRevC.82.055205
 K. Fukushima, Physical Review D, Vol. 77, 2008, Article ID: 114028. http://dx.doi.org/10.1103/PhysRevD.77.114028
 S. P. Klevansky, Reviews of Modern Physics, Vol. 64, 1992, pp. 649-708. http://dx.doi.org/10.1103/RevModPhys.64.649
 M. Buballa, Physics Reports, Vol. 407, 2005, pp. 205-376. http://dx.doi.org/10.1016/j.physrep.2004.11.004
 S. Carignano, D. Nickel and M. Buballa, Physical Review D, Vol. 82, 2010, Article ID: 054009. http://dx.doi.org/10.1103/PhysRevD.82.054009
 R. Rapp, T. Schafer, E. V. Shuryak and M. Velkovsky, Physical Review Letters, Vol. 81, 1998, pp. 53-56. http://dx.doi.org/10.1103/PhysRevLett.81.53
 J.-L. Kneur, M. B. Pinto and R. O. Ramos, Physical Review C, Vol. 81, 2010, Article ID: 065205. http://dx.doi.org/10.1103/PhysRevC.81.065205
 J.-L. Kneur, M. B. Pinto, R. O. Ramos and E. Staudt, International Journal of Modern Physics E, Vol. 21, 2012, Article ID: 1250017. http://dx.doi.org/10.1142/S0218301312500176
 Y. Nambu and G. Jona-Lasinio, Physical Review, Vol. 124, 1961, pp. 246-254. http://dx.doi.org/10.1103/PhysRev.124.246
 V. Koch, T. S. Biro, J. Kunz and U. Mosel, Physics Letters B, Vol. 185, 1987, pp. 1-5. http://dx.doi.org/10.1016/0370-2693(87)91517-6
 K. Fukushima and T. Hatsuda, Reports on Progress in Physics, Vol. 74, 2011, Article ID: 014001. http://dx.doi.org/10.1088/0034-4885/74/1/014001
 P. M. Stevenson, Physical Review D, Vol. 23, 1981, pp. 2916-2944. http://dx.doi.org/10.1103/PhysRevD.23.2916