Model analysis on thermal UV-cutoff effects on the critical boundary in hot QCD

We study the critical boundary on the quark-mass plane associated with the chiral phase transition in QCD at finite temperature. We point out that the critical boundaries obtained from the Lattice QCD simulation and the chiral effective model are significantly different; in the (Polyakov-loop coupled) Nambu--Jona-Lasinio (NJL) model we find that the critical mass is about one order of magnitude smaller than the value reported in the Lattice QCD case. It is known in the Lattice QCD study that the critical mass goes smaller in the continuum limit along the temporal direction. To investigate the temporal UV-cutoff effects quantitatively we consider the (P)NJL model with only finite $N_\tau$ Matsubara frequencies taken in the summation. We confirm that the critical mass in such a UV-tamed NJL model becomes larger with decreasing $N_\tau$, which demonstrates a correct tendency to explain the difference between the Lattice QCD and chiral model results.