Chiral meson masses at the critical point from QCD in the improved ladder approximation

Chiral meson masses at the critical point is investigated using QCD in the improved ladder approximation. We calculate the effective potential at finite temperature $T$ and quark chemical potential $\mu$ and find the critical point at $T \simeq 95$ MeV, $\mu \simeq 290$ MeV. The chiral meson masses are determined from the second derivative of the effective potential at its minimum. We find that the sigma goes to massless at the critical point while pion remains massive. Our results are consistent with that of the linear sigma model in contrast to the Nambu--Jona-Lasinio model.