  We discuss the chiral phase transition in hot and dense QCD with three light
flavors. Inspired by the well known fact that the U_A(1) anomaly could induce
first order phase transitions, we study the effect of the possible restoration
of the U_A(1) symmetry at finite density. In particular, we explore the link
between the U_A(1) restoration and the recent lattice QCD results of de
Forcrand and Philipsen, in which the first order phase transition region near
zero chemical potential (mu) shrinks in the quark mass and mu space when mu is
increased. Starting from the Ginzburg-Landau theory for general discussions, we
then use the Nambu--Jona-Lasinio model for quantitative studies. With the
partial U_A(1) restoration modeled by the density dependent 't Hooft
interaction, we fit the shrinking of the critical surface found in de Forcrand
and Philipsen's lattice calculation at low mu. At higher mu, the critical
surface might shrink or expand, depending on the scenarios. This raises the
possibility that despite the shrinking of the critical surface at lower mu, the
QCD critical end point might still exist due to the expansion at higher mu. In
this case, very high precision lattice data will be needed to detect the
back-bending of the critical surface with the currently available analytic
continuation or Taylor expansion approaches. Lattice computations could,
however, test whether the U_A(1) restoration is responsible for the shrinking
of the critical surface by computing eta' mass or the topological
susceptibility at small mu.
