Renormalization group flow of linear sigma model with $U_A(1)$ anomaly

In the presence of finite $U_A(1)$ breaking, chiral phase transition of massless two-flavor QCD is studied by tracing the renormalization group flow of the corresponding effective theory. In the framework of the $\epsilon$ expansion, it is found that the nature of the phase transition depends on the initial condition for the parameters of the effective theory and that, when it undergoes second order phase transition, one of the universal exponents shows a different value from that in the standard $O(4)$ linear sigma model. We discuss that the origin of the difference is attributed to a non-decoupling effect. The present status of the calculation of the effective potential is presented.