  The nature of chiral phase transition of massless two flavor QCD depends on
the fate of flavor singlet axial symmetry $U_A(1)$ at the critical temperature
($T_c$). Assuming that a finite $U_A(1)$ breaking remains at $T_c$, the
corresponding three dimensional effective theory is composed of four massless
and four massive scalar fields. We study the renormalization group flow of the
effective theory in the $\epsilon$-expansion, using a mass dependent
renormalization scheme, and determine the region of the attractive basin
flowing into the $O(4)$ fixed point with a focus on its dependence on the size
of the $U_A(1)$ breaking. The result is discussed from a perspective of the
decoupling of massive fields. It is pointed out that, although the effective
theory inside the attractive basin eventually reaches the $O(4)$ fixed point,
the approaching rate, one of the universal exponents, is different from that of
the standard $O(4)$ model. We present the reason for this peculiarity, and
propose a novel possibility for chiral phase transition in two-flavor QCD.
