We compute nonperturbatively the renormalization constants of composite operators on a quenched ${16}^3\times 28$ lattice with lattice spacing $a=0.20\mathrm{fm}$ for the overlap fermion by using the regularization-independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations $Z_A=Z_V$ and $Z_S=Z_P$ and find that they agree well (less than 1%) above $\mu =1.6\mathrm{GeV}$. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the $\overline{\mathrm{MS}}$ scheme. The wave function renormalization $Z_{\psi }$ is determined from the vertex function of the axial current and $Z_A$ from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the $(pa{)}^2$ errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

• Received 3 August 2005

DOI:https://doi.org/10.1103/PhysRevD.72.114509