Nonperturbative renormalization of composite operators with overlap fermions

We compute nonperturbatively the renormalization constants of composite operators on a quenched 163×28 lattice with lattice spacing a=0.20fm 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 ZA=ZV and ZS=ZP and find that they agree well (less than 1%) above μ=1.6GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the MS̄ scheme. The wave function renormalization Zψ is determined from the vertex function of the axial current and ZA 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.