Nonperturbative renormalization of composite operators with overlap fermions

Abstract

We compute non-perturbatively the renormalization constants of composite operators on a quenched $16^3\times 28$ lattice with lattice spacing $a$ = 0.20 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 $\hat{I}¼$ = 1.6 GeV. %even for our lattice with a coarse lattice spacing. 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 $Z_{\ddot{I}}ˆ$ 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.

40 pages, 20 figures