Nonperturbative renormalization of composite operators with overlap fermions

Abstract

We compute nonperturbatively the renormalization constants of composite operators on a quenched ${16}^{3}\ifmmode\times\else\texttimes\fi{}28$ lattice with lattice spacing $a=0.20\text{ }\text{ }\mathrm{fm}$ 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 $\ensuremath{\mu}=1.6\text{ }\text{ }\mathrm{GeV}$. 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 ${Z}_{\ensuremath{\psi}}$ 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.