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 $\mu$ = 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 $Z_{\psi }$ 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.

arXiv comment40 pages, 20 figures

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Cited by in corpus (12)

• Overlap Valence on 2+1 Flavor Domain Wall Fermion Configurations with Deflation and Low-mode Substitution
• Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice
• Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
• Non-perturbative renormalization of overlap quark bilinears on 2+1-flavor domain wall fermion configurations
• Three loop anomalous dimensions of higher moments of the non-singlet twist-2 Wilson and transversity operators in the MSbar and RI' schemes
• Three loop MSbar operator correlation functions for deep inelastic scattering in the chiral limit
• Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
• Non-perturbative renormalization of bilinear operators with dynamical overlap fermions
• Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme
• Chiral extrapolation beyond the power-counting regime
• RI'/SMOM scheme amplitudes for deep inelastic scattering operators at one loop in QCD
• Bilinear quark operator renormalization at generalized symmetric point