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arXiv · hep-lat/0312011

Non-perturbative calculation of $Z_V$ and $Z_A$ in domain-wall QCD on a finite box

PACS Collaboration·S. Aoki·M. Fukugita·N. Ishizuka·Y. Iwasaki·K. Kanaya·T. Kaneko·Y. Kuramashi·M. Okawa·Y. Taniguchi·A. Ukawa·T. Yoshie
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Abstract

We report on a non-perturbative evaluation of the renormalization factors for the vector and axial-vector currents, $Z_V$ and $Z_A$, in the quenched domain-wall QCD (DWQCD) with plaquette and renormalization group improved gauge actions. We take the Dirichlet boundary condition for both gauge and domain-wall fermion fields on the finite box, and introduce the flavor-chiral Ward-Takahashi identities to calculate the renormalization factors. As a test of the method, we numerically confirm the expected relation that $Z_V \simeq Z_A$ in DWQCD. Employing two different box sizes for the numerical simulations at several values of the gauge coupling constant $g^2$ and the domain-wall height $M$, we extrapolate $Z_V$ to the infinite volume to remove $a/L$ errors. We finally give the interpolation formula of $Z_V$ in the infinite volume as a function of $g^2$ and $M$.

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PACS Collaboration, S. Aoki, M. Fukugita, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, M. Okawa, Y. Taniguchi, A. Ukawa, T. Yoshie. 2003-12-07. Non-perturbative calculation of $Z_V$ and $Z_A$ in domain-wall QCD on a finite box. https://doi.org/10.1103/physrevd.70.034503

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