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

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

2003-12-07

arxiv.org/abs/hep-lat/0312011v1

Phys.Rev. D70 (2004) 034503

Physics

High Energy Physics

High Energy Physics - Lattice

37 pages, 8 figures

Scientific paper

10.1103/PhysRevD.70.034503

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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