By Fukaya, H

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The low-mode-approximated correlator is compared with the corresponding exact one. The 20+|Q| low-modes are not sufficient to evaluate the axial correlators but they are enough for the pseudo-scalar correlators at long distances. 2), which is most sensitive to Fπ and not contaminated by the parameters m0 and α. 16 shows. a ¯ A naive definition of the axial vector current is Aaµ (x) = ψ(x)γ 5 γµ (τ /2)ψ(x), constructed from the overlap fermion field ψ(x). Note that it is not the conserved current associated with the lattice chiral symmetry, and (finite) renormalization is needed to relate it to the continuum axial-vector current.

6) Thus, our lattice QCD simulation is performed as follows, 1. Choose a starting link variable configuration. 2. Choose η ≡ (D + m)−1 φh to be a field of Gaussian noise (heat-bath). 3. Choose the momentum of link variables, πµ (x) from a Gaussian noise. 4. Nmds molecular dynamics with the step-size ∆τ are done. 5. Accept or reject the new configuration (Metropolis test). 6. Store the (new or old) configuration. 7. Return to step 2. 7) involves the calculation of (D + m)−1 , which requires a very expensive computational cost in the chiral limit, m → 0, since a lot of low eigenvalues appear.

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