0 0.01 0.02 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (aQ) 2 0 0.01 0.02 m$_{q}$=0.015 m$_{q}$=0.025 m$_{q}$=0.035 m$_{q}$=0.050 m$_{s}$=0.08 m$_{s}$=0.10 $_{V+A}$(Q) FIG. 4: Difference between the lattice data and the fit function (14). Dashed line shows a guiding line representing the 1 /Q 6 behavior. α (5) s ( M$_{Z}$ ) = 0 . 1181(3) at the Z boson mass scale. Here, the error is statistical only. Various sources of the systematic error are discussed in the next section. First of all, our fit procedure of VPF may induce systematic error due to the use of uncorrelated fit. Namely, in the fit described above, we did not take the correlation among different Q 2 points into account and estimated the statistical error for the fit parameters using the jackknife method. In order to estimate the associated error, we calculated the statistical correlation of different Q 2 points and found it very strong (50–100%). If we construct χ 2 taking account of the correlation, the value of χ $^{2}$/dof is of order 100. This unacceptably large value occurs because the fit function (14) does not contain the discretization effects that violate Lorentz symmetry. Indeed, if we restrict the data points for those that each momentum component is equal to or smaller than 2 π/ 16, the χ $^{2}$/dof is reduced to 1.7, without changing the central 12 A. Uncorrelated fit IV. SYSTEMATIC ERRORS AND FINAL RESULT