0.1 0.15 aQ 2sin(aQ ) 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 (aQ) 2 0.1 0.15 m$_{s}$=0.08 m$_{s}$=0.10 FIG. 2: Comparison of Π$_{V}$$_{+}$$_{A}$( Q ) with different momentum definitions. Lattice data at m$_{q}$ = 0 . 015. Figure 1 shows a ( aQ ) 2 dependence of Π$_{V}$$_{+}$$_{A}$( Q ) in a window 0 . 4 ≤ ( aQ ) 2 ≤ 1 . 0. Fit curves shown in this plot are those of (14) with the value of parameters extracted from the fit in the range 0 . 463 ≤ ( aQ ) 2 ≤ 0 . 994. The upper limit of the range is chosen to avoid significant lattice artifact, which is estimated by a difference of the lattice momentum aQ$_{µ}$ from the other definition a ˆ Q$_{µ}$ . In fact, the result is unchanged within 1 σ level when we use these different definitions of the momentum as Figure 2 shows, as far as ( aQ ) 2 is lower than 1.0. Beyond this value we observe significant deviations between the different definitions. We also impose a constraint aQ$_{µ}$ < π/ 4 for each momentum component to avoid large lattice artifacts. In order to determine the lower limit, we investigate the stability of the fit results. Figure 3 shows the dependence of fit parameters on the value of the lower limit ( aQ ) 2 $_{min}$. We observe that around ( aQ ) 2 min = 0.4–0.5 all the parameters are stable. It is interesting to see where the 1 /Q 4 term becomes significant. In Figure 3, the fit results without the 1 /Q 4 terms are also shown by filled symbols. It turned out that the value of Λ (3) MS is consistent with the 1 /Q 4 fits when ( aQ ) 2 min is greater than 0.5, which means that the 1 /Q 4 terms become relevant below this value. In fact, if we extend this fit including the data points slightly below ( aQ ) 2 = 0 . 5, the value of Λ (3) MS becomes significantly lower; the χ $^{2}$/ dof of the fit becomes too large ( ∼ 3.0), which suggests that the fit is no longer valid. 10