content_image/360665.jpg content_image/360666.jpg content_image/360667.jpg
<img src='content_image/360665.jpg'>

<img src='content_image/360666.jpg'>

<img src='content_image/360667.jpg'>

Strictly speaking, χ $^{2}$/ dof does not have a statistical meaning as the correlation among the data at difference Q 2 is ignored in the fit used here. We discuss on the statistical correlations among the data points in the next section. 

The limitation of the OPE formula including up to 1 /Q 4 terms can be investigated by looking at its departure from the lattice data at lower values of Q $^{2}$. In Figure 4 we plot the difference of the lattice data from the fit curve including the 1 /Q 4 terms. The Q 2 region in this plot is extended towards the value below ( aQ ) 2 $_{min}$. From this plot, we observe that the next order 1 /Q 6 contribution becomes significant below ( aQ ) 2 ≃ 0.4. We therefore set ( aQ ) 2 min = 0 . 463 in our analysis including the 1 /Q 4 terms. 

After doing a simultaneous fit of the VPF data at all sea quark masses, the QCD parame- ter is obtained as Λ (3) MS = 0.247(5) GeV. By matching onto four- and then to five-flavor QCD at charm and bottom quark masses respectively, the strong coupling constant is obtained as 

