content_image/333963.jpg content_image/333971.jpg
## I. Final result 

<img src='content_image/333963.jpg'>

Table I shows a summary of our estimate of the systematic errors in our determination of α$_{s}$ ( M$_{Z}$ ). We quote final result of the strong coupling constant at the Z boson mass scale as 

<img src='content_image/333971.jpg'>

Here, the first error is statistical error and the second is a sum of the various systematic errors in quadrature. 

This result is consistent with other recent lattice QCD results 0.1174(12) [9], 0.1183(8) [31], 0.1192(11) [32], 0.1205(8)(5)( + 0 − $_{17}$)[33], and with the world average 0.1184(7) including various high-energy experiments [1, 2] (updated on-line in 2010). 

## V. CONCLUSIONS 

Determination of the strong coupling constant α$_{s}$ ( µ ) may be achieved through a pertur- bative expansion of any physical quantity in terms of α$_{s}$ ( µ ) at a given scale µ . Experimental determination typically uses a perturbative amplitude of quarks at high energy. Comparison with the lattice QCD calculation provides a highly non-trivial test of QCD, as lattice uses 

