Wilsonian effective action for SU(2) Yang-Mills theory with(8)

The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the fl

The resulting?βfunction is a factor of44/7smaller than theβfunction of full Yang-Mills theory for SU(2).This is an expected result,since we did not integrate over all degrees of freedom of the gauge?eld;the n integration still remains.Nevertheless,the ?βfunction implies asymptotic freedom,which indicates that the decomposition of the

Yang-Mills?eld is not a pathologically absurd choice.It is interesting to observe that the C and W determinants contribute positively to?βg2,whereas the Faddeev-Popov and theφdeterminant contribute negatively;the latter,which arises from the W?xing,even dominates:?7/3=[6C?4FP+40W?49φ]/3.

The third term of Eq.(14)contains information about the renormalization of the gauge parameterαunder the?ow:

1

αg2+

5

16π2

t,??t?αR=

7

28

?αR ?g2R

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