Higher order correction to the RG $\beta $-function for the 3-d Anderson localization transition at unitary symmetry

We have recently calculated the $\beta $-function of the conductance for Anderson Metal-Insulator transition including contributions from the ballistic regime. In three dimensional unitary case, the result of two-loop order diagrams is $\beta $(g)=1-a/g, where a is a constant and g is the dimensionless conductance. However, this result is valid only if there is no diagram with extra diffusons which contributes to the order of 1/g. We show that diagrams with extra diffuson propagators only have higher order contributions in the ballistic regime, which confirms our previous result.