I am trying to compute, using mathematica, the renormalization $Z$s (of the field, mass and coupling) in $\phi^4$ theory (using dimentional regularization). I have done so in two different subtraction schemes, the mass-shell subtraction scheme and minimal subtraction.
The ratios of the respective $Z$s in the two schemes is 1 for the mass and coupling constant (when the epsilon of dimreg goes to zero).
For the field Z, I find a ratio of 6. Has someone seen this before? Is there a way to verify it? I've been told that anomalous dimensions should be the same in different subtraction schemes but: computing the beta function and other anomalous dimensions in the mass-shell scheme is quite difficult because the Zs depend on the mass. How can I verify my result of 6?