Is there some agreement about if the Wick rotation must produce exactly the same mass that the un-rotated equation, or is it more important to preserve some other quantity, say orbital momentum or whatever? I am thinking on Hans' relativistic [tex] \beta^2 \over \sqrt {1-\beta^2} [/tex] because if we ask this quantity to be preserved up to sign, then the masses of W and Z are mapped to the (imaginary masses) of [candidate] Higgs boson and Top quark, which is pretty puzzling: 80.37 GeV becomes 122.38 i Gev and 91.187 GeV becomes 176.15 i GeV.
The Wick rotation preserves the spectrum, so it's not possible to change the masses of states. You are trading Lorentz invariance for Euclidean invariance, the values of the particular invariants will not change.