Mass independence of critical exponents in perturbation theory

The suggestion of Dash and Harrington that the critical exponent γ at the fixed point may be found in perturbation theory by its independence of the mass is investigated in the Reggeon calculus and in phi4 theory in three dimensions (phi4)3. We discuss an ambiguity due to the choice of energy scale and find an invariant criterion for determining the point of mass independence. Neither the Reggeon calculus nor (phi4)3 satisfies this criterion, and no natural choice of energy scale works for (phi4)3 in second order