Conformal Behavior at Four Loops and Scheme (In)Dependence

Preprint number: CP3-Origins-2014-30 DNRF90 and DIAS-2014-30
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We search for infrared zeros of the beta function and evaluate the anomalous dimension of the mass at the associated fixed point for asymptotically free vector-like fermionic gauge theories with gauge group $$SU(N)$$. The fixed points of the beta function are studied at the two, three and four loop level in two different explicit schemes. These are the modified regularization invariant, RI’, scheme and the minimal momentum subtraction, mMOM, scheme. We then compare to earlier identical investigations performed in the modified minimal subtraction, $$\overline{\text{MS}}$$, scheme.

It is found that the value of the anomalous dimension of the mass is smaller at three and four loops than at two loops. This seems to be a generic pattern that is observed in all three different schemes. The results indicate that previous similar higher order observations of a small value of the anomalous dimension of the mass at the fixed point carry little scheme dependence and therefore is quite trustable.