Scheme-independent series expansions at an infrared zero of the beta function in asymptotically free gauge theories

Abstract

We consider an asymptotically free vectorial gauge theory, with gauge group G and Nf fermions in a representation R of G, having an infrared (IR) zero in the beta function at αIR. We present general formulas for scheme-independent series expansions of quantities, evaluated at αIR, as powers of an Nf-dependent expansion parameter, Δf. First, we apply these to calculate the derivative dβ/dα evaluated at αIR, denoted βIR′, which is equivalent to the anomalous dimension of the Tr(FμνFμν) operator, to order Δf4 for general G and R, and to order Δf5 for G=SU(3) and fermions in the fundamental representation. Second, we calculate the scheme-independent expansions of the anomalous dimension of the flavor-nonsinglet and flavor-singlet bilinear fermion antisymmetric Dirac tensor operators up to order Δf3. The results are compared with rigorous upper bounds on anomalous dimensions of operators in conformally invariant theories. Our other results include an analysis of the limit Nc→, Nf→ with Nf/Nc fixed, calculation and analysis of Padé approximants, and comparison with conventional higher-loop calculations of βIR′ and anomalous dimensions as power series in α.