Scheme-independent calculations of physical quantities in an N=1 supersymmetric gauge theory

We consider an asymptotically free, vectorial, N=1 supersymmetric gauge theory with gauge group G and Nf pairs of chiral superfields in the respective representations R and R of G, having an infrared fixed point (IRFP) of the renormalization group at αIR. We present exact results for the anomalous dimensions of various (gauge-invariant) composite chiral superfields γΦprod at the IRFP and prove that these increase monotonically with decreasing Nf in the non-Abelian Coulomb phase of the theory and that scheme-independent expansions for these anomalous dimensions as powers of an Nf-dependent variable, Δf, exhibit monotonic and rapid convergence to the exact γΦprod throughout this phase. We also present a scheme-independent calculation of the derivative of the beta function, dβ/dα|α=αIR, denoted βIR′, up to O(Δf3) for general G and R, and, for the case G=SU(Nc), R=F, we give an analysis of the properties of βIR′ calculated to O(Δf4).