Higher-order scheme-independent series expansions of γψ¯ψ,IR and βIR′ in conformal field theories

We study a vectorial asymptotically free gauge theory, with gauge group G and Nf massless fermions in a representation R of this group, that exhibits an infrared (IR) zero in its beta function, β, at the coupling α=αIR in the non-Abelian Coulomb phase. For general G and R, we calculate the scheme-independent series expansions of (i) the anomalous dimension of the fermion bilinear, γψψ,IR, to O(Δf4) and (ii) the derivative β′=dβ/dα, to O(Δf5), both evaluated at αIR, where Δf is an Nf-dependent expansion variable. These are the highest orders to which these expansions have been calculated. We apply these general results to theories with G=SU(Nc) and R equal to the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. It is shown that for all of these representations, γψψ,IR, calculated to the order Δfp, with 1≤p≤4, increases monotonically with decreasing Nf and, for fixed Nf, is a monotonically increasing function of p. Comparisons of our scheme-independent calculations of γψψ,IR and βIR′ are made with our earlier higher n-loop values of these quantities, and with lattice measurements. For R=F, we present results for the limit Nc→ and Nf→ with Nf/Nc fixed. We also present expansions for αIR calculated to O(Δf4).