Infrared fixed point physics in so (Nc) and Sp (Nc) gauge theories

We study properties of asymptotically free vectorial gauge theories with gauge groups G=SO(Nc) and G=Sp(Nc) and Nf fermions in a representation R of G, at an infrared (IR) zero of the beta function, αIR, in the non-Abelian Coulomb phase. The fundamental, adjoint, and rank-2 symmetric and antisymmetric tensor fermion representations are considered. We present scheme-independent calculations of the anomalous dimensions of (gauge-invariant) fermion bilinear operators γψψ,IR to O(Δf4) and of the derivative of the beta function at αIR, denoted βIR′, to O(Δf5), where Δf is an Nf-dependent expansion variable. It is shown that all coefficients in the expansion of γψψ,IR that we calculate are positive for all representations considered, so that to O(Δf4), γψψ,IR increases monotonically with decreasing Nf in the non-Abelian Coulomb phase. Using this property, we give a new estimate of the lower end of this phase for some specific realizations of these theories.