Abstract
We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$) gauge theories with fermions transforming according to two different representations. We first study a theory with $N_f$ fermions in the fundamental representation and $N_{f'}$ fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit $N_c \to \infty$, $N_f \to \infty$ with $N_f/N_c$ fixed and finite. We then study the $N_c \to \infty$ limit of a theory with fermions in the adjoint and rank-2 symmetric or antisymmetric tensor representations.
Highlights
We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SUðNcÞ gauge theories with fermions transforming according to two different representations
We first study a theory with Nf fermions in the fundamental representation and Nf0 fermions in the adjoint or symmetric or antisymmetric rank-2 tensor representation, in the limit Nc → ∞, Nf → ∞ with Nf=Nc fixed and finite
In this paper we extend the recent study in Ref. [1] on calculations of scheme-independent series expansions for the anomalous dimensions and the derivative of the beta function at an infrared fixed point (IRFP) of the renormalization group in gauge theories with two different fermion representations
Summary
In this paper we extend the recent study in Ref. [1] on calculations of scheme-independent series expansions for the anomalous dimensions and the derivative of the beta function at an infrared fixed point (IRFP) of the renormalization group in gauge theories with two different fermion representations. Previous works have investigated these properties for a variety of theories with a general gauge group G and Nf fermions ψi, i 1⁄4 1; ...; Nf transforming according to a single representation R of G, using perturbative calculations of the anomalous dimension of the operator ψψ, denoted γψψ , and of the derivative of the beta function, dβ=dα 1⁄4 β0, both evaluated at the IRFP [3,4,5], [9,10,11,12,13,14,15,16] We denote these as γψψ;IR and β0IR.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have