Higher-Order Scheme-Independent Series Expansions of $\gamma_{\bar\psi\psi,IR}$ and $\beta'_{IR}$ in Conformal Field Theories

Understand

We study a vectorial asymptotically free gauge theory, with gauge group $G$ and $N_f$ massless fermions in a representation $R$ of this group, that exhibits an infrared (IR) zero in its beta function, $\beta$, at the coupling $\alpha=\alpha_{IR}$ 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, $\gamma_{\bar\psi\psi,IR}$, to $O(\Delta_f^4)$ and (ii) the derivative $\beta' = d\beta/d\alpha$, to $O(\Delta_f^5)$, both evaluated at $\alpha_{IR}$, where $\Delta_f$ is an $N_f$-dependent expansion variable.
• These are the highest orders to which these expansions have been calculated.
• We apply these general results to theories with $G={\rm SU}(N_c)$ and $R$ equal to the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations.