Physics of the Non-Abelian Coulomb Phase: Insights from Pad\'e Approximants

Understand

We consider a vectorial, asymptotically free SU($N_c$) gauge theory with $N_f$ fermions in a representation $R$ having an infrared (IR) fixed point.

• We calculate and analyze Pad\'e approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, $\gamma_{\bar\psi\psi,IR}$, to $O(\Delta_f^4)$, and the derivative of the beta function, $\beta'_{IR}$, to $O(\Delta_f^5)$, where $\Delta_f$ is an $N_f$-dependent expansion variable.
• We consider the fundamental, adjoint, and rank-2 symmetric tensor representations.
• The results are applied to obtain further estimates of $\gamma_{\bar\psi\psi,IR}$ and $\beta'_{IR}$ for several SU($N_c$) groups and representations $R$, and comparisons are made with lattice measurements.