Preprint number: CP3-Origins-2017-34 DNRF90

Authors:

We study properties of asymptotically free vectorial gauge theories with

gauge groups $G={rm SO}(N_c)$ and $G={rm Sp}(N_c)$ and $N_f$ fermions in a

representation $R$ of $G$, at an infrared (IR) zero of the beta function,

$alpha_{IR}$, 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

$gamma_{barpsipsi,IR}$ to $O(Delta_f^4)$ and of the derivative of the

beta function at $alpha_{IR}$, denoted $beta’_{IR}$, to $O(Delta_f^5)$,

where $Delta_f$ is an $N_f$-dependent expansion variable. It is shown that

all coefficients in the expansion of $gamma_{barpsipsi,IR}$ that we

calculate are positive for all representations considered, so that to

$O(Delta_f^4)$, $gamma_{barpsipsi,IR}$ increases monotonically with

decreasing $N_f$ 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.