Preprint number: CP3-Origins-2016-39 DNRF90

Authors:

External link: arXiv.org

We consider an asymptotically free vectorial gauge theory, with gauge group $G$

and $N_f$ fermions in a representation $R$ of $G$, having an infrared (IR) zero

in the beta function at $alpha_{IR}$. We present general formulas for

scheme-independent series expansions of quantities, evaluated at $alpha_{IR}$,

as powers of an $N_f$-dependent expansion parameter, $Delta_f$. First, we

apply these to calculate the derivative $dbeta/dalpha$ evaluated at

$alpha_{IR}$, denoted $beta’_{IR}$, which is equal to the anomalous dimension

of the ${rm Tr}(F_{munu}F^{munu})$ operator, to order $Delta_f^4$ for

general $G$ and $R$, and to order $Delta_f^5$ for $G={rm SU}(3)$ and fermions

in the fundamental representation. Second, we calculate the scheme-independent

expansions of the anomalous dimension of the flavor-nonsinglet and

flavor-singlet bilinear fermion antisymmetric Dirac tensor operators up to

order $Delta_f^3$. The results are compared with rigorous upper bounds on

anomalous dimensions of operators in conformally invariant theories. Our other

results include an analysis of the limit $N_c to infty$, $N_f to infty$

with $N_f/N_c$ fixed, calculation and analysis of Pad’e approximants, and

comparison with conventional higher-loop calculations of $beta’_{IR}$ and

anomalous dimensions as power series in $alpha$.