T. A. Ryttov | Searcharxiv

arXiv2016

Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories

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 $α_{IR}$. We present general formulas for scheme-independent series expansions of quantities, evaluated at $α_{IR}$, as powers of an $N_f$-dependent expansion parameter, $Δ_f$. First, we apply these to calculate the derivative $dβ/dα$ evaluated at $α_{IR}$, denoted $β'_{IR}$, which is equivalent to the anomalous dimension of the ${\rm Tr}(F_{μν}F^{μν})$ operator, to order $Δ_f^4$ for general $G$ and $R$, and to order $Δ_f^5$ 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 $Δ_f^3$. 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 Padé approximants, and comparison with conventional higher-loop calculations of $β'_{IR}$ and anomalous dimensions as power series in $α$.

hep-th↗

arXiv2007

Minimal Walking Technicolor: Set Up for Collider Physics

Different theoretical and phenomenological aspects of the Minimal and Nonminimal Walking Technicolor theories have recently been studied. The goal here is to make the models ready for collider phenomenology. We do this by constructing the low energy effective theory containing scalars, pseudoscalars, vector mesons and other fields predicted by the minimal walking theory. We construct their self-interactions and interactions with standard model fields. Using the Weinberg sum rules, opportunely modified to take into account the walking behavior of the underlying gauge theory, we find interesting relations for the spin-one spectrum. We derive the electroweak parameters using the newly constructed effective theory and compare the results with the underlying gauge theory. Our analysis is sufficiently general such that the resulting model can be used to represent a generic walking technicolor theory not at odds with precision data.

hep-ph↗