Walking Technicolor and Electroweak Radiative Corrections

TL;DR

This work studies how walking technicolor (WTC) dynamics modify the electroweak S parameter compared with QCD-like technicolor (QTC). Using the Peskin-Takeuchi dispersive formula, Analytic Continuation by Duality (ACD), and an operator-product expansion (OPE) input, the authors relate S to high-energy TC condensates and anomalous dimensions without solving the full spectrum. They find that QTC generically yields large positive S, while WTC entails a large, uncertain cancellation between a positive f_TC^2/m_C^2 contribution and a negative term tied to the large anomalous dimension, potentially yielding a small S; however, substantial theoretical uncertainties remain. Consequently, current S limits do not exclude WTC, and the results highlight the crucial role of anomalous dimensions in electroweak radiative corrections and the need for refined nonperturbative control of TC dynamics.

Abstract

We examine the effect of walking technicolor dynamics on the electroweak $S$ parameter and contrast it with the effect of QCD-like technicolor dynamics. Our main tools are the operator product expansion for the high-momentum behavior of the electroweak gauge boson vacuum polarizations and the analyticity of these polarizations which relate their low and high momentum behaviors. We show that whereas in large QCD-like technicolor models $S$ is large and positive, in walking technicolor models a negative contribution is emphasized, related to the large anomalous dimension of the technifermion condensate. Thus in walking technicolor $S$ is determined by a large cancellation of two competing effects. This may result in much smaller values of $S$ than in QCD-like technicolor, although considerable uncertainties are involved. We conclude that it is impossible to rule out walking technicolor based on the present experimental limits on $S$ and the present theoretical technology.