Minimal Walking Technicolor: Set Up for Collider Physics

TL;DR

This work constructs a collider-ready, low-energy effective theory for Minimal Walking Technicolor by embedding composite scalars, pseudoscalars, and vector mesons into a SU(4)→SO(4) framework and coupling them to Standard Model fields. It leverages generalized Weinberg sum rules to connect the effective theory to the underlying strongly coupled dynamics, showing that walking behavior can yield relatively light spin-one resonances with a modest S parameter, especially when new leptons offset precision constraints. The authors provide explicit Lagrangians, mass relations, and parameter mappings to enable phenomenological studies at colliders, while maintaining generality for walking and non-walking (QCD-like) dynamics. Overall, the paper offers a comprehensive and practical framework to explore dynamical electroweak symmetry breaking in collider phenomenology with controlled theoretical consistency.

Abstract

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.

Figures (3)

• Figure 1: In the picture above we have set $10^3 \hat{S}=1$, corresponding to $S\simeq 0.11$. In the appendix we have provided the relation between $\hat{S}$ and the traditional S. Here we have imposed the first and the second WSR for $a=0$. This corresponds to an underlying gauge theory with a standard running behavior of the coupling constant.
• Figure 2: In the two pictures above we have set $10^3 \hat{S}=1$, corresponding to $S\simeq 0.11$, and the different curves are obtained by varying $\tilde{g}$ from one (the thinnest curve) to eight (the thickest curve). We have imposed the first WSR. Left Panel: We plot the allowed values of $M_A-M_V$ as function of $M_A$. Right Panel: We compute the value that $a$ should assume as function of $M_A$ in order for the second WSR to be satisfied in the walking regime. Note that $a$ is expected to be positive or zero.
• Figure 3: The ellipses represent the 68% confidence region for the $S$ and $T$ parameters. The upper ellipse is for a reference Higgs mass of the order of a TeV, the lower curve is for a light Higgs with mass around 114 GeV. The contribution from the MWT theory per se and of the leptons as function of the new lepton masses is expressed by the dark grey region. The left panel has been obtained using a SM type hypercharge assignment while the right hand graph is for $y=1$.