# An Effective Lagrangian for Low-Scale Technicolor

## TL;DR

This paper develops an effective Lagrangian framework for low-scale technicolor, modeling interactions of technivectors and technipions near their mass scale to support collider phenomenology.

## Contribution

It introduces a detailed effective Lagrangian based on hidden local symmetry formalism for low-scale technicolor, enhancing theoretical understanding of technivector interactions.

## Key findings

- Provides a comprehensive Lagrangian for technivectors and technipions.
- Incorporates higher-derivative and Wess-Zumino-Witten interactions.
- Supports collider search strategies for technicolor signatures.

## Abstract

We present an effective Lagrangian for low-scale technicolor. It describes the interactions at energies near the mass of the lowest-lying bound states of the lightest technifermion doublet -- the spin-one $\rho_T,\omega_T, a_T, f_T$ and the corresponding technipions $\pi_T$. This Lagrangian is intended to put on firmer ground the technicolor straw-man phenomenology used for collider searches of low-scale technicolor. The technivectors are described using the hidden local symmetry (HLS) formalism of Bando et al. The Lagrangian is based on $SU(2)\otimes U(1)\otimes U(2)_L \otimes U(2)_R$, where $SU(2)\otimes U(1)$ is the electroweak gauge group and $U(2)_L \otimes U(2)_R$ is the HLS gauge group. Special attention is paid to the higher-derivative standard HLS and Wess-Zumino-Witten interactions needed to describe radiative and other decays of the $a_T$ and $\rho_T/\omega_T$, respectively.