Derivation of Electroweak Chiral Lagrangian from One Family Technicolor Model

TL;DR

This paper derives the electroweak chiral Lagrangian from a one family technicolor model, calculating its coefficients dynamically and confirming their proportionality to technicolor and technifermion numbers, thus supporting previous theoretical arguments.

Contribution

It provides a first-principles derivation of the electroweak chiral Lagrangian coefficients from the technicolor model, validating their dependence on model parameters.

Findings

Coefficients are proportional to $N_{TC}$ and $N_{TF}$.

Results confirm previous theoretical expectations.

Demonstrates a dynamical computation method for effective Lagrangian coefficients.

Abstract

Based on previous studies deriving the chiral Lagrangian for pseudo scalar mesons from the first principle of QCD in the path integral formalism, we derive the electroweak chiral Lagrangian and dynamically compute all its coefficients from the one family technicolor model. The numerical results of the $p^4$ order coefficients obtained in this paper are proportional to the technicolor number $N_{\rm TC}$ and the technifermion number $N_{\rm TF}$, which agrees with the arguments in previous works, and which confirms the reliability of this dynamical computation.