$Z_6$ symmetry of the Standard Model and Technicolor theory

TL;DR

This paper explores extending the $Z_6$ symmetry of the Standard Model to Technicolor theories, identifying specific models where this symmetry can be preserved, and analyzing hypercharge assignments for minimal models.

Contribution

It demonstrates that only certain SU(N) Technicolor models, specifically SU(4) Farhi-Susskind, can maintain the $Z_6$ symmetry, and shows how hypercharge assignments can preserve this symmetry in minimal models.

Findings

Only SU(4) Farhi-Susskind model can have the $Z_6$ symmetry.

Hypercharge assignment in minimal SU(2) Technicolor can preserve the symmetry.

The $Z_6$ symmetry can be extended to specific Technicolor models.

Abstract

We consider the possibility to continue the $Z_6$ symmetry of the Standard Model to the Technicolor theories. Among the SU(N) Weinberg - Susskind models and the SU(N) Farhi - Susskind models for $N>2$ only the SU(4) Farhi - Susskind model may possess the mentioned symmetry. We also show that the hypercharge assignment of Minimal Walking SU(2) Technicolor model may be chosen in such a way that the additional discrete symmetry is preserved.