Hypercolor tower

TL;DR

This paper proposes a comprehensive ultraviolet completion of the Standard Model using an infinite sequence of Hypercolor gauge groups, incorporating technicolor and additional symmetries to address fermion masses and anomaly cancellation.

Contribution

It introduces a novel gauge group structure with an infinite Hypercolor sequence and a discrete symmetry, providing a new framework for fermion mass generation and anomaly-free hypercharge assignments.

Findings

Existence of a hypercharge assignment with no chiral anomaly.

Preservation of a discrete symmetry extending Z6 of the Standard Model.

A model where fermion masses are independent of technicolor dynamics.

Abstract

We construct the ultraviolet completion of the Standard Model that contains an infinite sequence of Hypercolor gauge groups. So, the whole gauge group of the theory is $... \otimes SU(5)\otimes SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$. Here SU(4) is the Technicolor group of Farhi - Susskind model. The breakdown of chiral symmetry due to the the Technicolor gives rise to finite $W$ and $Z$ boson masses in a usual way. The other Hypercolor groups are not confining. We suggest the hypothesis that the fermion masses are not related in any way to technicolor gauge group. We suppose that the fermion mass formation mechanism is related to the energies much higher than the technicolor scale. Formally the fermion masses appear in our model as an external input. In the construction of the theory we use essentially the requirement that it posseses an additional discrete symmetry $\cal Z$ that is the continuation of the $Z_6$ symmetry of the Standard Model. It has been found that there exists such a choice of the hypercharges of the fermions that the chiral anomaly is absent while the symmetry $\cal Z$ is preserved.