Z6 symmetry of the Standard Model and Technicolor theory

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.

A Superstructure Over the Farhi–susskind Technicolor Model

“…Recently we have shown [1] that the Z 6 symmetry of the Standard Model [2,3,4,5,6] (SM) can be continued to the Technicolor models (TC). It was shown that among various models only a few ones possess the new discrete symmetry Z.…”

“…That's why we do not consider it as realistic and the only possibility remains that is the SU(4) Farhi -Susskind model. This model (together with the Standard Model) has the gauge group SU(4)⊗ SU(3) ⊗ SU(2) ⊗ U (1). The hypercharge assignment for the technifermions is fixed by the additional discrete symmetry up to an integer number.…”

“…The structure of the gauge group SU(4) ⊗SU(3) ⊗SU( 2) ⊗U(1) prompts its possible continuation as the infinite sequence of SU(N) subgroups: G = ... ⊗ SU(6) ⊗ SU(5) ⊗ SU(4) ⊗ SU(3) ⊗ SU(2) ⊗ U(1)/Z, (1) where Z is the discrete group to be specified below.…”

“…In the present paper we construct such a continuation. We arrange the fermions of the model in the fundamental representations of SU(N) subgroups of (1). In general case the model with the gauge group (1) suffers from chiral anomalies of different types.…”

“…We arrange the fermions of the model in the fundamental representations of SU(N) subgroups of (1). In general case the model with the gauge group (1) suffers from chiral anomalies of different types. It is not obvious a priori that there exists the hypercharge assignment of the fermions such that the chiral anomalies are absent while the additional discrete symmetry is preserved.…”