The observability of an additional discrete symmetry in the Standard Model

Standard Model may be defined with the additional discrete symmetry, i.e. with the gauge group SU (3) × SU (2) × U (1) / Z (Z = Z₆, Z₃ or Z₂) instead of the usual SU (3) × SU (2) × U (1). It has the same perturbation expansion as the conventional one. However, it may describe nature in a different way at the energies compared to the triviality bound (of about 1 TeV). In this Letter we present a possibility to observe this difference assuming that the gauge group of the Standard Model is embedded into the gauge group of an a priori unknown model, which describes physics at a TeV scale. In particular, due to the additional Z₃ or Z₆ symmetry, monopoles with masses of the order of 10 TeV should appear, which may become the lightest topologically stable monopoles. We illustrate our results by consideration of the petite unification of quarks and leptons.