Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic to SU(3)_c X SU(2)_L X U(1)_Y

TL;DR

This paper investigates how changing the gauge group structure in the Standard Model to a locally isomorphic but globally different group can lead to quantized hypercharges, identifying a unique group that achieves the correct hypercharge quantization.

Contribution

It demonstrates that among all groups locally isomorphic to the Standard Model gauge group, only a specific semidirect product group produces the observed hypercharge quantization.

Findings

Identifies the unique group structure that yields correct hypercharge quantization.

Shows that hypercharges are restricted to specific fractional values in the modified gauge group.

Establishes the role of global group properties in hypercharge quantization.

Abstract

In the Standard Model the hypercharges of quarks and leptons are not determined by the gauge group itself. In a recent paper [C. Hattori et al. Phys. Rev. D83, 015009 (2011)] it is shown that, if the direct product gauge group G_SM is slightly modified to the semidirect product group G'_SM, hypercharges are restricted to quantized values as n/6 mod Z (n = 0,1,3,4). In this brief paper, we examine all of the compact Lie groups locally isomorphic to G_SM, and show that G'_SM (or its isomorphisms) is the unique possibility that yields the correct hypercharge quantization.