Noncommutative Standard Model: Model Building

TL;DR

This paper constructs a noncommutative version of the Standard Model by resolving gauge group and charge quantization issues, leading to a model with unique CP violation and neutrino interactions.

Contribution

It introduces a novel noncommutative Standard Model framework by overcoming key theoretical challenges in gauge groups and charge quantization.

Findings

Resolved noncommutative gauge group issues.

Built a consistent noncommutative Standard Model.

Identified inherent CP violation and new neutrino interactions.

Abstract

A noncommutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: 1) although we can have noncommutative U(n) (which we denote by $U_{\star}(n)$) gauge theory we cannot have noncommutative SU(n) and 2) the charges in noncommutative QED are quantized to just $0, \pm 1$. We show how the problem with charge quantization, as well as with the gauge group, can be resolved by taking $U_{\star}(3)\times U_{\star}(2)\times U_{\star}(1)$ gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the noncommutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the noncommutative Standard Model (NCSM). In addition, among several peculiar features of our model, we address the {\it inherent} CP violation and new neutrino interactions.