$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right)$ as a symmetry of division algebraic ladder operators

TL;DR

This paper explores a division algebra-based model resembling $SU(5)$ grand unified theory, which potentially avoids proton decay by restricting certain algebraic transitions, resulting in a modified Standard Model gauge group with an extra $U(1)_X$ symmetry.

Contribution

It introduces a novel algebraic framework using division algebras to construct a GUT-like model that suppresses proton decay and extends the Standard Model gauge group with an additional $U(1)_X$ symmetry.

Findings

Proposes a division algebra-based ladder operator model similar to $SU(5)$.

Suggests proton decay is suppressed due to forbidden algebraic transformations.

Identifies a gauge group $G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb{Z}_6$ with an extra $U(1)_X$ symmetry.

Abstract

We demonstrate a model which captures certain attractive features of $SU(5)$ theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, and $\mathbb{O}$. From the $SU(n)$ symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow's $SU(5)$ grand unified theory. However, in this case, the transitions leading to proton decay are expected to be blocked, given that they coincide with presumably forbidden transformations which would incorrectly mix distinct algebraic actions. As a result, we find that we are left with $G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb{Z}_6$. Finally, we point out that if $U(n)$ ladder symmetries are used in place of $SU(n)$, it may then be possible to find this same $G_{sm}=SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb{Z}_6$, together with an extra $U(1)_X$ symmetry, related to $B-L$.