Can (noncommutative) geometry accommodate leptoquarks?

TL;DR

This paper explores whether noncommutative geometry can incorporate leptoquarks into the Standard Model, analyzing geometric interpretations and comparing theoretical predictions with experimental bounds, ultimately finding contradictions.

Contribution

It provides a detailed analysis of adding leptoquarks to the noncommutative geometric formulation of the Standard Model and assesses their compatibility with experimental data.

Findings

Leptoquarks introduced without $S_0$-reality symmetry conflict with experiments.

Both Connes-Lott and spectral action approaches face contradictions when including leptoquarks.

The geometric framework cannot accommodate leptoquarks consistent with current experimental bounds.

Abstract

We investigate the geometric interpretation of the Standard Model based on noncommutative geometry. Neglecting the $S_0$-reality symmetry one may introduce leptoquarks into the model. We give a detailed discussion of the consequences (both for the Connes-Lott and the spectral action) and compare the results with physical bounds. Our result is that in either case one contradicts the experimental results.