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Unified Pati-Salam from Noncommutative Geometry: Overview and Phenomenological Remarks

Ufuk Aydemir

TL;DR

The paper addresses the lack of clear new-physics signals at the LHC by leveraging noncommutative geometry and the spectral action to derive unified geometric frameworks that include the Standard Model and gravity, and then to realize Pati-Salam gauge structures with gauge-coupling unification. It identifies three NCG-based PS models (A, B, C) with restricted scalar content, and highlights Model C, which accommodates a TeV-scale leptoquark $S_1$ with left-handed couplings that can address flavor anomalies such as $R_{D^{(*)}}$ while automatically avoiding proton decay due to the absence of diquark couplings. The framework provides a predictive, geometrically motivated path to beyond-Standard-Model physics with concrete phenomenological implications for flavor observables and collider searches. Overall, the work suggests that the spectral action in NCG offers a unified, testable approach to connecting geometry to particle physics and guiding future experimental probes.

Abstract

The lack of clear new-physics signals at the LHC searches motivates models that can guide current and future collider searches. The spectral action principle within the noncommutative geometry (NCG) framework yields such models with distinctive phenomenology. This formalism derives the actions of the Standard Model, General Relativity, and beyond from the underlying algebra, putting them on a common geometric footing. Certain versions of Pati-Salam (PS) models with gauge coupling unification and limited scalar content can be derived from an appropriate noncommutative algebra. In this paper, I review these gauge-coupling-unified Pati-Salam models and discuss their phenomenological aspects, focusing on the $S_1$ scalar leptoquark.

Unified Pati-Salam from Noncommutative Geometry: Overview and Phenomenological Remarks

TL;DR

The paper addresses the lack of clear new-physics signals at the LHC by leveraging noncommutative geometry and the spectral action to derive unified geometric frameworks that include the Standard Model and gravity, and then to realize Pati-Salam gauge structures with gauge-coupling unification. It identifies three NCG-based PS models (A, B, C) with restricted scalar content, and highlights Model C, which accommodates a TeV-scale leptoquark with left-handed couplings that can address flavor anomalies such as while automatically avoiding proton decay due to the absence of diquark couplings. The framework provides a predictive, geometrically motivated path to beyond-Standard-Model physics with concrete phenomenological implications for flavor observables and collider searches. Overall, the work suggests that the spectral action in NCG offers a unified, testable approach to connecting geometry to particle physics and guiding future experimental probes.

Abstract

The lack of clear new-physics signals at the LHC searches motivates models that can guide current and future collider searches. The spectral action principle within the noncommutative geometry (NCG) framework yields such models with distinctive phenomenology. This formalism derives the actions of the Standard Model, General Relativity, and beyond from the underlying algebra, putting them on a common geometric footing. Certain versions of Pati-Salam (PS) models with gauge coupling unification and limited scalar content can be derived from an appropriate noncommutative algebra. In this paper, I review these gauge-coupling-unified Pati-Salam models and discuss their phenomenological aspects, focusing on the scalar leptoquark.

Paper Structure

This paper contains 6 sections, 19 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Minimal NCG framework; Spectral Standard Model (with gravity)
  3. Pati-Salam models from NCG with gauge coupling unification
  4. Basics
  5. Remarks on the low energy phenomenology
  6. Summary and Outlook

Figures (2)

  • Figure 1: (a) SM and (b) $S_1$ leptoquark contribution to $\overline{B}_0\to D^{(*)+}\tau^-\overline{\nu_{\tau\!L}}$. Adapted from Ref. Aydemir:2018cbb.
  • Figure 2: Leading order contribution to $a_{\mu}$ from a $S_1$ leptoquark.