$B$-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry

TL;DR

This paper explores whether scalar leptoquarks that could explain B-decay anomalies can be embedded in noncommutative geometry-based Pati-Salam models, finding a unique candidate compatible with unification and proton stability.

Contribution

It demonstrates the existence of a specific scalar leptoquark within NCG Pati-Salam models that can account for B-decay anomalies without inducing proton decay.

Findings

Identifies a unique scalar leptoquark with TeV-scale mass.

Shows unification with a single intermediate symmetry breaking step.

Ensures no proton decay due to absence of diquark couplings.

Abstract

Motivated by possible scalar-leptoquark explanations of the recently reported $B$-decay anomalies, we investigate whether the required leptoquarks can be accommodated within models based on noncommutative geometry (NCG). The models considered have the gauge structure of Pati-Salam models, $SU(4)\times SU(2)_L\times SU(2)_R$, with gauge coupling unification at a single scale. In one of the models, we find a unique scalar leptoquark with quantum numbers $(3,1,-\frac{1}{3})_{321}$, originating from a complex multiplet $(6,1,1)_{422}$, which can potentially explain the $B$-decay anomalies if its mass is on the order of a few TeV. The unification of couplings can be realized with the inclusion of a single step of intermediate symmetry breaking. The scalar leptoquark under consideration does not contribute to proton decay due to the absence of diquark couplings, as dictated by the underlying noncommutative geometry.