SU(5) Unification with TeV-scale Leptoquarks

TL;DR

This paper investigates SU(5) unification with TeV-scale leptoquarks, analyzing parameter space, unification scales, proton decay constraints, and potential explanations for LHCb anomalies, finding viable models with leptoquarks as light as 400 GeV.

Contribution

It provides a detailed exploration of SU(5) unification with light scalar leptoquarks, including parameter space, unification scale adjustments, and phenomenological implications.

Findings

Leptoquarks below ~16 TeV are necessary for unification.

Unification scale can exceed 10^{16} GeV with certain splittings.

Leptoquarks as light as 400 GeV are still allowed by LHC bounds.

Abstract

It was previously noted that SU(5) unification can be achieved via the simple addition of light scalar leptoquarks from two split $\bf10$ multiplets. We explore the parameter space of this model in detail and find that unification requires at least one leptoquark to have mass below $\approx16\,$TeV. We point out that introducing splitting of the $\bf24$ allows the unification scale to be raised beyond $10^{16}$ GeV, while a U(1)$_{PQ}$ symmetry can be imposed to forbid dangerous proton decay mediated by the light leptoquarks. The latest bounds from LHC searches are combined and we find that a leptoquark as light as 400 GeV is still permitted. Finally, we discuss the interesting possibility that the leptoquarks required for unification could also be responsible for the $2.6\sigma$ deviation observed in the ratio $R_K$ at LHCb.