Accidental permutation symmetries as a test for Grand Unification: the supersymmetric $SU(5)$ case

TL;DR

This paper explores how accidental permutation symmetries in supersymmetric $SU(5)$ grand unified theories can be tested at the LHC through specific observables involving squark decays, providing a novel way to verify grand unification.

Contribution

It introduces new tests based on permutation symmetries in the squark sector to challenge the $SU(5)$ GUT hypothesis using LHC data, especially in Natural Supersymmetry scenarios.

Findings

Permutation symmetries can be tested via squark decay observables.

Relations among flavour-violating and chirality-flipping decays serve as tests.

Application demonstrated in Natural Supersymmetry scenarios.

Abstract

Unification of matter fields implies the existence of accidental permutation symmetries, which potentially remain immune to large quantum corrections up to the TeV scale. We investigate the case of a supersymmetric $SU(5)$ grand unified theory, where such a permutation symmetry is present in the up-type squark sector. We present a variety of tests allowing to challenge the $SU(5)$ hypothesis based on the observation of squarks at the LHC. These tests appear as relations among observables involving flavour-violating or chirality-flipping decays of squarks. Moreover, they rely on top-polarimetry and charm-tagging. As an example, we discuss the application to the scenario of Natural Supersymmetry, while more examples can be found in the related journal publications.