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

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.