We point out that the hypothesis of an SU(5)-like supersymmetric Grand Unified Theory (GUT) implies a generic relation within the flavour structure of up-type squarks. Contrary to other well-known SU(5) relations between the down-quark and charged lepton sectors, this relation remains exact in the presence of any corrections and extra operators. Moreover it remains valid to a good precision at the electroweak scale, and opens thus new possibilities for testing SU(5)-like GUTs. We derive the low-energy effective theory of observable light up-type squarks, that also constitutes a useful tool for squark phenomenology. We use this effective theory to determine how to test SU(5) relations at the LHC. Focusing on scenarios with light stops, compatible with Natural SUSY, it appears that simple tests involving ratios of event rates are sufficient to test the hypothesis of an SU(5)-like GUT theory. The techniques of charm-tagging and top-polarimetry are a crucial ingredient of these tests.

We elaborate on a recently found SU (5) relation confined to the up-(s)quark flavour space, that remains immune to large quantum corrections up to the TeV scale. We investigate the possibilities opened by this new window on the GUT scale in order to find TeV-scale SU (5) tests realizable at the LHC. These SU (5) tests appear as relations among observables involving either flavour violation or chirality flip in the up-(s)quark sector. The power of these tests is systematically evaluated using a frequentist, p-value based criterion. SU (5) tests in the Heavy supersymmetry (SUSY), Natural supersymmetry and Top-charm supersymmetry spectra are investigated. The latter scenario features light stops and scharms and is well-motivated from various five-dimensional constructions. A variety of SU (5) tests is obtained, involving techniques of top polarimetry, charm-tagging, or Higgs detection from SUSY cascade decays. We find that O(10) to O(100) events are needed to obtain 50% of relative precision at 3σ significance for all of these tests. In addition, we propose a set of precision measurements in ultraperipheral collisions in order to search for the flavour-changing dipole operators of Heavy supersymmetry.

We elaborate on a recently found SU(5) relation confined to the up-(s)quark flavour space, that remains immune to large quantum corrections up to the TeV scale. We investigate the possibilities opened by this new window on the GUT scale in order to find TeV-scale SU(5) tests realizable at the LHC. These SU(5) tests appear as relations among observables involving either flavour violation or chirality flip in the up-(s)quark sector. The power of these tests is systematically evaluated using a frequentist, p-value based criterion. SU(5) tests in the Heavy supersymmetry (SUSY), Natural supersymmetry and Top-charm supersymmetry spectra are investigated. The latter scenario features light stops and scharms and is well-motivated from various five-dimensional constructions. A variety of SU (5) tests is obtained, involving techniques of top polarimetry, charm-tagging, or Higgs detection from SUSY cascade decays. We find that O(10) to O(100) events are needed to obtain 50% of relative precision at 3σ significance for all of these tests. In addition, we propose a set of precision measurements in ultraperipheral collisions in order to search for the flavour-changing dipole operators of Heavy supersymmetry.