| Summary: | 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.
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