Tasting the SU(5) nature of supersymmetry at the LHC

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 3-sigma 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.