Relating LHC event rates to supersymmetric Grand Unified Theories containing $SU(5)$

TL;DR

This paper explores how specific $SU(5)$ relations in supersymmetric GUTs can be tested at the LHC through observable flavor violation and chirality flip processes, providing new experimental avenues for GUT-scale physics.

Contribution

It introduces a novel $SU(5)$ relation immune to quantum corrections and proposes multiple LHC-based tests to probe GUT-scale physics in supersymmetric models.

Findings

$O(10)$ to $O(100)$ events needed for 50 ext{\%} precision at 3$\sigma$

Proposed tests involve flavor violation, chirality flips, top polarimetry, charm-tagging, Higgs detection

Relations among observables can reveal $SU(5)$ GUT signatures at TeV scale

Abstract

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. We present a variety of tests, which appear as relations among observables involving flavour violation or chirality flips and rely on the techniques of top polarimetry, charm-tagging, or Higgs detection from cascade decays. We discuss the cases of natural Supersymmetry and top-charm Supersymmetry as example cases. We find that $O(10)$ to $O(100)$ events are needed to obtain 50\% of relative precision at 3$\sigma$ significance for all proposed tests.