Natural Dark Matter in Generalized No-scale $\mathcal{F}$-$SU(5)$ at the HL-LHC and LUX-ZEPLIN Experiment

Abstract

Is a supersymmetric bulk region with sub-200 GeV neutralinos and right-handed sleptons still feasible? Initially the bulk was the discovery target of the supersymmetry (SUSY) pioneers in the 1980s, though reality crashed those ambitions over the subsequent years and decades, presumptively excluding these light neutralinos and sleptons, inviting finely tuned dark matter scenarios to satisfy emerging high-precision relic density measurements. The answer to this important question is $yes$, if we consider the GUT model $\mathcal{F}$-$SU(5)$, namely, flipped $SU$(5) supplemented with a string derived TeV-scale extra $10+\overline{10}$ vector-like multiplet and charged vector-like singlet $(XE,XE^c)$, dubbed flippons. We pair $\mathcal{F}$-$SU(5)$ with effective supernatural supersymmetry (SUSY), known as generalized No-Scale Supergravity (SUGRA). This merging of $\mathcal{F}$-$SU(5)$ with generalized No-Scale SUGRA solves the SUSY electroweak fine-tuning problem and includes natural dark matter (NDM) that meets the latest 5$σ$ Planck satellite observations through annihilation only. The NDM in this model is imminently under test by the LUX-ZEPLIN 1000-day experiment, thus prospective observed events by LUX-ZEPLIN in 2026-27 will compel confirmation by the high-luminosity LHC (HL-LHC) energizing in 2030. Therefore, we present the parameter space observable at both LUX-ZEPLIN and the HL-LHC that is consistent with all presently operating experiments, including the LHC Run 3 gluino and squark constraints. Our results predict sub-200 GeV neutralinos and right-handed sleptons in the bulk that are not beyond detection, though more massive electroweakinos greater than 600 GeV are also allowed.