From the LZ Event to Grand Unification: Heavy Higgsinos and Proton Decay

Abstract: The recently reported LUX-ZEPLIN (LZ) event has renewed interest in inelastic Higgsino dark matter. While a weak-scale Higgsino provides a simple interpretation of the event, such a scenario is in tension with the IceCube bound from dark-matter capture and annihilation in the Sun. This tension can be avoided for a much heavier Higgsino, with a mass of order $10^5$ GeV and a neutral-state mass splitting of $\simeq 400$ keV, which in turn points to gaugino masses around $10^7$ GeV. Such a heavy supersymmetric spectrum is often thought to be unfavorable for supersymmetric grand unified theories (GUTs), since it tends to worsen gauge coupling unification and lower the unification scale, potentially leading to excessively rapid proton decay. In this work, we revisit this expectation in minimal supersymmetric SU(5), taking into account the GUT-scale threshold corrections. We show that the resulting unification conditions allow the SU(5) gauge bosons to remain sufficiently heavy when the adjoint-Higgs self-coupling is small, thereby suppressing dimension-six proton decay. At the same time, the color-triplet Higgs mass can remain near the conventional GUT scale, $M_{H_C}\sim 10<sup>{16}$ GeV, particularly when the gluino is significantly heavier than the wino. Remarkably, in this region the dimension-five decay mode $p\to K<sup>+\barν$ can have a lifetime within the reach of next-generation proton-decay searches, including Hyper-Kamiokande, JUNO, and DUNE. We also discuss supersymmetry-breaking scenarios that can give rise to the required supersymmetric mass spectrum.