A heavy Higgsino that avoids the solar-neutrino bound
The starting point is the recently reported LUX-ZEPLIN event at a recoil energy of about 248 keV. A Higgsino dark-matter particle whose two neutral states are nearly degenerate and couple off-diagonally to the Z boson can shift the recoil spectrum into the observed range, so a splitting of a few hundred keV makes the Higgsino an attractive explanation.
A weak-scale Higgsino, however, runs into a separate constraint. Higgsinos captured in the Sun can annihilate and produce energetic neutrinos, and the resulting IceCube bound disfavors the small splittings that the LZ event seems to prefer. The paper notes that independent analyses obtain lower bounds on the Higgsino mass splitting of about 0.5 to 0.6 MeV.
The escape route examined here is a much heavier Higgsino: a mass of order 10^5 GeV with a neutral-state splitting of about 400 keV can accommodate the LZ event while evading the solar-neutrino constraint. In the minimal supersymmetric Standard Model, that tiny splitting for such a heavy Higgsino requires bino and wino masses of order 10^7 GeV, because the splitting is generated by mixing with those gauginos and is suppressed by their masses.
Why heavy gauginos were expected to spoil unification
Very heavy Higgsinos and gauginos are often regarded as unfavorable for supersymmetric grand unification. They modify the running of the gauge couplings and can lower the unification scale, which in turn could make proton decay mediated by the heavy SU(5) gauge bosons, called X bosons, too rapid to satisfy experimental limits.
The paper tests this expectation in minimal supersymmetric SU(5) rather than assuming it. The relevant calculation evolves the measured gauge couplings to high energies while including threshold corrections at the supersymmetry scale and at the grand-unification scale. This procedure constrains two GUT-scale mass parameters: the color-triplet Higgs mass M_HC and the combination M_GUT = (M_X^2 M_Sigma)^(1/3), where M_X is the X-boson mass and M_Sigma is the adjoint-Higgs mass.
Unification fixes a mass combination, not the X-boson mass
The key structural point is that gauge coupling unification determines M_GUT but does not by itself fix M_X. Because only the combination (M_X^2 M_Sigma)^(1/3) is pinned down, the adjoint Higgs can be much lighter than the X bosons if its self-coupling is sufficiently small. That allows M_X to remain large even when the overall gaugino scale is very high.
This matters because the dimension-six proton-decay rate mediated by X-boson exchange scales as M_X^(-4). Raising M_X therefore suppresses that decay mode. The paper quantifies the requirement using the current limit on the p to pi-zero e-plus lifetime, tau > 2.4 x 10^34 years, and finds that the bound can be avoided for an adjoint-Higgs self-coupling of order 10^-2 or below across the parameter region of interest.
A gluino heavier than the wino keeps the triplet Higgs heavy
The color-triplet Higgs mass is determined separately by the unification condition, and here the gaugino mass ratios matter. The paper evaluates M_HC and M_GUT in the plane of M_2/M_1 and M_3/M_2, fixing the overall gaugino mass scale by requiring a neutral-Higgsino splitting of 400 keV, with a Higgsino mass of 100 TeV, sfermion and heavy-Higgs masses of 100 TeV, and tan beta of 3.
The large Higgsino mass tends to raise M_HC, but making the gluino significantly heavier than the wino lowers it. The two effects can compensate, so M_HC can remain close to the conventional supersymmetric GUT scale of about 10^16 GeV. The paper also finds that M_GUT is typically of order 10^15 GeV for this heavy gaugino spectrum, lower than the conventional supersymmetric unification scale, and that M_HC and M_GUT come closer together as M_3/M_2 increases, improving the quality of unification.
Dimension-six and dimension-five decays respond differently
The paper separates two proton-decay channels that readers could easily conflate. The dimension-six mode p to pi-zero e-plus is mediated by SU(5) gauge-boson exchange and is suppressed by making the adjoint-Higgs self-coupling small, which raises M_X. The dimension-five mode p to K-plus anti-nu is mediated by color-triplet Higgs exchange and depends on the sfermion mass scale through dressing diagrams, so it is not controlled by the same knob.
Assuming the adjoint-Higgs coupling is small enough to suppress the gauge-boson contribution, the paper focuses on the dimension-five channel. It scans sfermion masses from about 10^5 GeV to 10^7 GeV, a range chosen to explore the phenomenologically viable parameter space broadly rather than to match one specific supersymmetry-breaking scenario.
In this region, the reduction of M_HC caused by a gluino much heavier than the wino enhances the dimension-five rate. The result is that a sizable parameter region consistent with the present bound on p to K-plus anti-nu lies within the projected sensitivities of next-generation searches, including Hyper-Kamiokande, JUNO, and DUNE. The paper also notes that if the adjoint-Higgs coupling sits near its upper bound, the X-boson-mediated p to pi-zero e-plus rate could be close to current sensitivity and become observable in future searches.
The required mass hierarchy points to specific breaking patterns
The preferred spectrum has a characteristic ordering: the Higgsino mass is below the sfermion masses, which are below the gaugino masses, written as |mu| < m_sfermion < |M_i|. The lower end of the sfermion range is motivated by requiring the lightest sfermion to be heavier than the roughly 100 TeV Higgsino so that the Higgsino remains the stable lightest supersymmetric particle and can constitute dark matter. Keeping sfermions below about 10^4 TeV, well under the 10^7 GeV gauginos, also allows the gauginos to decay efficiently into sfermions and Standard Model fermions.
The paper discusses several frameworks that could produce such a hierarchy. Gaugino mediation or no-scale supergravity can give sfermions lighter than gauginos, though achieving a large separation between squark and electroweak-gaugino masses is nontrivial when the gluino is heavy. The non-universal pattern with M_3 much greater than M_2 can arise naturally in anomaly mediation and in other mechanisms generating non-universal gaugino masses.
An especially attractive possibility discussed is that the MSSM matter fields are Nambu-Goldstone multiplets, with scalar soft masses protected from generic supergravity contributions and controlled instead by explicit breaking of the underlying global symmetry. In that picture, the dimension-five proton-decay rate depends sensitively on the sfermion spectrum, so future proton-decay measurements could probe the pattern and magnitude of that symmetry breaking.
Proton decay becomes the testable signature of this scenario
The paper's central reversal is that the heavy spectrum suggested by the LZ event need not be incompatible with supersymmetric grand unification. In minimal supersymmetric SU(5), a small adjoint-Higgs self-coupling keeps the X bosons heavy enough to suppress dimension-six proton decay, while a gluino significantly heavier than the wino keeps the color-triplet Higgs near 10^16 GeV and preserves high-quality gauge coupling unification.
The most decision-relevant consequence is the split between the two decay modes. The dimension-six channel can be pushed safely below current bounds, but the dimension-five channel p to K-plus anti-nu can remain within reach of Hyper-Kamiokande, JUNO, and DUNE in a sizable region of the parameter space. For readers weighing whether a heavy Higgsino is consistent with grand unification, the practical priority is therefore the gluino-to-wino mass ratio and the adjoint-Higgs self-coupling: the same hierarchy that keeps M_HC near the conventional GUT scale also makes dimension-five proton decay the signature to watch.
Sources used in this answer
From the LZ Event to Grand Unification: Heavy Higgsinos and Proton Decay
A Higgsino near 10^5 GeV with a roughly 400 keV neutral-state splitting can fit minimal supersymmetric SU(5) unification and current proton-decay bounds when the adjoint-Higgs self-coupling is small and the gluino is significantly heavier than the wino, with dimension-five p to K-plus anti-nu decay potentially within reach of next-generation searches.