Generalized Minimal Supergravity (GmSUGRA)

• Generalized Minimal Supergravity (GmSUGRA) is a gravity-mediated SUSY-breaking framework that relaxes universality while retaining grand-unified correlations.
• It facilitates electroweak supersymmetry by decoupling heavy colored states and allowing lighter sleptons and electroweakinos, reopening bulk and resonance dark-matter regions.
• The framework’s one-loop RG invariance and high-dimensional operators yield predictive gaugino and scalar mass relations, offering clear signatures for collider and dark matter searches.

Searching arXiv for recent and foundational papers on GmSUGRA. Searching arXiv for "Generalized Minimal Supergravity GmSUGRA MSSM". Generalized Minimal Supergravity (GmSUGRA) is a gravity-mediated supersymmetry-breaking framework in which the restrictive universality assumptions of minimal supergravity are relaxed while a grand-unified origin of soft terms is retained. In its canonical formulation, high-dimensional operators in the gauge kinetic function and GUT-breaking sector generically spoil exact gauge-coupling unification and universal gaugino masses at the unification scale, but leave linear relations among gauge couplings and among gaugino masses, characterized by an index $k$ calculable in a given GUT and, in principle, measurable from low-energy data (Li et al., 2010). In MSSM applications, this structure has been used to realize electroweak supersymmetry, with multi-TeV colored states and much lighter sleptons and electroweakinos, and to reopen dark-matter regions—especially bino–slepton bulk, $Z$-pole, and Higgs-pole regimes—that are strongly constrained in stricter CMSSM/mSUGRA constructions (Khan et al., 27 Sep 2025).

1. Origins and formal definition

The original GmSUGRA construction arises from the observation that, once high-dimensional operators involving GUT-breaking fields are included in the gauge kinetic function, the Standard Model gauge couplings need not be equal at the GUT scale and the gaugino masses need not be universal there (Li et al., 2010). Rather than exact equalities, one obtains linear relations. In the standard parametrization,

$$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$

In the simplified case $f_i=T+a_iS$, the index is

$k=\frac{a_2-a_3}{a_1-a_3}.$

A central result of the foundational formulation is that $M_i/\alpha_i$ are one-loop RG invariants, so the same gaugino-mass relation remains valid from the GUT scale to the electroweak scale up to small two-loop corrections (Li et al., 2010). This turns $k$ into both a structural parameter of the ultraviolet theory and a phenomenological discriminator. In traditional $SU(5)$ and many $SO(10)$ constructions, including adjoint-breaking realizations, the characteristic value is $k=5/3$ (Li et al., 2010).

This formulation differs sharply from mSUGRA/CMSSM. In mSUGRA one assumes

$Z$0

together with universal scalar masses and universal trilinears. In GmSUGRA, non-universality is not arbitrary; it is correlated by group theory, higher-dimensional operators, and the structure of the SUSY-breaking sector. That distinction is essential: GmSUGRA is not merely “non-universal mSUGRA,” but a constrained deformation of it.

2. High-scale soft terms and canonical MSSM implementations

In the MSSM phenomenology literature based on the $Z$1 realization, one usually assumes gauge-coupling unification at $Z$2, $Z$3, and then the generalized relation reduces to a purely gaugino-mass constraint. Depending on which parameters are chosen as inputs, one may write

$Z$4

equivalently

$Z$5

or

$Z$6

This leaves only two independent GUT-scale gaugino parameters, rather than the single universal $Z$7 of mSUGRA (Khan et al., 27 Sep 2025).

The scalar sector departs even more strongly from CMSSM universality. In the $Z$8-motivated constructions used in recent MSSM analyses, the squark soft masses satisfy

$Z$9

$$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$0

$$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$1

Here $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$2 is a universal scalar mass associated with $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$3 multiplets and an adjoint field, while slepton masses are treated as independent inputs. In the light-slepton limit $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$4, these relations become approximately

$$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$5

so the squarks are heavy and quasi-degenerate while sleptons can remain parametrically light (Khan et al., 27 Sep 2025).

The Higgs soft masses $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$6 are typically free at the GUT scale, and trilinears are not unified: $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$7 in the light-neutralino bulk analysis of 2025 (Khan et al., 27 Sep 2025). This freedom is used simultaneously to realize radiative electroweak symmetry breaking, a 125 GeV Higgs, and a split spectrum with light electroweak states and heavy colored states.

3. Electroweak supersymmetry and spectrum engineering

A defining phenomenological consequence of GmSUGRA is the realization of electroweak supersymmetry: heavy squarks and/or gluino around a few TeV together with sleptons, sneutrinos, bino, winos, and/or higgsinos within one TeV (Li et al., 2014). In the 2014 EWSUSY analysis, the allowed mass ranges consistent within $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$8 of the $$\frac{1}{\alpha_2}-\frac{1}{\alpha_3} = k\left(\frac{1}{\alpha_1}-\frac{1}{\alpha_3}\right), \qquad \frac{M_2}{\alpha_2}-\frac{M_3}{\alpha_3} = k\left(\frac{M_1}{\alpha_1}-\frac{M_3}{\alpha_3}\right).$$9 discrepancy for the lightest neutralino, charginos, stau, stau neutrinos, and first two-family sleptons are $f_i=T+a_iS$0 GeV, $f_i=T+a_iS$1 GeV, $f_i=T+a_iS$2, and $f_i=T+a_iS$3 GeV, respectively, while the colored sector populates substantially heavier intervals (Li et al., 2014).

Natural-SUSY analyses sharpen this picture. For parameter space with low-energy electroweak fine-tuning measures less than 50, the surviving dark-matter patterns reduce to the $f_i=T+a_iS$4-pole, Higgs-pole, and Higgsino LSP scenarios, while gluino and the first two generations of squarks are heavier than 2 TeV, $f_i=T+a_iS$5 are in the mass range $f_i=T+a_iS$6 TeV, and sleptons are lighter than 1 TeV (Ahmed et al., 2017). The relevant weak-scale condition is

$f_i=T+a_iS$7

with the electroweak fine-tuning measure

$f_i=T+a_iS$8

The persistence of points with $f_i=T+a_iS$9 under present collider and direct-detection bounds indicates that GmSUGRA can decouple the colored sector without forcing $k=\frac{a_2-a_3}{a_1-a_3}.$0 or the slepton sector into obviously unnatural regimes (Ahmed et al., 2017).

The sign of $k=\frac{a_2-a_3}{a_1-a_3}.$1 has become a moving target in this spectrum engineering. Earlier EWSUSY fits emphasized $k=\frac{a_2-a_3}{a_1-a_3}.$2 because a positive SUSY contribution to $k=\frac{a_2-a_3}{a_1-a_3}.$3 was desirable. More recent studies explicitly revisit both $k=\frac{a_2-a_3}{a_1-a_3}.$4 and $k=\frac{a_2-a_3}{a_1-a_3}.$5, motivated by the possibility that the muon anomalous magnetic moment is already consistent with the Standard Model prediction (Khan et al., 23 Jun 2025). In the revised 2025 survey, the $k=\frac{a_2-a_3}{a_1-a_3}.$6 scenario yields a broader allowed parameter space, including sbottom-neutralino coannihilation solutions absent for $k=\frac{a_2-a_3}{a_1-a_3}.$7 (Khan et al., 23 Jun 2025).

4. Dark-matter regimes and the reopening of the bulk region

One of the most consequential modern uses of GmSUGRA is the restoration of the classical bino–slepton bulk region. In this regime, the lightest neutralino is an almost pure bino and annihilates dominantly through $k=\frac{a_2-a_3}{a_1-a_3}.$8- and $k=\frac{a_2-a_3}{a_1-a_3}.$9-channel right-handed slepton exchange,

$M_i/\alpha_i$0

To isolate bulk annihilation from coannihilation, recent analyses define the mass-splitting ratio

$M_i/\alpha_i$1

with the conservative bulk criterion $M_i/\alpha_i$2 (Khan et al., 2023). In the 2023 $M_i/\alpha_i$3 study, the viable right-handed stau bulk region yielded upper bounds of about $M_i/\alpha_i$4 GeV for the lightest neutralino and $M_i/\alpha_i$5 GeV for the right-handed stau, while the right-handed selectron NLSP case was excluded by LHC supersymmetry searches (Khan et al., 2023). The 2025 $M_i/\alpha_i$6 update broadened the bulk solution and obtained

$M_i/\alpha_i$7

again with the right-handed stau as the viable NLSP and the right-handed selectron NLSP excluded by current LHC data (Khan et al., 27 Sep 2025).

GmSUGRA also supports the standard resonance mechanisms. The $M_i/\alpha_i$8-pole corresponds to $M_i/\alpha_i$9, and the Higgs-pole to $k$0. In the recent light-neutralino analyses, benchmark points appear near $k$1 GeV and $k$2 GeV, and the broader 2025 pole study locates viable clusters around $k$3 GeV and $k$4 GeV (Khan et al., 21 Jan 2025). The broader EWSUSY scan further finds coannihilation with stau, chargino, stop, sbottom, and gluino, together with $k$5-funnel, Higgs-resonance, and $k$6-resonance mechanisms (Khan et al., 23 Jun 2025).

A recurrent theme is the dependence on the sign of $k$7. The latest LHC and LZ constraints exclude light higgsinos in the $k$8- and $k$9-pole regions for $SU(5)$0, whereas for $SU(5)$1 very light higgsinos can still be consistent with current electroweakino searches and LZ in the $SU(5)$2- and $SU(5)$3-pole regions (Khan et al., 21 Jan 2025). This does not mean that $SU(5)$4 is generically favored in all observables, but it does mean that direct-detection and collider limits now shape the neutralino sector more strongly than older $SU(5)$5-driven priors.

5. Precision observables, direct detection, and collider tests

The experimental profile of GmSUGRA is unusually correlated. Because the $SU(5)$6 gaugino relation and the scalar relations can keep $SU(5)$7 and right-handed slepton masses small while driving $SU(5)$8 and squark masses large, present LHC bounds on colored superpartners are often automatically satisfied in the relevant light-neutralino sectors (Khan et al., 27 Sep 2025). The strongest present exclusions instead come from electroweak production and direct detection.

For the right-handed stau bulk region, neutralino–nucleon scattering is suppressed by the nearly pure bino composition and very heavy higgsinos. Benchmark points exhibit $SU(5)$9 and $SO(10)$0, lying below current XENONnT and LZ bounds, although many of these points fall within the expected reach of the projected 1000-day LZ sensitivity (Khan et al., 27 Sep 2025). Pole solutions with larger bino–higgsino mixing are more exposed: for $SO(10)$1, constructive interference in the spin-independent amplitude sharply constrains light-higgsino $SO(10)$2-pole solutions, while for $SO(10)$3, destructive interference allows a narrow window to survive (Khan et al., 21 Jan 2025).

The muon anomalous magnetic moment illustrates the time dependence of GmSUGRA phenomenology. Earlier EWSUSY analyses treated the $SO(10)$4 discrepancy as a strong target and found large viable parameter space, with the LSP neutralino at least as heavy as 550 GeV and most of the viable parameter space probeable at the future HL-LHC, though some corners would require the HE-LHC (Ahmed et al., 2021). Updated lattice-QCD and Fermilab-based comparisons, however, reduce the discrepancy to about $SO(10)$5, so a positive SUSY correction is no longer compulsory. In the 2025 light-neutralino bulk study, $SO(10)$6 with $SO(10)$7 yields a small negative contribution and

$SO(10)$8

comfortably within $SO(10)$9 of the current experimental central value when combined with the updated Standard Model expectation (Khan et al., 27 Sep 2025). The broader 2025 EWSUSY reassessment similarly concludes that the SUSY contribution remains within a $k=5/3$0 deviation from the Standard Model prediction (Khan et al., 23 Jun 2025).

Collider prospects remain strong. Future $k=5/3$1 colliders including FCC-ee and CEPC are expected to pair-produce light sleptons and neutralinos in the $k=5/3$2–$k=5/3$3 GeV range, making the characteristic bulk spectrum a particularly clean target (Khan et al., 27 Sep 2025). At hadron colliders, compressed electroweak sectors, stau final states, and heavy-Higgs channels dominate the search strategy; gluino coannihilation regions are already strongly constrained by current LHC data (Khan et al., 23 Jun 2025).

6. Extensions, nomenclature, and broader significance

Beyond neutralino dark matter, GmSUGRA has been used to derive one-loop RG-stable relations among scalar and gaugino masses in $k=5/3$4 and $k=5/3$5 models, providing a collider-level discriminator between mSUGRA and generalized constructions (Balazs et al., 2010). It has also been used to repair wrong GUT-scale fermion mass relations through high-dimensional operators in the superpotential and, notably, in the Kähler potential. In that context, the realistic relation

$k=5/3$6

can emerge from GUT-structured wave-function normalization factors, not only from superpotential Clebsch coefficients (Balazs et al., 2011).

The framework also accommodates nonstandard dark sectors. In an axino-LSP scenario with a bino-like neutralino NLSP, GmSUGRA naturally produces a light bino around or below 100 GeV together with right-handed sleptons under 300 GeV. For bino lifetimes in the range $k=5/3$7 to $k=5/3$8, this leads to HL-LHC displaced-photon plus large missing-transverse-momentum signatures, and the relevant axion coupling $k=5/3$9 can be probed up to $Z$00 GeV at $Z$01 level for the right-handed slepton mass under 300 GeV and the lightest neutralino mass under 100 GeV (Zhang et al., 2023).

A nomenclature caveat is necessary. One strand of the literature uses “generalized mSUGRA” for Giudice–Masiero extensions of minimal supergravity in which Kähler-potential terms modify the Higgs-sector $Z$02 and $Z$03 relations while leaving the rest of the high-scale structure close to standard mSUGRA (Dudas et al., 2012). By contrast, the dominant phenomenological usage associated with Li, Nanopoulos, and subsequent MSSM studies refers to GUT-structured non-universality in gaugino masses, scalar masses, and often trilinears (Li et al., 2010). This suggests that “GmSUGRA” denotes a family of closely related supergravity constructions rather than a unique parameter point or a single ultraviolet completion.

Taken together, the literature presents GmSUGRA as a structured alternative to CMSSM/mSUGRA: sufficiently constrained to retain GUT-motivated predictivity, sufficiently flexible to realize electroweak supersymmetry, and sufficiently rich to support revived bulk dark matter, pole solutions, long-lived electroweak sectors, and collider-testable high-scale correlations.