Higgsino Discovery Plane

• The Higgsino discovery plane is a two-dimensional parameter space defined by mass and splitting, unifying search strategies for nearly pure higgsinos.
• It integrates collider signatures, such as VBF production with soft leptons, with naturalness and electroweak studies across diverse SUSY frameworks.
• Precision analyses using MadGraph, PYTHIA, and detector simulations establish discovery and exclusion contours applicable to HL-LHC and future collider experiments.

The Higgsino discovery plane is a two-dimensional parameter space used to summarize the experimental reach for higgsino-like electroweakinos or higgsino dark matter. In the compressed-spectrum HL-LHC study of Cardona et al., it is the plane of $m(\tilde\chi_2^0)$ against $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$ for an almost pure higgsino triplet with $|\mu|\ll M_1,M_2$, $\Delta m=2$–$50$ GeV, and $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$; the plane then displays discovery and exclusion contours from VBF production with large missing momentum and soft leptons (Natalia et al., 2021). Across the later literature, the same expression is used for several related planes with different axes, including $(m_\chi,\langle\sigma v\rangle)$ for indirect detection, $(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$ in NMSSM higgsino–singlino studies, $(\mu,M_2)$ for mixed wino–higgsino phenomenology, $(m_{\tilde\chi_1^0},\tau)$ for disappearing-track searches, and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$0 in natural-SUSY reinterpretations (Rodd et al., 2024).

1. Definition and coordinate systems

In the compressed-higgsino LHC usage, the horizontal axis is $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$1 and the vertical axis is $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$2. The underlying spectrum assumption is that $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$3, $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$4, and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$5 form an almost pure higgsino triplet, with the mass splitting generated by small gaugino mixing (Natalia et al., 2021). In Baer et al., the same plane is adopted as the natural frame for ATLAS and CMS exclusions, with the simplifying assumption that the $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$6 and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$7 gaps are comparable (Baer et al., 2020).

Different communities use the same label for different observables because the plane is chosen to align the kinematic control variable with the dominant experimental bottleneck. This suggests that the phrase denotes a search-oriented representation rather than a unique canonical object.

Setting	Axes	Representative study
Compressed VBF higgsinos at HL-LHC	$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$8, $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$9	Cardona et al. (Natalia et al., 2021)
Natural-SUSY collider studies	$|\mu|\ll M_1,M_2$0 or $|\mu|\ll M_1,M_2$1, $|\mu|\ll M_1,M_2$2	Baer et al. (Baer et al., 2020)
NMSSM higgsino–singlino sector	$|\mu|\ll M_1,M_2$3, $|\mu|\ll M_1,M_2$4	Ellwanger (Ellwanger, 2016)
Mixed wino–higgsino MSSM	$|\mu|\ll M_1,M_2$5, $|\mu|\ll M_1,M_2$6	Carpenter et al. (Carpenter et al., 2023)
Long-lived pure higgsinos	$|\mu|\ll M_1,M_2$7, $|\mu|\ll M_1,M_2$8 or $|\mu|\ll M_1,M_2$9	Ibe et al. (Fukuda et al., 2017)
Indirect detection of thermal higgsino DM	$\Delta m=2$0, $\Delta m=2$1 or $\Delta m=2$2	Rodd et al. (Rodd et al., 2024)

2. Canonical HL-LHC compressed-higgsino plane from VBF

Cardona et al. formulate the most explicit collider realization of the Higgsino discovery plane for compressed higgsino-like models. The dominant VBF processes are

$\Delta m=2$3

arising from $\Delta m=2$4-channel $\Delta m=2$5 fusion, with an important $\Delta m=2$6-channel $\Delta m=2$7 contribution. The leading-order production is written schematically as

$\Delta m=2$8

In practice, the study uses MadGraph5_aMC@NLO v2.6.3.2 at LO with NNPDF3.0 NLO PDFs, interfaced to PYTHIA8 for showering, with no explicit NLO $\Delta m=2$9-factor and a $50$0 PDF uncertainty assigned to the LO-matched samples (Natalia et al., 2021).

The event topology is VBF plus large $50$1 plus one or two soft leptons. The selection requires at least two jets with $50$2 GeV, $50$3, and $50$4; $50$5 GeV; no $50$6-tagged jets with $50$7 GeV and $50$8; no hadronic $50$9 candidates with $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$0 GeV and $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$1; exactly two tagging jets with $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$2, $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$3, and $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$4 TeV; and either one soft lepton with $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$5 and $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$6 between the quoted minima and maxima, or two same-flavor opposite-sign soft leptons with $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$7 and $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$8 for $$m(\tilde\chi_1^\pm)\simeq \tfrac12[m(\tilde\chi_2^0)+m(\tilde\chi_1^0)]$$9 (Natalia et al., 2021).

The signal and backgrounds are generated with MadGraph5_aMC@NLO v2.6.3.2 plus NNPDF3.0 NLO PDF, interfaced to PYTHIA 8.2 and fast-simulated with DELPHES 3.4.1 using a CMS card. The background model includes $(m_\chi,\langle\sigma v\rangle)$0jets, $(m_\chi,\langle\sigma v\rangle)$1jets, $(m_\chi,\langle\sigma v\rangle)$2jets, single-top, Higgs, and triboson channels (Natalia et al., 2021).

3. Statistical construction and HL-LHC reach

For cut optimization, Cardona et al. use

$(m_\chi,\langle\sigma v\rangle)$3

corresponding to a $(m_\chi,\langle\sigma v\rangle)$4 combined systematic on $(m_\chi,\langle\sigma v\rangle)$5. The final reach is obtained from a binned profile-likelihood fit to $(m_\chi,\langle\sigma v\rangle)$6 in single-lepton channels and $(m_\chi,\langle\sigma v\rangle)$7 in dilepton channels. The nuisance model includes a $(m_\chi,\langle\sigma v\rangle)$8 PDF normalization uncertainty, a $(m_\chi,\langle\sigma v\rangle)$9 forward-jet reconstruction uncertainty, a correlated $(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$0 soft-lepton identification uncertainty, and jet-energy scale/resolution effects of $(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$1–$(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$2 per bin (Natalia et al., 2021).

At an integrated luminosity of $(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$3, the combined single- plus dilepton analysis gives the following reach:

Analysis	$(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$4 / $(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$5 reach	$(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$6 CL exclusion
Single-$(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$7 only	$(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$8 GeV $(m_{\tilde\chi_1^\pm},m_{\tilde\chi_1^0})$9 / $(\mu,M_2)$0 GeV	—
Di-$(\mu,M_2)$1 only	$(\mu,M_2)$2 GeV $(\mu,M_2)$3 / $(\mu,M_2)$4 GeV	—
Combined	$(\mu,M_2)$5 GeV / $(\mu,M_2)$6 GeV	$(\mu,M_2)$7 GeV

In the combined plane, the $(\mu,M_2)$8 contour is approximately a vertical line at $(\mu,M_2)$9 GeV, independent of $(m_{\tilde\chi_1^0},\tau)$0 from $(m_{\tilde\chi_1^0},\tau)$1 to $(m_{\tilde\chi_1^0},\tau)$2 GeV; the $(m_{\tilde\chi_1^0},\tau)$3 contour lies at $(m_{\tilde\chi_1^0},\tau)$4 GeV; and the $(m_{\tilde\chi_1^0},\tau)$5 CL upper exclusion reaches $(m_{\tilde\chi_1^0},\tau)$6 GeV (Natalia et al., 2021). The same study places these contours relative to existing constraints: LEP excludes chargino masses up to $(m_{\tilde\chi_1^0},\tau)$7 GeV for $(m_{\tilde\chi_1^0},\tau)$8 GeV and up to $(m_{\tilde\chi_1^0},\tau)$9 GeV for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$00 GeV, while ATLAS/CMS Drell–Yan searches at $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$01 TeV are only sensitive for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$02 GeV and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$03 GeV (Natalia et al., 2021). A common misconception is that these nearly vertical contours are generic; in the literature summarized here they are specific to the VBF plus soft-lepton strategy and its particular systematics model.

4. Naturalness structure and precision-oriented generalizations

Baer et al. connect the $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$04 plane to electroweak naturalness and stringy naturalness. In the pure-higgsino limit, they use

$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$05

with a one-loop shift that remains under a few GeV for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$06 GeV in typical NUHM2 or GMM$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$07 scans. Their naturalness measure follows

$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$08

with contributions from $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$09, $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$10, and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$11. Natural points with $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$12 cluster in $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$13–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$14 GeV and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$15–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$16 GeV, while stringy naturalness further prefers $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$17–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$18 GeV and strongly disfavors $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$19 GeV because very large gaugino masses are required (Baer et al., 2020). In the same framework, present ATLAS soft-opposite-sign dilepton plus jet plus $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$20 exclusions reach roughly $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$21–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$22 GeV for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$23 GeV, HL-LHC projections extend to $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$24 GeV for ATLAS and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$25 GeV for CMS, and a $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$26 TeV HE-LHC reaches $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$27 GeV (Baer et al., 2020).

At a lepton collider, the plane is often recast as $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$28 versus $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$29. In the ILC study based on full Geant4 simulation of the ILD detector, the machine operates at $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$30 GeV with $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$31, and benchmark scenarios with $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$32 between $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$33 and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$34 GeV yield mass measurements at typical precision $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$35–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$36 for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$37–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$38 GeV and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$39–$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$40 GeV; by scanning $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$41, the study finds a $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$42 discovery for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$43 GeV if $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$44 GeV, and a $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$45 CL exclusion down to $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$46 GeV using ISR tagging (Baer et al., 2019). A later EWPO reinterpretation uses the same plane to compare direct hadron-collider reach with indirect sensitivity from $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$47 and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$48: ILC250 covers $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$49 GeV for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$50 GeV, CEPC reaches $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$51 GeV for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$52 GeV, and FCC-ee via $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$53 would cover nearly the entire $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$54 GeV region (Baer et al., 22 Sep 2025).

A different natural-SUSY reinterpretation uses $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$55 on the horizontal axis and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$56 on the vertical axis. In the gravitino-LSP study, the HL-LHC at $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$57 TeV and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$58 reaches higgsino masses up to $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$59 GeV and nearly $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$60 of the GAMBIT samples with $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$61 GeV and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$62 (Dai et al., 2023).

5. NMSSM, mixed electroweakino, and long-lived extensions

In the NMSSM higgsino–singlino sector, the Higgsino discovery plane is commonly the $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$63 plane, where $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$64 and the singlino mass is controlled by $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$65 plus mixing effects. Ellwanger uses micrOMEGAs_3 and NMSSMTools_5.0.1 to identify allowed white regions after relic-density, spin-independent, and spin-dependent limits, including the $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$66-resonance strip, the $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$67 funnels, and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$68-channel chargino exchange for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$69. Recasting Run I ATLAS trilepton plus $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$70 and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$71 analyses with CheckMATE gives no $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$72 CL exclusion in the allowed white regions, while HL-LHC at $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$73 probes $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$74 in $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$75 GeV for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$76, leaving the most natural region with $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$77 GeV and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$78 GeV untested (Ellwanger, 2016).

Carpenter et al. define a different collider plane in $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$79 with the bino decoupled and classify the phenomenology by $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$80. They separate the parameter space into disappearing tracks for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$81 GeV, soft leptons for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$82 GeV, and mono-$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$83 for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$84 GeV. Using a joint likelihood over eight $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$85 bins in a hadronically tagged mono-$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$86 search, they project $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$87 CL exclusions up to $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$88 GeV for pure higgsinos and near-complete coverage of the natural region $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$89 GeV by the end of the HL-LHC run; the stated $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$90 discovery reach extends to $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$91 GeV for pure higgsinos and $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$92 GeV for well-mixed states (Carpenter et al., 2023).

For almost pure higgsinos, the plane may instead be $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$93 or $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$94. In the limit $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$95, the electroweak one-loop splitting is

$$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$96

which implies $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$97 cm for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$98. Ibe et al. propose a two-hit pixel-detector disappearing-track search with a displaced-vertex veto and quote, for $$\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$$99 cm, a projected $|\mu|\ll M_1,M_2$00 CL reach of $|\mu|\ll M_1,M_2$01 GeV and a $|\mu|\ll M_1,M_2$02 reach of $|\mu|\ll M_1,M_2$03 GeV at the HL-LHC, improving to $|\mu|\ll M_1,M_2$04 GeV and $|\mu|\ll M_1,M_2$05 GeV at a future $|\mu|\ll M_1,M_2$06 TeV collider (Fukuda et al., 2017). Saito et al. recast the same idea for a $|\mu|\ll M_1,M_2$07 TeV collider and give a $|\mu|\ll M_1,M_2$08, $|\mu|\ll M_1,M_2$09 discovery reach of $|\mu|\ll M_1,M_2$10 TeV at $|\mu|\ll M_1,M_2$11 ns, with plausible detector improvements extending nearly pure higgsino coverage to $|\mu|\ll M_1,M_2$12 TeV (Saito et al., 2019).

6. Indirect-detection planes, astrophysical dependence, and interpretive issues

For indirect detection, the Higgsino discovery plane is the $|\mu|\ll M_1,M_2$13 plane, or equivalently $|\mu|\ll M_1,M_2$14 with $|\mu|\ll M_1,M_2$15. Rodd et al. formulate the photon flux as

$|\mu|\ll M_1,M_2$16

with $|\mu|\ll M_1,M_2$17 and the observed counts obtained by folding with the effective area and energy dispersion. For the thermal higgsino, they take $|\mu|\ll M_1,M_2$18 TeV and choose $|\mu|\ll M_1,M_2$19 TeV, with leading tree-level rates $|\mu|\ll M_1,M_2$20 and $|\mu|\ll M_1,M_2$21, plus a one-loop line rate $|\mu|\ll M_1,M_2$22 and endpoint photons that give an $|\mu|\ll M_1,M_2$23 enhancement. Using FIRE-2 hydrodynamic profiles together with NFW and Einasto, they find that CTA South in a two-template analysis discovers the thermal higgsino at $|\mu|\ll M_1,M_2$24 for most profiles, while SWGO is weaker by a factor $|\mu|\ll M_1,M_2$25 in $|\mu|\ll M_1,M_2$26 and current Fermi and H.E.S.S. limits still fall short of $|\mu|\ll M_1,M_2$27 by $|\mu|\ll M_1,M_2$28–$|\mu|\ll M_1,M_2$29 depending on the profile (Rodd et al., 2024).

The same study emphasizes that profile uncertainty is structurally important: the twelve FIRE-2 profiles show $|\mu|\ll M_1,M_2$30–$|\mu|\ll M_1,M_2$31 variations in the central $|\mu|\ll M_1,M_2$32-factor, Romulus is among the most cuspy, Thelma among the most cored, and the ON/OFF subtraction strategy loses a factor $|\mu|\ll M_1,M_2$33 in sensitivity relative to full-template fitting (Rodd et al., 2024). It also identifies what appears to be an inconsistency in previous H.E.S.S. inner-Galaxy analyses related to the analysis effective area, with a possible weakening of claimed cross-section sensitivity by around an order of magnitude (Rodd et al., 2024). This is an important caution: discovery contours in the indirect-detection plane are not purely instrumental objects but are conditional on the Galactic density profile and background model.

Later CTAO-North forecasts sharpen the same point. Using large-zenith-angle Galactic Center observations from La Palma, with $|\mu|\ll M_1,M_2$34 hr/yr and a $|\mu|\ll M_1,M_2$35 TeV thermal higgsino target, the projected test statistic reaches $|\mu|\ll M_1,M_2$36 in 2028 and $|\mu|\ll M_1,M_2$37 in 2030 for an Auriga-median profile, but only $|\mu|\ll M_1,M_2$38 and $|\mu|\ll M_1,M_2$39 for Einasto, and $|\mu|\ll M_1,M_2$40 and $|\mu|\ll M_1,M_2$41 for FIRE-2 median; the resulting plane therefore separates decisive discovery, marginal hint, and no-reach regimes primarily by halo profile rather than by particle parameters alone (Abe et al., 9 Jun 2025). Earlier CTA forecasts already found a mean expected $|\mu|\ll M_1,M_2$42 CL limit of $|\mu|\ll M_1,M_2$43 at $|\mu|\ll M_1,M_2$44 TeV, with a $|\mu|\ll M_1,M_2$45 discovery threshold about a factor $|\mu|\ll M_1,M_2$46 above this and explicit sensitivity to the thermal higgsino near $|\mu|\ll M_1,M_2$47 TeV (Rinchiuso et al., 2020). In split supersymmetry, a related $|\mu|\ll M_1,M_2$48 Higgsino discovery plane overlays the thermal band at $|\mu|\ll M_1,M_2$49 TeV with direct-detection and electron-EDM reach, showing substantial overlap around $|\mu|\ll M_1,M_2$50 TeV and $|\mu|\ll M_1,M_2$51–$|\mu|\ll M_1,M_2$52 TeV (Co et al., 2022).

Taken together, these usages show that the Higgsino discovery plane is a unifying but context-dependent device. In compressed collider searches it isolates the competition between production threshold and visible softness; in naturalness studies it maps the allowed band of $|\mu|\ll M_1,M_2$53 or $|\mu|\ll M_1,M_2$54; in disappearing-track searches it converts a radiative splitting into a lifetime target; and in indirect detection it makes the thermal higgsino a fixed point near $|\mu|\ll M_1,M_2$55–$|\mu|\ll M_1,M_2$56 TeV whose observability is controlled jointly by $|\mu|\ll M_1,M_2$57, spectral modeling, and the inner-halo $|\mu|\ll M_1,M_2$58-factor.