--- title: Higgsino Discovery Plane url: https://www.emergentmind.com/topics/higgsino-discovery-plane type: topic --- # Higgsino Discovery Plane 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 [2102.10194]. 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 $(\mu,\Delta_{\rm EW})$ in natural-SUSY reinterpretations [2405.13104]. ## 1. Definition and coordinate systems In the compressed-higgsino LHC usage, the horizontal axis is $m(\tilde\chi_2^0)$ and the vertical axis is $\Delta m \equiv m(\tilde\chi_2^0)-m(\tilde\chi_1^0)$. The underlying spectrum assumption is that $\tilde\chi_1^0$, $\tilde\chi_1^\pm$, and $\tilde\chi_2^0$ form an almost pure higgsino triplet, with the mass splitting generated by small gaugino mixing [2102.10194]. In Baer et al., the same plane is adopted as the natural frame for ATLAS and CMS exclusions, with the simplifying assumption that the $\tilde\chi_2^0-\tilde\chi_1^0$ and $\tilde\chi_1^\pm-\tilde\chi_1^0$ gaps are comparable [2007.09252]. 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 | $m(\tilde\chi_2^0)$, $\Delta m$ | Cardona et al. [2102.10194] | | Natural-SUSY collider studies | $m(\tilde\chi_2^0)$ or $m(\tilde\chi_1^0)$, $\Delta m$ | Baer et al. [2007.09252] | | NMSSM higgsino–singlino sector | $m_{\chi_1^\pm}$, $m_{\chi_1^0}$ | Ellwanger [1612.06574] | | Mixed wino–higgsino MSSM | $\mu$, $M_2$ | Carpenter et al. [2309.07213] | | Long-lived pure higgsinos | $m_{\tilde\chi_1^0}$, $\tau$ or $c\tau$ | Ibe et al. [1703.09675] | | Indirect detection of thermal higgsino DM | $m_\chi$, $\langle\sigma v\rangle$ or $\mu=\langle\sigma v\rangle/\langle\sigma v\rangle_{\rm higgsino}$ | Rodd et al. [2405.13104] | ## 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 \[ pp\to \tilde\chi_2^0\,\tilde\chi_1^+\,jj,\qquad pp\to \tilde\chi_2^0\,\tilde\chi_2^0\,jj,\qquad pp\to \tilde\chi_1^+\,\tilde\chi_1^-\,jj, \] arising from $t$-channel $WZ/WW/ZZ$ fusion, with an important $s$-channel $WW\to {\rm Higgs}\to \tilde\chi\tilde\chi$ contribution. The leading-order production is written schematically as \[ \sigma_{\rm LO}(pp\to\tilde\chi_2^0\,\tilde\chi_1^+\,jj) = \sum_{a,b}\int dx_1dx_2\, f_{a/p}(x_1)\,f_{b/p}(x_2) \int d\Phi_4\,|\mathcal M_{ab\to\tilde\chi_2^0\tilde\chi_1^+qq'}|^2. \] 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 $K$-factor and a $12\%$ PDF uncertainty assigned to the LO-matched samples [2102.10194]. The event topology is VBF plus large $E_T^{\rm miss}$ plus one or two soft leptons. The selection requires at least two jets with $p_T>30$ GeV, $|\eta|<5.0$, and $\Delta R(j_1,j_2)>0.3$; $E_T^{\rm miss}>150$ GeV; no $b$-tagged jets with $p_T>30$ GeV and $|\eta|<2.5$; no hadronic $\tau$ candidates with $p_T>20$ GeV and $|\eta|<2.5$; exactly two tagging jets with $\eta(j_1)\eta(j_2)<0$, $|\Delta\eta_{jj}|>5.5$, and $m_{jj}>0.5$ TeV; and either one soft lepton with $|\eta(\ell)|<2.4$ and $p_T$ between the quoted minima and maxima, or two same-flavor opposite-sign soft leptons with $|\eta(\ell)|<2.4$ and $8/5~{\rm GeV}3$ GeV and up to $92$ GeV for $\Delta m<3$ GeV, while ATLAS/CMS Drell–Yan searches at $13$ TeV are only sensitive for $\Delta m\gtrsim10$ GeV and $m(\tilde\chi_2^0)\lesssim200$ GeV [2102.10194]. 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 $(m(\tilde\chi_2^0),\Delta m^0)$ plane to electroweak naturalness and stringy naturalness. In the pure-higgsino limit, they use \[ m_{\chi_1^+}^* \simeq \frac{m_{\chi_2^0}+m_{\chi_1^0}}{2}, \] with a one-loop shift that remains under a few GeV for $m_2\lesssim400$ GeV in typical NUHM2 or GMM$'$ scans. Their naturalness measure follows \[ \Delta_{\rm EW}=\max_i |{\rm contribution}_i|/(m_Z^2/2), \] with contributions from $-m_{H_u}^2$, $-\mu^2$, and $-\Sigma_u^u$. Natural points with $\Delta_{\rm EW}<30$ cluster in $m_2\lesssim350$–$400$ GeV and $\Delta m^0\simeq4$–$20$ GeV, while stringy naturalness further prefers $\Delta m^0\sim4$–$10$ GeV and strongly disfavors $\Delta m^0\lesssim4$ GeV because very large gaugino masses are required [2007.09252]. In the same framework, present ATLAS soft-opposite-sign dilepton plus jet plus $E_T^{\rm miss}$ exclusions reach roughly $m_2\lesssim180$–$200$ GeV for $\Delta m\gtrsim10$ GeV, HL-LHC projections extend to $m_2\simeq300$ GeV for ATLAS and $\simeq250$ GeV for CMS, and a $27$ TeV HE-LHC reaches $m_2\simeq400$ GeV [2007.09252]. At a lepton collider, the plane is often recast as $m(\chi_1^0)$ versus $\Delta m$. In the ILC study based on full Geant4 simulation of the ILD detector, the machine operates at $\sqrt s=500$ GeV with $1000~{\rm fb}^{-1}$, and benchmark scenarios with $\Delta m$ between $20$ and $4$ GeV yield mass measurements at typical precision $0.5$–$1\%$ for $\mu\sim100$–$150$ GeV and $\Delta m=4$–$20$ GeV; by scanning $(\mu,\Delta m)$, the study finds a $5\sigma$ discovery for $\mu\lesssim225$ GeV if $\Delta m\gtrsim3$ GeV, and a $95\%$ CL exclusion down to $\Delta m\sim1$ GeV using ISR tagging [1912.06643]. A later EWPO reinterpretation uses the same plane to compare direct hadron-collider reach with indirect sensitivity from $m_W$ and $\sin^2\theta_{\rm eff}$: ILC250 covers $\mu\lesssim200$ GeV for $\Delta m^0\lesssim20$ GeV, CEPC reaches $\mu\lesssim300$ GeV for $\Delta m^0\lesssim20$ GeV, and FCC-ee via $m_W$ would cover nearly the entire $\mu\lesssim360$ GeV region [2509.18288]. A different natural-SUSY reinterpretation uses $\mu$ on the horizontal axis and $\Delta_{\rm EW}$ on the vertical axis. In the gravitino-LSP study, the HL-LHC at $14$ TeV and $3000~{\rm fb}^{-1}$ reaches higgsino masses up to $575$ GeV and nearly $100\%$ of the GAMBIT samples with $|\mu|\leq500$ GeV and $\Delta_{\rm EW}<100$ [2311.10999]. ## 5. NMSSM, mixed electroweakino, and long-lived extensions In the NMSSM higgsino–singlino sector, the Higgsino discovery plane is commonly the $(m_{\chi_1^\pm},m_{\chi_1^0})$ plane, where $m_{\chi_1^\pm}\simeq|\mu|$ and the singlino mass is controlled by $2\kappa s=2(\kappa/\lambda)\mu$ 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 $A_1$-resonance strip, the $Z/H_1/H_2$ funnels, and $t$-channel chargino exchange for $m_{\chi_1^0}>m_W$. Recasting Run I ATLAS trilepton plus $E_T^{\rm miss}$ and $WH$ analyses with CheckMATE gives no $95\%$ CL exclusion in the allowed white regions, while HL-LHC at $3000~{\rm fb}^{-1}$ probes $m_{\chi_1^\pm}$ in $[150,300]$ GeV for $m_{\chi_1^0}\lesssim m_{\chi_1^\pm}-M_Z$, leaving the most natural region with $m_{\chi_1^\pm}<150$ GeV and $m_{\chi_1^0}<5$ GeV untested [1612.06574]. Carpenter et al. define a different collider plane in $(\mu,M_2)$ with the bino decoupled and classify the phenomenology by $\Delta m\equiv m_{\tilde\chi_1^\pm}-m_{\tilde\chi_1^0}$. They separate the parameter space into disappearing tracks for $\Delta m\lesssim1$ GeV, soft leptons for $\Delta m\gtrsim4$ GeV, and mono-$V+E_T^{\rm miss}$ for $1\lesssim\Delta m\lesssim4$ GeV. Using a joint likelihood over eight $E_T^{\rm miss}$ bins in a hadronically tagged mono-$V$ search, they project $95\%$ CL exclusions up to $\mu\sim550$ GeV for pure higgsinos and near-complete coverage of the natural region $\mu,M_2<500$ GeV by the end of the HL-LHC run; the stated $5\sigma$ discovery reach extends to $\mu\sim300$ GeV for pure higgsinos and $450$ GeV for well-mixed states [2309.07213]. For almost pure higgsinos, the plane may instead be $(m_{\tilde\chi},c\tau)$ or $(m_{\tilde\chi_1^0},\tau)$. In the limit $M_1,M_2\gg|\mu|$, the electroweak one-loop splitting is \[ \Delta m_{\rm rad}\approx 340\text{--}355~{\rm MeV}, \] which implies $c\tau\sim1$ cm for $\tilde\chi^\pm\to\tilde\chi_1^0\pi^\pm$. Ibe et al. propose a two-hit pixel-detector disappearing-track search with a displaced-vertex veto and quote, for $c\tau=1$ cm, a projected $95\%$ CL reach of $580$ GeV and a $5\sigma$ reach of $450$ GeV at the HL-LHC, improving to $1050$ GeV and $900$ GeV at a future $33$ TeV collider [1703.09675]. Saito et al. recast the same idea for a $100$ TeV collider and give a $30~{\rm ab}^{-1}$, $5\sigma$ discovery reach of $1.02$ TeV at $\tau=0.02$ ns, with plausible detector improvements extending nearly pure higgsino coverage to $m_{\tilde\chi_1^0}\simeq1.4$ TeV [1901.02987]. ## 6. Indirect-detection planes, astrophysical dependence, and interpretive issues For indirect detection, the Higgsino discovery plane is the $(m_\chi,\langle\sigma v\rangle)$ plane, or equivalently $(m_\chi,\mu)$ with $\mu=\langle\sigma v\rangle/\langle\sigma v\rangle_{\rm higgsino}$. Rodd et al. formulate the photon flux as \[ \Phi(\Delta\Omega,E)=\frac{\langle\sigma v\rangle_\gamma}{8\pi m_\chi^2} \int_{\Delta\Omega} d\Omega \int_{\rm los} dl\,\rho^2(l)\times \frac{dN_\gamma}{dE}, \] with $J(\Delta\Omega)\equiv\int_{\Delta\Omega}d\Omega\int_{\rm los}dl\,\rho^2(l)$ and the observed counts obtained by folding with the effective area and energy dispersion. For the thermal higgsino, they take $m_\chi=1.08\pm0.02$ TeV and choose $1.08$ TeV, with leading tree-level rates $\langle\sigma v\rangle_{WW}\simeq8\times10^{-27}~{\rm cm}^3/{\rm s}$ and $\langle\sigma v\rangle_{ZZ}\simeq5\times10^{-27}~{\rm cm}^3/{\rm s}$, plus a one-loop line rate $\langle\sigma v\rangle_{\rm line}\simeq1\times10^{-28}~{\rm cm}^3/{\rm s}$ and endpoint photons that give an $O(1)$ 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 $>5\sigma$ for most profiles, while SWGO is weaker by a factor $\sim2$ in $\langle\sigma v\rangle$ and current Fermi and H.E.S.S. limits still fall short of $\mu=1$ by $O(1)$–$O(10)$ depending on the profile [2405.13104]. The same study emphasizes that profile uncertainty is structurally important: the twelve FIRE-2 profiles show $O(1)$–$O(10)$ variations in the central $J$-factor, Romulus is among the most cuspy, Thelma among the most cored, and the ON/OFF subtraction strategy loses a factor $>2$ in sensitivity relative to full-template fitting [2405.13104]. 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 [2405.13104]. 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 $100$ hr/yr and a $1.1$ TeV thermal higgsino target, the projected test statistic reaches $22$ in 2028 and $60$ in 2030 for an Auriga-median profile, but only $1.5$ and $4.0$ for Einasto, and $0.2$ and $0.5$ 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 [2506.08084]. Earlier CTA forecasts already found a mean expected $95\%$ CL limit of $2\times10^{-26}~{\rm cm}^3/{\rm s}$ at $m_\chi=1$ TeV, with a $5\sigma$ discovery threshold about a factor $\sim2$ above this and explicit sensitivity to the thermal higgsino near $m_\chi\simeq1$ TeV [2008.00692]. In split supersymmetry, a related $(\mu,M_2)$ Higgsino discovery plane overlays the thermal band at $\mu\approx1.1$ TeV with direct-detection and electron-EDM reach, showing substantial overlap around $\mu=1.1$ TeV and $M_2=2$–$10$ TeV [2206.11912]. 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 $\Delta m$ or $\mu$; 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 $m_\chi\simeq1.08$–$1.1$ TeV whose observability is controlled jointly by $\langle\sigma v\rangle$, spectral modeling, and the inner-halo $J$-factor. Source: https://www.emergentmind.com/topics/higgsino-discovery-plane