Stealth SUSY Squark-Pair Production

• The paper explains how near-degenerate hidden sectors in stealth SUSY cause squark decays to yield low missing energy, challenging standard SUSY searches.
• Methodologies leverage NLO and NLL calculations combined with parton-shower matching to accurately simulate event kinematics and improve sensitivity.
• Implications include adopting high jet and photon multiplicity selections to extend exclusion limits and probe otherwise inaccessible SUSY parameter space.

Stealth supersymmetry (SUSY) squark-pair production denotes the collider process in which squarks, produced via strong interactions, undergo decays that lead to final states with little or no missing transverse energy (Eₜ^miss), primarily due to a nearly supersymmetric, mass-degenerate hidden sector. In such scenarios, standard search strategies based on high Eₜ^miss are blind, necessitating analyses that exploit alternative topological or kinematic features. Below is an in-depth treatment of stealth SUSY squark-pair production, drawing extensively on experimental and theoretical literature up to September 2025.

1. Stealth Mechanism and Production Channel Definition

Stealth SUSY models incorporate a hidden sector characterized by minimal SUSY breaking (i.e., small @@@@1@@@@ splitting δm between a singlet S and its superpartner Ṡ), which ensures nearly degenerate masses. In the canonical stealth scenario, the decay chain for squark-pair production is

$$\tilde{q} \to q~(\tilde{\chi}_1^0 \to \gamma~(\tilde{S} \to \tilde{G}~(S \to gg))),$$

where $\tilde{q}$ is the squark, $q$ the associated quark, $\tilde{\chi}_1^0$ the bino-like lightest visible sector neutralino, $\tilde{S}$ the singlino, $S$ the singlet, and $\tilde{G}$ the gravitino. With $\delta m = m_S - m_{\tilde{S}} \ll m_S$, the gravitino receives only a small fraction of the neutralino momentum, resulting in final states with low $E_T^{miss}$ (Collaboration, 2012, Collaboration, 2023, Kim et al., 2018, Alvarez et al., 20 Sep 2025).

Squark pair production itself occurs via gluon-gluon and quark-antiquark fusion, governed by strong interaction cross sections which are calculable at next-to-leading order (NLO) in SUSY-QCD. In the Minimal Supersymmetric Standard Model (MSSM), colored particles are produced only in pairs due to R-parity conservation (Beenakker et al., 2011, Krämer et al., 2012).

2. Simulation Methodologies and Kinematic Observables

Signal events for squark-pair production in stealth SUSY are simulated with generators (PYTHIA, MadGraph, Prospino) and detector simulations (PGS, Delphes) that include calorimeter effects, jet clustering (anti-$k_t$, $R=0.4 \text{–} 1.0$), and hadronic energy resolution (Usubov, 2010, Flores et al., 2019, Alvarez et al., 20 Sep 2025). Jets are reconstructed with high $p_T$ requirements ($> 50$ GeV for leading jets), though stealth decay topologies often favor large-radius (fat) jets ($R=1.0$) with $p_T > 200$–450 GeV and central rapidity ($|\eta|<1.5$).

Classical variables for SUSY discovery lose their discriminating power in the stealth context, but others remain valuable:

• $E_T^{miss}$ and $H_T^{miss}$: While $E_T^{miss}$ is globally suppressed in stealth decays, it remains sensitive to initial-state radiation and rare decay channels.
• $S_T$ (scalar sum of transverse momenta): Defined by $S_T = \sum p_T(\text{jets, photons, } E_T^{miss})$, $S_T$ acts as a discriminator for the event's hardness (Collaboration, 2012, Collaboration, 2023).
• Angular separations: Cuts on $\Delta R$ between photons/jets exploit the collimated nature of boosted decay products or the broader fakes in QCD backgrounds (Alvarez et al., 20 Sep 2025, Flores et al., 2019).
• Jet/photon multiplicity: Requiring multiple large-radius jets and photons suppresses SM backgrounds more effectively than conventional $E_T^{miss}$ cuts.

Event selection is thus characterized not by $E_T^{miss}$, but by high jet multiplicity, photon multiplicity, and nontrivial $\Delta R$ (Alvarez et al., 20 Sep 2025, Flores et al., 2019).

3. Missing Energy Suppression and Critical Role of Branching Ratios

The stealth mechanism operates via finely tuned mass splittings that suppress missing energy:

$$\Delta m = m_{\text{NLSP}} - m_S - m_{\text{LSP}} \simeq 0.5\text{–}1~\text{GeV},$$

as in the NMSSM realization with singlino LSP and bino NLSP (Kim et al., 2018). This configuration results in minimal momentum transfer to the LSP; visible decay products (photons, jets) become the primary search handles.

However, alternative decay channels—such as loop-induced radiative decays ($\tilde{\chi}_1^0 \to \gamma~\tilde{S}$) or three-body decays via off-shell $Z$ ($$\tilde{\chi}_1^0 \to \tilde{S}+Z^* \to \tilde{S}+f\bar{f}$$)—rapidly reintroduce missing energy. Even $\mathcal{O}(10\%)$ branching ratios into these modes can “wash out” stealth benefits, increasing sensitivity in conventional SUSY searches and lifting exclusion limits on gluino/squark masses by several hundred GeV (Kim et al., 2018). Thus, the branching ratios must satisfy

$$\mathrm{BR}(\tilde{\chi}_1^0 \to \tilde{S}+S) \approx 1 - \mathrm{BR}(\tilde{\chi}_1^0 \to \tilde{S}+f\bar{f}) - \mathrm{BR}(\tilde{\chi}_1^0 \to \tilde{S}+\gamma),$$

with the two-body stealth decay mode dominant to avoid conventional MET-driven exclusions.

4. Advanced Theoretical Calculations and Uncertainties

Stealth squark-pair production rates are evaluated at NLO in SUSY-QCD, with soft-gluon emission resummation at NLL or NNLL accuracy (Beenakker et al., 2011, Krämer et al., 2012, Collaboration, 2023). The Mellin-space matched cross section reads:

$$\tilde{\sigma}^{\mathrm{(res)}}_{ij \to kl}(N,\{m^2\},\mu^2) = \sum_I \tilde{\sigma}^{(0)}_{ij \to kl,I}(N,\{m^2\},\mu^2) ~ C_{ij\to kl,I}(N,\{m^2\},\mu^2) ~ \Delta_i ~ \Delta_j ~ \Delta^{(s)}_{ij\to kl,I},$$

where $\Delta_i$ encapsulates collinear radiation, and $\Delta^{(s)}$ soft-gluon resummation (Beenakker et al., 2011).

Total cross section predictions include renormalization/factorization scale uncertainties (typically propagated by varying $\mu$ from $0.5\mu_0$ to $2\mu_0$) and parton distribution function (PDF) uncertainties. For instance, combining uncertainties yields a theory error band of $\sim$20% at NLO+NLL (Krämer et al., 2012, Collaboration, 2023).

Parton-shower matching, using frameworks like POWHEG-BOX interfaced with Pythia6/Herwig++ (Gavin et al., 2013, Gavin et al., 2014), is essential for exclusive observable predictions and for realistic event descriptions when imposing experimental kinematic cuts. Benchmarks show inclusive K-factors $\sim$1.2–1.4, but differential “local” K-factors vary by up to $\pm20$% (Gavin et al., 2013).

In R-symmetric SUSY models (MRSSM), squark-pair production is fundamentally altered:

• Only mixed-chirality sfermion pairs are allowed ($q q \to \tilde{q}_L \tilde{q}_R$), leading to suppressed tree-level rates (Diessner et al., 2017).
• Enhanced NLO corrections (K-factors up to 10–20% higher than MSSM) due to super-oblique effects and Dirac gluino mass enter via

$$\sigma_{\text{super-oblique}} \propto \left( \frac{\alpha_s}{2\pi} \right) [\log(m_{O_s}^2/m_{\tilde{g}}^2) + \log(m_{O_p}^2/m_{\tilde{g}}^2)] \; \sigma_{LO},$$

where $m_{O_s}, m_{O_p}$ are sgluon masses.

5. Experimental Analyses and Sensitivity Extension

Stealth SUSY searches are designed to exploit event features independent of missing energy. Notable approaches include:

• Photon and jet multiplicity with $S_T$ selection: CMS analyses at $\sqrt{s}=7$–13 TeV (Collaboration, 2012, Collaboration, 2014, Collaboration, 2023) require $\geq$2 photons and $\geq$4 jets, with $S_T$ thresholds up to $2400$ GeV.
• Fat-jet reconstruction and angular topology: Selection criteria such as $N_\text{jets}^{R=1.0}>3$, $\Delta R_{\gamma_1,\gamma_2}>0.10$, and $\Delta R_{j_1,\gamma_1}>0.20$ boost sensitivity at low $E_T^\text{miss}$ (Flores et al., 2019, Alvarez et al., 20 Sep 2025).
• Invariant mass reconstruction ($m_{\gamma gg}$): The neutralino resonance can be reconstructed by combining the high-$p_T$ photon and gluon jets within a fat jet (Flores et al., 2019).
• Leptonic and $b$-jet final states: In extended scenarios, employing selection on $2j+4b+E_T^\text{miss}$ when squarks decay via cascades involving intermediate neutralinos and Higgs bosons (e.g., $\tilde{q} \to \chi_3^0 + j$, $\chi_3^0 \to \chi_1^0 + h$, $h \to bb$) (Arganda et al., 2021).

The background model for low $E_T^\text{miss}$, photon-plus-jets final state, following (Collaboration, 2023), is

$$b(N_j, S_T^i) = N^\text{norm}(N_j) \times f^{S_T}_i \times r(S_T, N_j),$$

using $N_j=2$ sideband templates and simulation-derived correction factors.

6. Exclusion Limits and Parameter Space Probed

Experimental results over the last decade show growing power in stealth SUSY searches:

• CMS at $\sqrt{s}=7$ TeV: squark masses $m_{\tilde{q}} < 1430$ GeV excluded (Collaboration, 2012).
• CMS at 8–13 TeV: exclusions extended up to $m_{\tilde{q}} \sim 1050$ GeV (photon analyses), and $m_{\tilde{q}} \sim 550$ GeV (lepton analyses) (Collaboration, 2014).
• Most stringent: CMS at $\sqrt{s}=13$ TeV, $138~\text{fb}^{-1}$, with limits reaching $m_{\tilde{q}} \sim 1850$ GeV for stealth squark-pair production (Collaboration, 2023).
• Missing-energy-independent selections, exploiting large-radius jet multiplicity and angular separations, push potential sensitivity up to $m_{\tilde{q}} \sim 2500$ GeV for bino mass of $650$ GeV (Alvarez et al., 20 Sep 2025).

These search strategies markedly complement conventional high-$E_T^\text{miss}$ analyses and unlock otherwise inaccessible regions of parameter space.

7. Implications and Future Directions

Stealth SUSY challenges standard SUSY search paradigms and necessitates precision modeling of both theoretical and detector effects. Key points:

• Extended sensitivity at low $E_T^\text{miss}$ is achievable with kinematic selections based on photon and jet topology, as opposed to missing energy.
• Precise mass configuration and controlled branching ratios are essential, as alternative decay channels rapidly nullify stealth protection.
• Complementarity with existing ATLAS and CMS high-$E_T^\text{miss}$ searches ensures broad coverage of the SUSY parameter space.
• Ongoing developments in parton-shower matching, NLO+NNLL cross-section calculations, and object reconstruction at future colliders (14–33 TeV) are critical (Cao et al., 2015, Das et al., 2017).
• Model-independent treatments highlight the fragility of stealth setups and inform future experimental strategies to avoid “blind spots” for unconventional SUSY signatures.

These elements jointly reinforce the necessity for both advanced phenomenological theory and innovative experimental practice in truly unveiling stealth SUSY squark-pair production at present and next-generation colliders.