In R-parity-conserving supersymmetry with a neutralino lightest supersymmetric particle, the observed cosmological dark matter relic density can be set by co-annihilation between the neutralino and nearly mass-degenerate sleptons — a regime highlighted as the motivation of the ATLAS 8 TeV direct slepton search (EPJ Web Conf. 71, 00034 (2014)) and favored in gauge- and anomaly-mediated supersymmetry breaking. The mechanism requires slepton–neutralino mass splittings of only a few to a few tens of GeV, exactly where the two-lepton plus missing-transverse-momentum signature becomes soft and collider sensitivity collapses. The problem is to determine, quantitatively, how much of this co-annihilation region is already excluded by existing searches and how much can be covered by the High-Luminosity LHC, by future lepton colliders, or by complementary direct-detection probes — and which parts, if any, remain inaccessible to all foreseen techniques.

Background

In R-parity-conserving supersymmetric (SUSY) extensions of the Standard Model, the lightest supersymmetric particle (LSP) is stable and provides a canonical weakly interacting massive particle (WIMP) dark matter candidate. Here the LSP is the lightest neutralino χ~10\tilde{\chi}_{1}^{0}, the lightest mass eigenstate of the neutral fermionic superpartners of the electroweak gauge and Higgs bosons; its thermal relic abundance is fixed by annihilation in the early universe and is measured today by the Planck satellite to about 0.12 times the critical density. Sleptons are the scalar superpartners of the charged leptons (selectron e~\tilde{e}, smuon μ~\tilde{\mu}, stau τ~\tilde{\tau}), each in left- and right-handed chirality eigenstates. In gauge-mediated and anomaly-mediated SUSY-breaking scenarios, sleptons can be among the lightest superpartners, and in many constrained models (such as the CMSSM, the constrained minimal supersymmetric standard model) the cosmologically favored parameter region is the slepton co-annihilation strip.

Co-annihilation (Griest and Seckel, 1991) is the mechanism by which a next-to-lightest supersymmetric particle close in mass to the LSP remains in thermal equilibrium at freeze-out, so that its annihilation and co-annihilation channels modify the LSP relic abundance; the slepton number density is Boltzmann-suppressed as e−Δm/Te^{-\Delta m/T} with Δm=mℓ~−mχ~10\Delta m = m_{\tilde{\ell}} - m_{\tilde{\chi}_{1}^{0}}, so the mechanism operates only when Δm\Delta m is comparable to the freeze-out temperature scale — a few to a few tens of GeV for electroweak-scale masses. Exact neutralino–slepton co-annihilation cross sections were computed by Nihei, Roszkowski and Ruiz de Austri (2002); a bino-like neutralino with a light nearly degenerate slepton is the minimal realization (the bino and higgsino are the superpartners of the U(1) gauge boson and of the Higgs bosons, respectively, and the lightest neutralino is in general a mixture of these with the wino, the W-boson superpartner).

The experimental handle is direct slepton pair production, pp→ℓ~+ℓ~−pp \to \tilde{\ell}^{+}\tilde{\ell}^{-} with ℓ~→ℓ χ~10\tilde{\ell} \to \ell\,\tilde{\chi}_{1}^{0}, giving two opposite-sign charged leptons plus missing transverse momentum (ETmissE_{\mathrm{T}}^{\mathrm{miss}} — the transverse-momentum imbalance carried by the two undetected neutralinos). LEP (the Large Electron–Positron collider at CERN) excluded slepton masses below roughly 80–90 GeV. With the 8 TeV LHC dataset (20.3 fb−1^{-1}), ATLAS searched in the e±μ∓e^{\pm}\mu^{\mp} channel (different lepton flavours, chosen to suppress the Drell–Yan background, i.e. lepton pairs produced through virtual photon or Z-boson exchange) and excluded a common left- and right-handed selectron/smuon mass between 90 and 320 GeV for a massless neutralino — the result presented by Claire David on behalf of ATLAS (EPJ Web Conf. 71, 00034 (2014)), whose introduction motivates light sleptons precisely by the co-annihilation connection to the dark matter relic density; the underlying analysis was published as JHEP 05 (2014) 071.

The essential difficulty is that the quoted limit applies to the large-Δm\Delta m part of the (mℓ~,mχ~10)(m_{\tilde{\ell}}, m_{\tilde{\chi}_{1}^{0}}) plane. As Δm\Delta m shrinks toward the values required for co-annihilation, the decay leptons become soft (low transverse momentum), fail standard lepton triggers and selections, and the sensitivity collapses back toward the LEP bound: the co-annihilation region lives inside the 'compressed spectrum' regime. Searches then must rely on a hard initial-state-radiation (ISR) jet recoiling against the slepton pair, on soft-lepton reconstruction, or on other handles, with steeply rising Standard Model backgrounds. The ATLAS 8 TeV slepton search presents direct pair production as the probe of this regime but does not quantify how much of the relic-density-favored region its limits actually cover. The question of coverage — what is excluded today, what the (HL-)LHC can cover, and what requires future facilities such as e+e−e^{+}e^{-} colliders — defines the problem. (HL-LHC denotes the high-luminosity phase of the LHC, with an order of magnitude more data.)

Problem Statement

Determine, quantitatively, the experimental accessibility of the slepton co-annihilation regime of neutralino dark matter. Within the supersymmetric parameter space in which the observed cosmological relic density is set by co-annihilation between a neutralino lightest supersymmetric particle and nearly mass-degenerate sleptons (including the selectron/smuon and stau cases, left- and right-handed chiralities, and bino- or higgsino-like neutralino composition, with the slepton–neutralino mass splitting small enough for co-annihilation to control the abundance):

(i) establish which regions are already excluded by existing experimental results (LEP slepton limits; LHC Run-1 (7–8 TeV, 2010–2012), Run-2 (13 TeV, 2015–2018) and Run-3 (13.6 TeV, 2022–2026) direct slepton, compressed-spectrum and corridor searches; direct-detection limits),

(ii) establish which regions can be probed by the HL-LHC, by future e+e−e^{+}e^{-} colliders — the International Linear Collider (ILC), the Compact Linear Collider (CLIC), the Future Circular Collider FCC-ee, and the Circular Electron Positron Collider (CEPC) — within their kinematic and projected luminosity reach, or by complementary indirect and direct probes, identifying the search techniques (ISR-assisted soft-lepton selections, disappearing-track and long-lived-particle signatures, precision observables) required in each case, and

(iii) establish which regions, if any, remain inaccessible to all foreseen experimental techniques — together with the concrete search strategies that would close the remaining gaps.

References

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