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A charged fermionic mass eigenstate formed by mixing charged electroweak gauginos and higgsinos in a supersymmetric model. Its production and decay can yield leptons and missing transverse momentum when a stable neutral lightest state is present.

A scalar sum of missing transverse momentum magnitude and selected high-energy transverse momenta, used as a hard-event-scale diagnostic in some supersymmetry searches. Which jets and leptons enter must be defined. It is not an invariant mass or the solid-state effective mass, and no universal equality with a produced particle mass holds.

Additional collisions overlapping an event in the same beam crossing or detector response window. Extra tracks and calorimeter deposits affect particle-jet reconstruction, isolation and missing transverse momentum. Vertex association, subtraction and response calibration reduce the effect but leave uncertainties that depend on collision conditions.

A broad search over event classes such as jets, leptons and missing transverse momentum, with bins chosen to cover several production or decay possibilities. It still has acceptance and model assumptions; inclusive does not mean sensitive to every supersymmetric spectrum.

The energy component of the difference between the known initial four-momentum and the measured visible final four-momenta. In equal-beam electron-Positron collisions it is $\sqrt{s}-{\sum }_i{E}_i$ in natural units. It can arise from escaping neutrinos, but also from detector losses; it is distinct from the missing invariant mass and missing transverse momentum.

Missing transverse momentum is the negative vector sum of reconstructed visible transverse momenta, with detector corrections specified. Under the ideal hypotheses of zero total incoming transverse momentum, complete visible reconstruction and exactly one invisible neutrino, momentum conservation givesThe neutrino is not directly seen. Even under these ideal hypotheses, its longitudinal momentum $p_{z\nu }$ is not measured. Beam remnants can carry substantial unobserved longitudinal momentum; the colliding quarks' longitudinal momenta are also unknown event by event. Imposing an assumed parent mass can constrain $p_{z\nu }$, but that imports a hypothesis rather than measuring it. Finite coverage, poorly reconstructed particle jets and other invisible particles can also generate or modify missing transverse momentum.

Gravitational evidence requires much more nonbaryonic matter than can be supplied by ordinary luminous material or by the baryon abundance permitted by nucleosynthesis. A stable, electrically neutral massive particle is a plausible cold component. Thermal production followed by cosmological particle freeze-out gives an additional motivation: an annihilation rate near a weak-interaction scale can leave an appreciable relic abundance. This is a mechanism and search hypothesis, not proof that the dark matter must be a WIMP or have any particular elastic-scattering cross section.

The plotted regions are conditional WIMP interpretations of different measurements. The experiments use different targets and distinguish signal from background differently:

The plot also includes CRESST experiment, whose cryogenic calcium-tungstate modules combine phonon and scintillation-light signals. Different nuclei contribute to its recoil interpretation. Its excess region is another conditional candidate region, not an extra confirmed detection.^[ref]

Around ten GeV, the shaded regions favour cross sections roughly $10^{-41}$–$10^{-40}\mathrm{c}{\mathrm{m}}^2$, while the XENON100 solid curve and the improved low-mass CDMS curve cut into or exclude much of those regions under the common elastic, spin-independent WIMP-nucleus scattering interpretation expressed per nucleon. There is tension within that shared model; the plot does not show mutually confirmed discoveries. electron backgrounds, threshold response, nuclear-recoil quenching factors, channeling assumptions and the halo velocity distribution can shift interpretations. Changing the interaction model can also alter target comparisons, but cannot establish a WIMP by assertion. The 100-live-day XENON100 result itself reported candidates compatible with estimated background.^[ref]

For a rough dimensional event estimate, $1\mathrm{c}{\mathrm{m}}^2=10^{-4}{\mathrm{m}}^2$ givesIf a collider production cross section had this value, that small yield, before acceptance and backgrounds, would not support a likely discovery. The plotted nuclear-scattering cross section is not the LHC production cross section, however. Converting between them needs a mediator, couplings, parton distributions and production kinematics; a light stable WIMP would normally be inferred from missing transverse momentum with a visible recoil object, not a visible WIMP track. The mass makes pair production kinematically accessible, but the plot and integrated collider luminosity alone do not decide discovery probability.

For the relic estimate, define $M=m{c}^2$ and $\theta =k_{B}T$. The sharp-freeze-out relic dilution model givesAssume stable particles, no subsequent annihilation, and $RT=\mathrm{constant}$. Conserved comoving particle number then givesThe present rest-energy density and its critical fraction areThus the supplied toy model yields a cosmologically substantial density, of the right broad scale to motivate a dark-matter candidate. It is not an independent precision prediction: $P$ is imposed and the abundance depends exponentially on it. If entropy degrees of freedom change, entropy conservation instead gives an extra factor $g_{\ast s,0}/g_{\ast s,f}$ in $n_0$ when using the photon temperature. The species content needed to evaluate that correction is not supplied. A realistic calculation also follows residual annihilations with the abundance Boltzmann equation rather than stopping exactly at equilibrium freeze-out.

supersymmetry pairs bosonic and fermionic degrees of freedom; broken supersymmetry permits partners heavier than known particles. At the Large Hadron Collider, strong production of squarks and gluinos is an important channel. If R-parity is conserved, partners are produced in pairs and their cascades end in a stable lightest supersymmetric particle. A neutral weakly interacting lightest supersymmetric particle escapes, giving missing transverse momentum together with jets and possibly leptons. Conservation is tested transversely because the initial parton longitudinal momenta are unknown.

The experimental observable isneutrinos produce genuine missing transverse momentum, and calorimeter mismeasurement or detector defects can imitate it. Searches use jet multiplicity, transverse momenta, missing momentum, angular separation cuts and a collider effective mass such as $m_{\mathrm{eff}}=p_T^{\mathrm{miss}}+\sum p_T^{\mathrm{jet}}$. Isolated-lepton selections explore complementary cascades. Trigger efficiency, jet energy scale, collision pileup and event cleaning affect acceptance.

A credible search estimates backgrounds from particle-physics control regions before inspecting the signal region. Invisible $Z\to \nu \bar{\nu }$ plus jets can be constrained using photon-plus-jets or visible $Z\to {\ell }^{+}{\ell }^{-}$ samples with control-region transfer factors. Lepton-enriched samples constrain $W$ and top backgrounds with lost leptons; multijet samples constrain fake missing momentum. A joint likelihood includes these observations and nuisance parameters for systematic uncertainties. Agreement with background gives upper bounds on signal rate and conditional mass exclusions. The pre-examination ATLAS 7 TeV analysis is a concrete example of this strategy and reported no significant excess.^[ref]

Electroweak production motivates multilepton searches; compressed spectra can give soft visible decay products and require special selections such as recoil against initial-state radiation. R-parity violation can instead remove the stable missing-particle signature, requiring other searches. An exclusion always depends on masses, branching fractions, production rates and decay assumptions; a null jets-plus-missing-momentum result does not exclude supersymmetry as a whole.

supersymmetry predicts partners with spins differing by one half. At a proton collider, strongly interacting squarks and gluinos can be pair produced if kinematically accessible. With conserved R-parity, their cascade decays end in a stable lightest supersymmetric particle, often a neutralino. The generic signature is energetic particle jets, possibly leptons or heavy-flavour jets, together with missing transverse momentum from invisible particles. Longitudinal missing momentum is not an equally clean observable because the initial parton momentum fractions are unknown.

A practical inclusive search defines collider signal regions using jet multiplicity, transverse momenta, missing transverse momentum and an event scale such asLeptonic and heavy-flavour selections probe other decay chains. For a compressed supersymmetric spectrum, the daughter particles can be soft, making a hard initial-state radiation jet useful for triggering and recoil. Direct chargino or neutralino production instead motivates multilepton searches. Decays with R-parity violation can yield high jet or lepton multiplicities with little missing momentum, and long-lived particles motivate displaced vertices, disappearing tracks or anomalous ionization. No single selection covers all these cases.

The difficult issue is background inference. Invisible $Z$ decay with jets is a real missing-momentum background: a photon-plus-jets sample or reconstructed $Z$ decays to charged leptons constrains its normalization and recoil shape through modeled transfer factors. A single-lepton collider control region constrains $W$ and top backgrounds whose charged lepton is missed in the collider signal region. Jet mismeasurement in ordinary multijet events gives instrumental missing momentum; angular cuts, detector-quality checks and control samples test that tail. Validation regions check these extrapolations without tuning on the final signal count.

detector acceptance, trigger efficiency, jet calibration, collider luminosity, theoretical production rates and transfer factors enter a likelihood as nuisance parameters. One compares the observed signal-region distribution with background-only and signal-plus-background hypotheses, using a profile likelihood and reporting exclusions for specified masses, branching fractions and spectra. As a pre-examination example, the 2014 ATLAS zero-lepton jets-plus-missing-momentum search used $20.3\mathrm{f}{\mathrm{b}}^{-1}$ at $8\mathrm{TeV}$ and found no significant excess. Its interpretation depended on R-parity conservation and a neutralino lightest state; different simplified models gave different mass exclusions.^[ref]

A null search excludes the tested parameter region, not supersymmetry as a whole. Conversely, a missing-momentum excess alone would not establish supersymmetry: one would need consistent masses, decay chains, couplings and eventually spin information. A stable particle on detector flight-time scales is not thereby proved stable for the age of the universe.

supersymmetry relates bosons and fermions through fermionic symmetry generators. A main motivation is the Lorentz scalar hierarchy problem: related boson and fermion loop contributions cancel particular ultraviolet sensitivities in an exactly supersymmetric theory. soft supersymmetry breaking leaves residual sensitivity to the superpartner scale, so a very heavy spectrum does not automatically solve naturalness. Supersymmetric matter content can also improve gauge-coupling unification, and a stable neutral lightest superpartner can be a dark-matter candidate. None of these motivations is itself experimental evidence; supersymmetry must be broken if ordinary particles and their partners have different observed masses.

If R-parity is conserved, superpartners are produced in pairs and cascades end in a stable lightest supersymmetric particle. A neutralino LSP can escape the detector, giving missing transverse momentum. Colored squarks and gluinos can generate energetic jets, sometimes b-tagged jets and leptons, plus that imbalance. An inclusive supersymmetry search classifies broad event samples by jet and lepton multiplicities, transverse momentum sums and missing momentum, without requiring a fully reconstructed decay chain.

Background controls are part of the physics argument. Lost-lepton W and top events can be constrained using lepton collider control regions; invisible-Z production can be related to visible-Z or photon samples with appropriate transfer factors. Instrumental imbalance in multijet events needs detector-quality checks and data sidebands. An excess in a collider signal region should survive uncertainty in those extrapolations, efficiencies and luminosity, with independently defined validation regions and attention to the number of searches performed.

An exclusive supersymmetry search targets a more specific production mode and decay pattern. Electroweak chargino-neutralino production can yield three leptons plus missing momentum; a cascade through a slepton can yield a dilepton invariant-mass edge that constrains mass combinations. Such searches often have cleaner backgrounds but depend more strongly on branching fractions and intermediate masses. An endpoint does not necessarily determine every absolute mass without additional observables.

Different spectra require different strategies. For a compressed supersymmetric spectrum, small parent-daughter mass differences make the visible decay products soft. initial-state radiation can recoil against the pair and provide a trigger, supplemented by soft-lepton reconstruction. The ATLAS compressed-spectrum study explicitly uses small neutralino mass differences and initial-state radiation to define a dedicated search rather than applying a hard-lepton selection indiscriminately.^[ref] If R-parity is violated, the LSP can decay visibly, so high-multiplicity jet or lepton channels may matter more than large missing momentum. CMS separately studied hadronic and leptonic final states for this reason.^[ref] Long-lived particles instead motivate displaced vertices, disappearing tracks, abnormal ionization or time-of-flight measurements. Thus there is no single model-independent missing-energy cut that covers every supersymmetric spectrum.

For the hypothetical relic-density calculation, use the supplied distribution and retain its prefactor exactly. Put $M=m{c}^2$, $\Theta =k_{B}T$ and ${\Theta }_0=k_B{T}_0$. Thennumber density, denoted $N$ in the paper, is written $n$ here to distinguish it from a total particle count. The cosmological particle freeze-out temperature in energy units isAssume a stable nonrelativistic relic, negligible further annihilation and $aT=\mathrm{constant}$ after cosmological particle freeze-out, using sharp-freeze-out relic dilution. Its comoving particle number is conserved, soThe particle mass cancels from this present number density under the stated approximation. Its present rest-energy density is $M{n}_0$, not merely $n_0$:This is only 0.371% of the critical density, not a universe-closing component. The correct further comparison is with the measured dark-matter fraction, not an assumption that all critical density must be dark matter. In standard cosmology this abundance would be a small subcomponent, despite a possible collider discovery.

The exponential freeze-out sensitivity makes the result highly sensitive to $P$. Also, thermal entropy release means $aT$ is not exactly constant through the whole cosmic history. If total comoving entropy is conserved, the above number density acquires a factor $g_{\ast s,0}/g_{\ast s,f}$, involving entropy degrees of freedom. Those degrees of freedom and a full annihilation history are not given, so no precise correction is justified from the supplied data.

Establishing the nature of dark matter would require more than measuring a missing particle's collider mass. Measure its spin, charges, interactions, decay lifetime or stability limits, and annihilation or coannihilation processes; compare the resulting relic calculation with cosmological observations. Seek compatible direct nuclear-recoil signals and indirect annihilation or decay products, while controlling astrophysical and detector backgrounds. A collider-invisible lifetime need not be cosmologically long, and nonthermal production could change the abundance. A consistent particle identity, cosmological abundance and independent non-collider evidence are needed to connect the hypothetical discovery to the dark matter.

The dominant semileptonic decay is $t\to b{W}^{+}\to b{\ell }^{+}{\nu }_{\ell }$. Replacing $b$ by $s$ or $d$ weights the amplitude by $V_{ts}$ or $V_{td}$ rather than $V_{tb}$. Neglecting the down-type masses,with the source's rounded matrix entries. For the $W$, three leptonic widths and two open up-type quark rows with three colours give nine common width units. Thus, ignoring QCD and final-mass corrections,Summing all three flavours gives approximately one third; summing only electron and muon modes gives approximately $22.2\%$. These are per-top branching ratios, not the separate branching ratio of a specified two-top event topology.

An isolated high-transverse-momentum charged lepton, missing transverse momentum from the neutrino, and a tagged bottom jet form a much cleaner signature than an entirely hadronic final state amid QCD jets. Electrons and muons are the easiest charged-lepton flavours to identify cleanly. Tau decays add neutrinos and often hadrons, making identification and reconstruction more difficult. The figure contains the quark/lepton-level charged-current diagram as well as the rare-loop examples used below.

For a $t\to cZ$ search, the cleanest neutral-boson reconstruction is $Z\to e^{+}{e}^{-}$ or ${\mu }^{+}{\mu }^{-}$: require an isolated opposite-sign same-flavour pair near the $Z$ mass and a jet forming the top mass with that pair. In top-pair events, tagging the other top through its ordinary $bW$ decay provides a bottom jet and, if its $W$ is leptonic, another isolated lepton and missing transverse momentum. Kinematic reconstruction and heavy-flavour information help reject vector-boson-plus-jets and other backgrounds. Hadronic or invisible $Z$ decays have higher rate but less distinctive backgrounds or incomplete mass reconstruction.

For the literal $t\to cZ\gamma$ channel, additionally require a prompt isolated photon and reconstruct the top with $Z+\gamma +$jet. For the alternative $t\to c\gamma$, use an isolated energetic photon and jet near the top mass, again exploiting the other top as a tag. These are search signatures; no present-day observation claim is needed to interpret the historical question.

At a hadron collider, select $W\to \ell \nu$ events and reconstruct the transverse massusing missing transverse momentum for the neutrino. Fit the shape, especially the region above the nominal Jacobian edge, with finite-width resonance templates convolved with detector resolution, recoil modelling and backgrounds. The Breit-Wigner width controls this off-shell tail. Calibrated momentum and missing-momentum resolutions must be separated from the physical width. This is a lineshape measurement; the lifetime is far too short for a direct flight-distance measurement.

Use leptonic decays: an isolated high transverse momentum positive electron or muon, together with substantial missing transverse momentum from the neutrino, provides a clean $W^{+}$ signature. The lepton transverse momentum has a Jacobian scale near $m_W/2$, and the lepton–missing-momentum transverse mass has an edge near $m_W$, broadened by width, recoil and resolution. Lepton identification, isolation and a prompt primary-vertex origin suppress Jets faking leptons and heavy-flavour decays. Missing-momentum quality requirements suppress mismeasured multijet events; a veto on a second oppositely charged lepton suppresses $Z\to {\ell }^{+}{\ell }^{-}$ when both are reconstructed. Hadronic $W$ decays have a much larger ordinary-QCD background.

For the selected muon channel, finite curvature resolution in the magnetic tracking system broadens the reconstructed transverse momentum spectrum. A high-$p_T$ track has small sagitta, so spatial measurement errors, alignment errors and magnetic-field calibration errors become important; at high momentum an approximately fixed uncertainty in $1/p_T$ gives $\delta p_T\propto p_T^2$. Multiple Coulomb scattering contributes at lower momenta. If the transverse mass is fitted, finite hadronic-recoil resolution additionally smears the inferred missing transverse momentum. These are experimental effects, distinct from the physical recoil and width in ii.

Choose $W^{+}\to {\mu }^{+}{\nu }_{\mu }$. Important backgrounds include quantum chromodynamics production of heavy-flavour hadrons with semileptonic decays, in-flight pion or kaon decays, and hadrons penetrating the calorimeters. These generally have accompanying jet activity; semileptonic decays can contain real neutrinos, while jet mismeasurement can fake missing transverse momentum. Heavy-flavour tracks can originate at a displaced decay vertex. Require a high-$p_T$ isolated muon, agreement between inner tracking and the external muon system, and substantial missing transverse momentum inconsistent with detector noise or a mismeasured jet.

The genuine electroweak backgrounds include $Z\to {\mu }^{+}{\mu }^{-}$ with one muon lost and $W\to \tau \nu \to \mu \nu \nu \nu$. Veto a second reconstructed opposite-sign muon and use the dimuon invariant mass when both are present to reject the Z boson channel. The tau-mediated spectrum is softer and contains extra missing particles; template fits and control samples estimate its residual contribution. Detector acceptance determines how much of the lost-muon background survives.

The useful modes are $\boxed{W^{+}\to e^{+}{\nu }_e\text{and}{W}^{+}\to {\mu }^{+}{\nu }_{\mu }}$ and their charge conjugates. An electron gives an isolated track and localized electromagnetic shower; a muon gives an isolated penetrating track. Both allow a well-calibrated charged-lepton transverse momentum and a missing transverse momentum measurement for the neutrino.

The tau lepton decays before detection, usually adding further neutrinos. Its visible momentum is only part of the original tau momentum, so the simple two-body endpoint is lost. For the direct electron and muon modes, the transverse massalso has an ideal endpoint at $M_W$ and avoids needing the unmeasured neutrino longitudinal momentum. Fits to this distribution or the charged-lepton $p_T$ spectrum determine $M_W$.

R-parity is the multiplicative number $R_p=(-1{)}^{3(B-L)+2s}$, where $B$ is baryon number, $L$ is lepton number and $s$ is spin. Standard Model particles are even and their superpartners are odd.

If conserved, an initially even state produces an even number of odd states, and the lightest odd state is stable. A neutral stable state may escape a detector and give missing transverse momentum. Stability alone does not establish its cosmological relic abundance.^[ref]

For a two-body W boson decay into a charged lepton $\ell$ and a neutrino, neglect both daughter masses and use natural units $c=1$. Let $\Delta \varphi$ be the angle between the daughter transverse momenta. Identifying the missing transverse momentum with the neutrino's givesThis observable uses no $p_{z\nu }$. The 1983 UA1 experiment paper already used transverse mass as a lower bound on parent mass, before making additional decay-model assumptions for a mass estimate.^[ref]

The bound follows directly from the energy–momentum relation. For each massless daughter write its four-momentum, using rapidity $y$ and azimuth $\varphi$, asUsing the Minkowski inner product with positive time sign, $p^2=E^2-|\mathbf{p}{|}^2$, the two daughter four-momenta give the true parent invariant mass $M$:Since $\cosh u\ge 1$, $m_T\le M$, with equality at equal daughter rapidities when both transverse momenta are nonzero. Thus the unmeasured longitudinal information can enlarge the true invariant mass, but cannot lower it below this ideal transverse mass.

For an original example, stipulate $p_{T\ell }=p_{T\nu }=40\mathrm{GeV}$ and $\Delta \varphi =\pi$. Then $m_T=80\mathrm{GeV}$. Equal rapidities give $M=80\mathrm{GeV}$; choosing $y_{\ell }-y_{\nu }=1$ with exactly the same transverse readout gives $M=80\cosh (1/2)\simeq 90.210\mathrm{GeV}$. One measured transverse configuration therefore permits different true parent masses.

A W boson decay can leave one visible charged lepton and a large missing transverse momentum; a Z boson decay can instead supply two visible leptons whose four-momenta determine an invariant mass. The two signatures answer the same existence question with different missing information. The electroweak unification history recognized by the 1979 Nobel Prize in Physics predates these 1983 observations: the W boson and Z boson were predictions to test, rather than particles first proposed in 1983.

The Super Proton-Antiproton Synchrotron stored counterrotating proton and antiproton beams; stochastic cooling made accumulation of the scarce antiprotons practical. Carlo Rubbia's 1984 lecture describes track reconstruction in a large drift chamber inside a magnetic field, surrounded by segmented particle calorimeters. Their nearly complete angular coverage allowed an imbalance test for unobserved neutrinos.^[ref]