In R-parity–conserving supersymmetry, sparticles are always produced in pairs and every SUSY decay chain ends at the lightest supersymmetric particle (LSP) — here the neutralino χ — which is stable, electrically neutral, and interacts only weakly. It leaves the detector unseen, exactly like a WIMP dark-matter candidate. This view is the transverse plane itself (top-down, looking down the beam axis), the standard way collider physicists read an event display.
Each decay step conserves 2D energy-momentum in this plane. In the parent's rest frame, a two-body decay M → m₁ + m₂ gives daughters equal and opposite momentum of magnitude:
p* = √[(M²−(m₁+m₂)²)(M²−(m₁−m₂)²)] / (2M)
Each daughter is then Lorentz-boosted into the lab frame using the parent's own velocity β = p/E, applied as a genuine 2D boost:
E' = γ(E + β·p)
p' = p + [(γ−1)(β·p)/β² + γE] β, γ = 1/√(1−β²)
Because the two gluinos are produced back-to-back, the total transverse momentum before any decay is zero. After the invisible χ's escape, the visible jets alone don't balance — the missing transverse energy vector is defined as the negative vector sum of every visible jet:
MET = − Σ p_T(visible jets) ≡ Σ p_T(χ)
The engine computes both sides independently — MET from the visible jets only, and the true total χ momentum from the (normally hidden) invisible tracks — and shows their difference below the readout. It is always ≈ 0 GeV (floating-point roundoff only), which is the live proof that momentum is exactly conserved at every vertex.
- Mg̃ / Mχ — set the gluino and neutralino masses; a bigger mass gap gives the decay products more kinetic energy (harder jets, larger MET).
- Direct vs Cascade — direct is g̃ → q + χ (1 jet per side); cascade inserts an intermediate squark, g̃ → q + q̃, q̃ → q + χ (2 jets per side, and an extra boost step).
- Collide — fires one new pp → g̃g̃ event and redraws every track from the real boosted 4-momenta.
- Reveal invisible tracks — normally only jets are drawn (as in a real detector); this overlay shows where the "invisible" χ actually went, to make the momentum imbalance concrete.
This exact missing-transverse-energy signature — jets recoiling against nothing — is the primary search strategy the ATLAS and CMS experiments use to hunt for gluinos, squarks and neutralino dark matter at the LHC.