Sparticle Cascade Decay & Missing Transverse Energy

Sparticle Pair Event

Gluino mass M_g̃ 1200 GeV

Neutralino (LSP) mass M_χ 150 GeV

Decay Chain

Auto-collide (every 1.6 s)

Reveal invisible χ tracks (cheat view)

Event Readout

Missing E_T (MET)

0 GeV

Visible ΣE_T

0 GeV

Jets this event

⟨MET⟩ last 20

0 GeV

How it works

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.

Each decay step conserves energy-momentum. 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:

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

MET = − Σ p_T(visible jets)  ≈  Σ p_T(χ)

M_g̃ / M_χ — 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.

Visible jet (quark) Invisible χ (LSP) MET vector

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