Past exam of the particle Astrophysics course of the University of Cambridge / 2015 / Paper 1 / 3 / b / Solution

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.