Supersymmetry Basics

Core Idea

Supersymmetry (SUSY) is a symmetry relating bosons and fermions: every Standard Model particle has a superpartner with spin differing by 1/2. SUSY solves the hierarchy problem by cancelling the quadratic divergences in the Higgs mass, provides a dark matter candidate (the lightest supersymmetric particle), and enables gauge coupling unification. The minimal supersymmetric Standard Model (MSSM) doubles the particle content and introduces over 100 new parameters, making it a rich but complex framework.

Explainer

Supersymmetry is the unique extension of the Poincare spacetime symmetry that relates particles of different spin. In a SUSY theory, every boson has a fermionic partner and vice versa: the electron (spin 1/2) has a scalar selectron (spin 0), the photon (spin 1) has a fermionic photino (spin 1/2), and the Higgs boson (spin 0) has a fermionic higgsino (spin 1/2). This doubling of the particle spectrum is the price of the symmetry, but the payoff is substantial: the quadratic divergences in the Higgs mass cancel exactly if SUSY is unbroken.

The MSSM (Minimal Supersymmetric Standard Model) is the simplest phenomenologically viable SUSY model. It contains superpartners for all SM particles: squarks and sleptons (spin-0 partners of quarks and leptons), gluinos (spin-1/2 partner of the gluon), charginos and neutralinos (spin-1/2 mixtures of wino, bino, and higgsino states), and two Higgs doublets (required by the structure of SUSY and holomorphy of the superpotential), giving five physical Higgs bosons (h, H, A, H+, H-). The 105 new parameters are the soft SUSY-breaking masses, mixing angles, and phases.

A key feature of the MSSM is R-parity, a discrete symmetry under which SM particles have R = +1 and superpartners have R = -1. If R-parity is conserved, superpartners are always produced in pairs and the lightest superpartner (LSP) is stable. A neutral LSP (typically the lightest neutralino) is an excellent dark matter candidate. R-parity also implies that SUSY events at the LHC always contain two LSPs escaping the detector, producing the characteristic missing transverse energy signature. SUSY searches at the LHC typically look for jets and/or leptons plus large missing energy.

The experimental status of SUSY is that no superpartners have been found. LHC searches have excluded gluinos below ~2.3 TeV and first/second generation squarks below ~1.8 TeV in simplified models. Light stops (below ~1.2 TeV in most scenarios) are excluded except in compressed spectra where the stop-LSP mass difference is small. These limits have pushed the MSSM into regions of parameter space where the hierarchy problem solution requires some fine-tuning (~1% level or worse), leading to debate about whether naturalness remains a reliable guide. SUSY remains theoretically attractive for its other virtues -- gauge coupling unification, dark matter, and its role in string theory -- and the search continues at the LHC, the HL-LHC, and future colliders.