Standard Model Supersymmetry Breaking

An optional symmetry

Supersymmetry is a proposed extension of the Standard Model of particle physics. It assigns to every known fermion, a matter particle such as the electron or quark, a bosonic partner with the same mass, and to every known boson, a force carrier such as the photon or gluon, a fermionic partner. The partners have names like selectron, squark, photino, and gluino. The proposal is attractive because it would solve the hierarchy problem, the puzzle of why the Higgs boson's mass is so much lighter than the Planck scale, and it offers a dark matter candidate in the lightest superpartner.

The problem is that exact supersymmetry is not observed. If an electron and its partner selectron had the same mass, selectrons would be easy to produce and detect. They are not. The Large Hadron Collider has set lower limits on superpartner masses, roughly 1.5 TeV for squarks and 2.0 TeV for gluinos, so any supersymmetry must be broken, meaning the partners must be heavier than their Standard Model counterparts. The mechanism of that breaking is unknown, with gravity-mediated, gauge-mediated, and anomaly-mediated scenarios all on the table.

In Recognition Science, the framework models this breaking as a consequence of its eight-tick recognition cycle. The framework's ledger, a discrete record of recognition events, assigns bosons even phases (0, 2, 4, 6) and fermions odd phases (1, 3, 5, 7) within the cycle. The framework's cost function J, which measures the price of a recognition event, gives different average values for the even and odd phase sets. The framework proposes that this difference in J-cost is what breaks the boson-fermion equivalence, making supersymmetry naturally broken rather than exact.

The module in the framework's machine-checked library of formal statements is explicitly a sketch, not a proof. Every declaration in it concludes in True or another tautology, so nothing in it is a result. The module records the intent to establish the breaking mechanism from J-cost asymmetry and lists falsification criteria: exact supersymmetry discovered, equal J-costs for bosons and fermions, or a wrong phase assignment would each refute the account. The framework does not require supersymmetry; it offers alternative explanations for the hierarchy problem and dark matter through its own structures.

The practical takeaway is that the framework is compatible with a broken supersymmetry but does not depend on it. The module sets a target for future work: to state the real claim as a formal proposition and prove it. Until then, the explanation is a sketch of intent, not an established derivation.

/-- RS perspective on supersymmetry breaking:

    1. **8-tick phases**: Bosons and fermions have different phases
    2. **J-cost asymmetry**: Different phases → different J-costs
    3. **SUSY breaking**: J_boson ≠ J_fermion
    4. **Scale**: From magnitude of J-cost difference
    5. **LHC limits**: Push SUSY to >1 TeV
    6. **RS flexibility**: Works with or without SUSY -/
def summary : List String := [
  "Bosons: even 8-tick phases",
  "Fermions: odd 8-tick phases",
  "J-cost asymmetry breaks SUSY",
  "Explains why SUSY must be broken",
  "RS doesn't require SUSY"
]

/-- The J-cost difference between bosons and fermions:

    Even phases: cos(nπ/4) = 1, 0, -1, 0 for n = 0, 2, 4, 6
    Odd phases: cos(nπ/4) = 1/√2, -1/√2, -1/√2, 1/√2 for n = 1, 3, 5, 7

    Average J-cost differs! This is the SUSY breaking parameter. -/
noncomputable def bosonJCostAverage : ℝ :=
  (Real.cos 0 + Real.cos (π/2) + Real.cos π + Real.cos (3*π/2)) / 4

What this page does not claim

No theorem proves that supersymmetry must be broken. No claim is made that the framework's explanation matches any measured superpartner mass.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/StandardModel/SupersymmetryBreaking.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: