superpartners
Definition enumerates four example superpartner pairs with mass splittings in GeV. Model builders studying J-cost asymmetries in the Standard Model cite it to anchor SUSY breaking discussions against LHC data. Construction is a direct list literal of SuperPair structures with no computation or lemmas.
claimDefine superpartners as the list of structures each holding a boson name, its fermionic partner name, and a real mass splitting: (selectron, electron, 1000), (squark, quark, 1500), (gluino, gluon, 2000), (photino, photon, 500) with values in GeV.
background
SuperPair is the structure that records a boson name, a fermion name, and the real-valued mass splitting between them. The module places this definition inside the Recognition Science account of supersymmetry breaking, where J-cost differs between bosonic and fermionic sectors because of the eight-tick phase structure. Upstream results include the unification theorem that supplies the three Aristotelian conditions on any recognizer and the PhiForcingDerived structures that calibrate J-cost.
proof idea
Direct list literal construction of four SuperPair values; no lemmas or tactics are invoked beyond the structure definition itself.
why it matters in Recognition Science
Supplies the concrete data consumed by the softBreaking definition and the susy_breaking_scale theorem. It instantiates the Recognition Science claim that J-cost asymmetry across the phi-ladder spontaneously breaks supersymmetry, consistent with the eight-tick octave and the requirement that D equals three spatial dimensions. It touches the open question of whether the listed splittings remain compatible with current LHC bounds.
scope and limits
- Does not derive the listed mass splittings from the J-cost equation.
- Does not prove that any superpartners exist in nature.
- Does not compute the numerical SUSY breaking scale.
- Does not address gauge coupling unification or dark matter candidates.
formal statement (Lean)
66def superpartners : List SuperPair := [
proof body
Definition body.
67 ⟨"selectron", "electron", 1000⟩, -- GeV
68 ⟨"squark", "quark", 1500⟩,
69 ⟨"gluino", "gluon", 2000⟩,
70 ⟨"photino", "photon", 500⟩
71]
72
73/-! ## Why SUSY is Attractive -/
74
75/-- Benefits of supersymmetry:
76
77 1. **Hierarchy problem**: Cancels quadratic divergences
78 2. **Gauge coupling unification**: Couplings meet at ~10¹⁶ GeV
79 3. **Dark matter candidate**: Lightest superpartner (LSP)
80 4. **String theory**: Requires SUSY for consistency -/