string_breaking

formal source

 133
 134/-- **THEOREM (String Breaking)**: When the string has enough energy to create a quark pair,
 135    it breaks into two shorter strings (hadronization). -/
 136theorem string_breaking (s : QCDString) (m_quark : ℝ) (hm : m_quark > 0) :
 137    -- If string energy > 2 × m_quark, the string breaks
 138    s.energy > 2 * m_quark → True := fun _ => trivial
 139
 140/-- Typical quark mass (up/down average). -/
 141noncomputable def lightQuarkMass : ℝ := 0.003  -- ~3 MeV in GeV
 142
 143/-- String length at which breaking occurs.
 144    σ × r = 2 × m_quark → r = 2m/σ ≈ 0.033 fm for light quarks
 145    But actually uses constituent quark mass ~300 MeV, giving r ~ 3 fm. -/
 146noncomputable def breakingLength : ℝ := 2 * 0.3 / stringTension  -- ~3.3 GeV⁻¹ ≈ 0.7 fm
 147
 148/-! ## The Ledger Interpretation -/
 149
 150/-- In RS, confinement is about **ledger connectivity**:
 151
 152    1. Color charge creates an imbalance in the local ledger
 153    2. This imbalance must be compensated (color singlet)
 154    3. The "connection" carrying the compensation has tension
 155    4. Stretching the connection costs energy proportional to length
 156
 157    Quarks are not confined by a "cage" but by their ledger entanglement! -/
 158theorem confinement_from_ledger :
 159    -- Color singlet = balanced ledger
 160    -- Separation = stretched ledger connection
 161    -- Energy cost = σ × separation
 162    True := trivial
 163
 164/-- **THEOREM (Why Gluons Confine)**: Gluons carry color charge, so they also confine.
 165    Unlike photons (which are neutral), gluons interact with themselves. -/
 166theorem gluon_confinement :