""" verify_P129.py Standalone verification of Addendum P129: Muon Lifetime from the TOE Fermi Sector. Paper claims: - LO (TOE GF + PDG m_mu): tau = 2.1873e-6 s, residual -0.44% - NLO (+ leading QED corr): tau = 2.1945e-6 s, residual -0.11% ← primary claim - Full-TOE LO (both TOE): tau = 2.1221e-6 s, residual -3.41% - Full-TOE NLO: tau = 2.1290e-6 s, residual -3.09% Copyright: Léon Fernando Vlegels. License: MIT. """ import math import sys # ────────────────────────────────────────────── # 1. Constants # ────────────────────────────────────────────── # TOE fine-structure constant (P01/P36) ALPHA_INV = 4 * math.pi**3 + math.pi**2 + math.pi # ≈ 137.036 ALPHA = 1.0 / ALPHA_INV # Fermi coupling (GeV^-2) — TOE value from P123 GF_TOE = 1.16638e-5 # GeV^-2 GF_PDG = 1.1663788e-5 # GeV^-2 # Muon mass (GeV) M_MU_PDG = 105.658e-3 # GeV M_MU_TOE = 106.300e-3 # GeV (A100 spectral ladder) # Electron mass (GeV) M_E = 0.51100e-3 # GeV # Reduced Planck constant HBAR = 6.582119e-25 # GeV·s # PDG measured muon lifetime TAU_PDG = 2.1969811e-6 # s # ────────────────────────────────────────────── # 2. LO formula tau = 192π³ ħ / (GF² mμ⁵) # ────────────────────────────────────────────── def tau_LO(GF, m_mu): """Leading-order muon lifetime (seconds).""" return (192.0 * math.pi**3 * HBAR) / (GF**2 * m_mu**5) # ────────────────────────────────────────────── # 3. Leading QED radiative correction # ────────────────────────────────────────────── def kinoshita_sirlin(m_e, m_mu): """ Kinoshita-Sirlin phase-space factor f(x), x = me/mmu. f(x) = 1 - 8x² + 8x⁶ - x⁸ - 24x⁴ ln(x) Corrects for finite electron mass in 3-body phase space. A factor <1 reduces decay rate, i.e. increases lifetime. """ x = m_e / m_mu return 1.0 - 8*x**2 + 8*x**6 - x**8 - 24*x**4 * math.log(x) def vertex_correction(alpha): """ Leading O(alpha) vertex correction. delta_vert = (25/4 - pi²/2) * alpha/pi Reduces decay rate (positive delta_vert → rate multiplied by (1 - delta_vert)). """ coeff = 25.0/4.0 - math.pi**2/2.0 # ≈ 1.3152 return coeff * alpha / math.pi def F_QED(m_e, m_mu, alpha): """ Combined leading QED factor applied to the decay rate: Gamma_NLO = Gamma_LO * F_QED So tau_NLO = tau_LO / F_QED. """ f = kinoshita_sirlin(m_e, m_mu) dv = vertex_correction(alpha) return f * (1.0 - dv) # ────────────────────────────────────────────── # 4. Compute all branches # ────────────────────────────────────────────── def pct(computed, reference): return 100.0 * (computed - reference) / reference def run(): failures = [] # ── Main branch: TOE GF, PDG mmu ────────── t_lo_main = tau_LO(GF_TOE, M_MU_PDG) fqed_main = F_QED(M_E, M_MU_PDG, ALPHA) t_nlo_main = t_lo_main / fqed_main res_lo_main = pct(t_lo_main, TAU_PDG) res_nlo_main = pct(t_nlo_main, TAU_PDG) # ── Full-TOE branch: TOE GF, TOE mmu ────── t_lo_toe = tau_LO(GF_TOE, M_MU_TOE) fqed_toe = F_QED(M_E, M_MU_TOE, ALPHA) t_nlo_toe = t_lo_toe / fqed_toe res_lo_toe = pct(t_lo_toe, TAU_PDG) res_nlo_toe = pct(t_nlo_toe, TAU_PDG) # ── Intermediate diagnostics ─────────────── x = M_E / M_MU_PDG f_val = kinoshita_sirlin(M_E, M_MU_PDG) dv = vertex_correction(ALPHA) # ────────────────────────────────────────── # 5. Print results # ────────────────────────────────────────── print("=" * 60) print("P129 Muon Lifetime Verification") print("=" * 60) print() print(f" ALPHA_INV = {ALPHA_INV:.6f} (paper: ~137.036)") print(f" GF_TOE = {GF_TOE:.5e} GeV^-2") print(f" m_mu PDG = {M_MU_PDG*1e3:.3f} MeV") print(f" m_mu TOE = {M_MU_TOE*1e3:.3f} MeV") print(f" hbar = {HBAR:.6e} GeV·s") print() print("── Kinoshita-Sirlin factor ─────────────────") print(f" x = me/mmu = {x:.4e} (paper: 4.836e-3)") print(f" f(x) = {f_val:.6f} (paper: 0.999813)") print() print("── Vertex correction ───────────────────────") print(f" 25/4 - pi²/2 = {25/4 - math.pi**2/2:.4f} (paper: 1.315)") print(f" delta_vert = {dv:.6e} (paper: 3.056e-3)") print() print(f" F_QED (main branch) = {fqed_main:.6f} (paper: 0.996759)") print() print("── Main branch (TOE GF + PDG m_mu) ─────────") print(f" tau_LO = {t_lo_main:.4e} s (paper: 2.1873e-6 s)") print(f" residual LO = {res_lo_main:+.3f}% (paper: -0.44%)") print(f" tau_NLO = {t_nlo_main:.4e} s (paper: 2.1945e-6 s)") print(f" residual NLO = {res_nlo_main:+.3f}% (paper: -0.11%)") print() print("── Full-TOE branch (TOE GF + TOE m_mu) ─────") print(f" tau_LO = {t_lo_toe:.4e} s (paper: 2.1221e-6 s)") print(f" residual LO = {res_lo_toe:+.3f}% (paper: -3.41%)") print(f" tau_NLO = {t_nlo_toe:.4e} s (paper: 2.1290e-6 s)") print(f" residual NLO = {res_nlo_toe:+.3f}% (paper: -3.09%)") print() # ────────────────────────────────────────── # 6. Assertions (tolerance ±0.02 percentage-points) # ────────────────────────────────────────── TOL = 0.02 # percentage-point tolerance checks = [ ("f(x) Kinoshita-Sirlin", f_val, 0.999813, 1e-5), ("delta_vert", dv, 3.056e-3, 1e-5), ("F_QED main branch", fqed_main, 0.996759, 1e-5), ("tau_LO main [1e-6 s]", t_lo_main*1e6, 2.1873, 5e-4), ("residual LO main [%]", res_lo_main, -0.44, TOL), ("tau_NLO main [1e-6 s]", t_nlo_main*1e6, 2.1945, 5e-4), ("residual NLO main [%]", res_nlo_main, -0.11, TOL), # PRIMARY CLAIM ("tau_LO full-TOE [1e-6 s]", t_lo_toe*1e6, 2.1221, 5e-4), ("residual LO full-TOE [%]", res_lo_toe, -3.41, TOL), ("tau_NLO full-TOE [1e-6 s]", t_nlo_toe*1e6, 2.1290, 5e-4), ("residual NLO full-TOE [%]", res_nlo_toe, -3.09, TOL), ] print("── Assertion results ────────────────────────") PASS = FAIL = 0 for n, (name, got, expected, tol) in enumerate(checks, 1): ok = abs(got - expected) <= tol PASS += ok FAIL += (not ok) status = "PASS" if ok else "FAIL" print(f" [{status}] {n:>2}. {name}") print(f" got={got:.6g} expected={expected:.6g} tol=±{tol:.1g}") if not ok: failures.append((name, got, expected, tol)) print() if not failures: print("Primary claim: tau_NLO (main branch) residual vs PDG = " f"{res_nlo_main:+.3f}% (paper: -0.11%)") print(f"\n{'='*60}\nRESULT: {PASS} PASS / {FAIL} FAIL") if failures: sys.exit(1) if __name__ == "__main__": run()