"""v169 -- The eta_B leptogenesis transfer: operationalising the Boltzmann path (NOT proving eta_B). The honest F_transfer test of the baryon asymmetry. eta_B has two readings in TFPT. As a DOWNSTREAM cosmology readout it is already hit: Omega_b = (1 - 1/4pi) phi0 = 0.04894, Omega_b h^2 ~ 0.02223, so eta_B ~ 273.9e-10 * Omega_b h^2 ~ 6.09e-10 (FR.ETAB.01). This module addresses the OTHER reading -- the fundamental thermal-leptogenesis Boltzmann computation, which is a physics interface, not a compiler theorem. It checks whether the standard route, FED BY TFPT's neutrino sector, can reach the observed asymmetry. [I] 1. STANDARD STRUCTURE. Type-I thermal leptogenesis with hierarchical RH neutrinos: Y_B = a_sph * eps_1 * kappa_f / (...), in the compact form eta_B ~ 0.96e-2 * eps_1 * kappa_f, with the sphaleron factor a_sph = 28/79 and g_* ~ 106.75 absorbed in the 0.96e-2. [.] 2. TFPT INPUTS (the genuine feed). Normal ordering (v9 texture): m1 ~ 0, m2 = sqrt(dm2_sol) ~ 0.0087 eV, m3 = sqrt(dm2_atm) ~ 0.050 eV; the CP phase delta_CP = 4pi/3 = 240 deg (the TFPT prediction, |sin| = 0.866). [.] 3. DAVIDSON-IBARRA CP ASYMMETRY (scenario in M1). eps_1 <= (3/16pi) M1 m3 / v^2; with the TFPT phase and M1 = 1e10 GeV, eps_1 ~ 8.5e-7. M1 (the lightest RH-neutrino mass) is a SCENARIO input, not a TFPT output. [.] 4. EFFICIENCY (scenario in the washout). kappa_f(m~1) = (3.3e-3/m~1 + (m~1/0.55e-3)^1.16)^{-1} (Buchmueller-Di Bari-Pluemacher); for m~1 in [m_* , m_atm] = [1.08e-3, 1e-2] eV, kappa_f ~ 0.03-0.19. [C] 5. KILL TEST -- THE ROUTE IS VIABLE, NOT PROVEN. Over the natural ranges M1 in [3e9, 3e10] GeV and m~1 in [m_*, m_atm], eta_B spans a band that BRACKETS the observed 6.1e-10 (a canonical point M1 = 1e10 GeV, m~1 = 5e-3 eV, delta_CP = 240 deg gives ~6.0e-10 -- NOT tuned). So the thermal-leptogenesis route, fed by TFPT's neutrino sector, REACHES the observed asymmetry. But M1 and the washout are scenario inputs, so eta_B stays [C]: a falsifiable physics interface, NOT a compiler prediction. If a precise Boltzmann/RGE computation excluded the window, the LEPTOGENESIS ROUTE would fall -- not the theory (the downstream Omega_b readout, FR.ETAB.01, is independent and already hit). Scope [C]: analytic thermal-leptogenesis estimate; the seesaw RGE running of Y_nu / M_i (PyR@TE with a seesaw model) is an O(1) correction, flagged, not included. Python-only (numerical; no exact-identity content for Wolfram). """ import math from tfpt_constants import check, summary, reset PI = math.pi V = 174.0 # GeV (Dirac-mass normalisation m_D = y v) A_SPH = 28.0 / 79.0 # sphaleron B-L -> B conversion GEV_PER_EV = 1e-9 DM2_SOL, DM2_ATM = 7.5e-5, 2.5e-3 # eV^2 (NuFIT, NO) M2 = math.sqrt(DM2_SOL) # eV M3 = math.sqrt(DM2_ATM) # eV DELTA_CP = 4 * PI / 3 # TFPT prediction, 240 deg M_STAR = 1.08e-3 # eV, equilibrium neutrino mass M_ATM = 1e-2 # eV, upper washout reference ETA_B_OBS = 6.1e-10 def _eps1(M1, phase): """Davidson-Ibarra maximal CP asymmetry x phase (masses -> GeV).""" return (3.0 / (16 * PI)) * M1 * (M3 * GEV_PER_EV) / V**2 * phase def _kappa(mtil): """Final efficiency factor (Buchmueller-Di Bari-Pluemacher interpolation).""" return 1.0 / (3.3e-3 / mtil + (mtil / 0.55e-3)**1.16) def _etaB(M1, mtil, phase): return 0.96e-2 * _eps1(M1, phase) * _kappa(mtil) def run(): reset() print("v169 eta_B leptogenesis transfer (Boltzmann path operationalised, [C])") # 1. standard structure check("STANDARD STRUCTURE [I]: type-I thermal leptogenesis, " "eta_B ~ 0.96e-2 eps_1 kappa_f with sphaleron a_sph = 28/79 = %.4f" % A_SPH, abs(A_SPH - 28/79) < 1e-12) # 2. TFPT inputs sin_phase = abs(math.sin(DELTA_CP)) check("TFPT INPUTS: normal ordering m2 = %.4f eV, m3 = %.4f eV (from " "dm2_sol, dm2_atm), CP phase delta_CP = 4pi/3 = 240 deg (|sin| = %.3f) " "-- the genuine TFPT feed (v9 texture + the predicted phase)" % (M2, M3, sin_phase), abs(M3 - 0.05) < 2e-3 and abs(sin_phase - math.sqrt(3)/2) < 1e-9) # 3. Davidson-Ibarra eps_1 (scenario M1) eps_ref = _eps1(1e10, sin_phase) check("DAVIDSON-IBARRA eps_1 (scenario M1): eps_1 <= (3/16pi) M1 m3/v^2; " "with the TFPT phase and M1 = 1e10 GeV, eps_1 = %.2e ~ 1e-6 (M1 is a " "scenario input, not a TFPT output)" % eps_ref, 5e-7 < eps_ref < 2e-6) # 4. efficiency (scenario washout) k_lo, k_hi = _kappa(M_ATM), _kappa(M_STAR) check("EFFICIENCY (scenario washout): kappa_f(m~1) Buchmueller-Di " "Bari-Pluemacher; for m~1 in [m_*, m_atm] kappa_f in [%.3f, %.3f] " "(~0.03-0.19)" % (k_lo, k_hi), 0.02 < k_lo < 0.05 and 0.15 < k_hi < 0.25) # 5. KILL TEST: observed eta_B inside the natural-scenario band band = [_etaB(M1, mtil, sin_phase) for M1 in (3e9, 1e10, 3e10) for mtil in (M_STAR, 5e-3, M_ATM)] lo, hi = min(band), max(band) eta_ref = _etaB(1e10, 5e-3, sin_phase) # canonical, NOT tuned check("KILL TEST [C] -- ROUTE VIABLE: over M1 in [3e9,3e10] GeV and m~1 in " "[m_*, m_atm], eta_B spans [%.2e, %.2e] which BRACKETS the observed " "%.1e; the canonical point (M1=1e10, m~1=5e-3, delta=240deg) gives " "eta_B = %.2e (NOT tuned). The leptogenesis route fed by TFPT's " "neutrino sector REACHES the observed asymmetry -- but M1/washout are " "scenario inputs, so eta_B stays [C], not a compiler prediction" % (lo, hi, ETA_B_OBS, eta_ref), lo <= ETA_B_OBS <= hi and 4e-10 < eta_ref < 9e-10) check("FALSIFIABILITY [C]: if a precise Boltzmann/RGE computation excluded " "the window, the LEPTOGENESIS ROUTE falls -- NOT the theory (the " "downstream Omega_b readout FR.ETAB.01, eta_B ~ 6.09e-10, is " "independent and already hit). The seesaw RGE running of Y_nu/M_i " "(PyR@TE seesaw model) is an O(1) correction, flagged, not included", True) return summary("v169 eta_B leptogenesis transfer") if __name__ == "__main__": raise SystemExit(1 if run() else 0)