#!/usr/bin/env python3 """ verify_P104.py -- Addendum 104: Absolute W-Boson Mass. This verifier checks the W/Z mass radiative-correction arithmetic in 104_Addendum_AbsoluteWMass.tex. The main corrected W-mass values are reproducible: leptonic-only gives about 78.66 GeV, leptonic+top gives about 79.04 GeV, and adding the hadronic Delta-alpha input gives about 80.19 GeV. The audit flags localized issues in the leptonic-running wording and in the claimed size of the top-mass residual. """ import math import sys from pathlib import Path sys.path.insert(0, str(Path(__file__).resolve().parent)) from verify_common import CheckResult, Verifier class ModernVerifier(Verifier): """Output adapter: modern check-line format. Tolerance logic is inherited unchanged from verify_common.Verifier; only printing and the footer differ.""" def __init__(self, name: str): self.name = name self.results = [] print(name) def record(self, label, ok, computed="", claimed="", detail=""): self.results.append(CheckResult(label, ok, computed, claimed, detail)) n = len(self.results) expected = (not ok) and ("Expected" in str(detail)) desc = f"{label} -- {detail}" if expected else label print(f" [{'PASS' if ok else 'FAIL'}] {n:>2}. {desc}") if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") if detail and not expected: print(f" {detail}") return ok def summary(self): passed = sum(r.ok for r in self.results) failed = len(self.results) - passed print(f"\n{'='*60}\nRESULT: {passed} PASS / {failed} FAIL") return 1 if failed else 0 v = ModernVerifier("P104 -- Absolute W-Boson Mass") ALPHA = 1 / 137.036 MZ = 91.1876 MW_TREE = 77.41 MW_PDG = 80.377 SW2 = 0.23192 GF = 1.1664e-5 MT_TOE = 176.101 MT_PDG = 172.69 DA_LEPT = 0.03142 DA_HAD = 0.02764 ME = 0.000511 MMU = 0.105658 MTAU = 1.77686 logs = [math.log(MZ / m) for m in (ME, MMU, MTAU)] sigma_lept = sum(logs) delta_alpha_leading_log = 2 * ALPHA * sigma_lept / (3 * math.pi) delta_alpha_with_constant = ALPHA / (3 * math.pi) * sum(2 * math.log(MZ / m) - 5 / 3 for m in (ME, MMU, MTAU)) drho_toe = 3 * GF * MT_TOE**2 / (8 * math.pi**2 * math.sqrt(2)) drho_pdg = 3 * GF * MT_PDG**2 / (8 * math.pi**2 * math.sqrt(2)) mw_lept = MW_TREE / math.sqrt(1 - DA_LEPT) mw_lept_top = MW_TREE * math.sqrt(1 + drho_toe) / math.sqrt(1 - DA_LEPT) mw_full = MW_TREE * math.sqrt(1 + drho_toe) / math.sqrt(1 - DA_LEPT - DA_HAD) mw_full_pdg_top = MW_TREE * math.sqrt(1 + drho_pdg) / math.sqrt(1 - DA_LEPT - DA_HAD) v.check("ln(MZ/me)", logs[0], 12.093, rel=1e-4) v.check("ln(MZ/mmu)", logs[1], 6.760, rel=1e-4) v.check("ln(MZ/mtau)", logs[2], 3.938, rel=1e-4) v.check("Sigma_lept", sigma_lept, 22.791, rel=3e-5) v.check("leading-log Delta alpha lept", delta_alpha_leading_log, 0.03529, rel=2e-4) v.check( "displayed leading-log formula gives proposition value 0.03142", delta_alpha_leading_log, 0.03142, rel=1e-3, detail="Expected fail: 0.03142 requires the standard -5/3 constants, not the displayed pure leading-log formula.", ) v.check("one-loop Delta alpha with -5/3 constants", delta_alpha_with_constant, 0.03142, rel=5e-5) v.check( "three-loop correction scale alpha^2/pi^2", ALPHA**2 / math.pi**2, 5e-5, rel=1e-1, detail="Expected fail: alpha^2/pi^2 is about 5.4e-6, one order of magnitude smaller.", ) v.check("TOE top mass squared", MT_TOE**2, 31011.6, rel=2e-6) v.check("Delta rho top from TOE mt", drho_toe, 0.009718, rel=5e-5) v.check("sqrt(1+Delta rho top)", math.sqrt(1 + drho_toe), 1.004862, rel=2e-5) v.check("sqrt(1-Delta alpha lept)", math.sqrt(1 - DA_LEPT), 0.98416, rel=5e-6) v.check("leptonic-only MW", mw_lept, 78.66, rel=1e-4) v.check("leptonic-only residual percent", 100 * (mw_lept - MW_PDG) / MW_PDG, -2.14, rel=2e-3) v.check("leptonic+top MW", mw_lept_top, 79.04, rel=5e-4) v.check("leptonic+top residual percent", 100 * (mw_lept_top - MW_PDG) / MW_PDG, -1.67, rel=3e-3) v.check("sqrt(1-Delta alpha lept-Delta alpha had)", math.sqrt(1 - DA_LEPT - DA_HAD), 0.96997, rel=6e-5) v.check("full MW with hadronic Delta alpha", mw_full, 80.19, rel=2e-4) v.check("full MW residual percent", 100 * (mw_full - MW_PDG) / MW_PDG, -0.23, rel=2e-2) v.check( "abstract -0.21 percent final residual", 100 * (mw_full - MW_PDG) / MW_PDG, -0.21, rel=2e-2, detail="Expected fail: the formula gives about -0.234%, consistent with the table's -0.23%, not -0.21%.", ) v.check( "PDG top Delta rho quoted", drho_pdg, 0.009393, rel=1e-3, detail="Expected fail: using G_F=1.1664e-5 and mt=172.69 gives about 0.009345.", ) v.check( "MW shift from TOE top to PDG top", mw_full - mw_full_pdg_top, 0.14, rel=5e-2, detail="Expected fail: in the paper's factorized formula the shift is about 0.015 GeV, not 0.14 GeV.", ) v.check( "full MW using PDG top", mw_full_pdg_top, 80.05, abs_tol=0.03, detail="Expected fail: the same formula gives about 80.17 GeV.", ) v.check( "full residual using PDG top", 100 * (mw_full_pdg_top - MW_PDG) / MW_PDG, -0.40, rel=5e-2, detail="Expected fail: the same formula gives about -0.25%.", ) cosw = math.sqrt(1 - SW2) mz_lept_top = 79.04 / cosw mz_full = 80.19 / cosw v.check("cos theta_W from sin^2=0.23192", cosw, 0.87644, rel=5e-5) v.check("MZ lept+top from corrected MW", mz_lept_top, 90.19, rel=1e-4) v.check("MZ full from corrected MW", mz_full, 91.52, rel=3e-4) v.check("MZ full residual percent", 100 * (mz_full - 91.1876) / 91.1876, 0.36, rel=6e-2) two_loop_estimate = ALPHA / math.pi * 80 * 0.1 v.check( "two-loop estimate alpha/pi * MW * 0.1", two_loop_estimate, 0.06, rel=1e-1, detail="Expected fail: the displayed estimate evaluates to about 0.019 GeV.", ) v.check("TOE top percent offset from PDG", 100 * (MT_TOE - MT_PDG) / MT_PDG, 1.98, rel=5e-3) sys.exit(v.summary())