Quantum Field Theory Course

Total: 440+ pages covering classical field theory through the Standard Model

Part VIII: Standard Model • Chapter 6

Precision Tests of the Standard Model

Experimental verification to extraordinary precision

The Most Tested Theory in Physics

The Standard Model has been tested to unprecedented precision—in some cases to better than 1 part in 10 billion. These tests fall into several categories:

  • • Z-pole physics: LEP/SLC measurements at MZ = 91.2 GeV
  • • W boson properties: Mass, width, couplings
  • • Top quark: Mass, production, decay
  • • QCD tests: αs running, jets, deep inelastic scattering
  • • Rare processes: B physics, muon g-2, EDMs
  • • Higgs properties: Mass, couplings, spin, parity

1. Z-Pole Physics (LEP/SLC)

LEP (1989-2000) and SLC (1989-1998) collided e+e- at √s ≈ MZ:

ObservableMeasured ValuePrecision
MZ91.1876 ± 0.0021 GeV2 × 10-5
ΓZ (total width)2.4952 ± 0.0023 GeV10-3
σhad⁰ (peak cross section)41.541 ± 0.037 nb10-3
Rℓ (hadronic/leptonic ratio)20.767 ± 0.02510-3
AFB0,ℓ (forward-backward asymmetry)0.01714 ± 0.000955 × 10-2

Key Result: Number of Neutrino Generations

From invisible Z width Γinv = ΓZ - Γvisible:

Nν = 2.984 ± 0.008

Conclusive proof of exactly 3 light neutrino species (mν < MZ/2)!

Electroweak Fit

Combining all Z-pole observables with W mass and top mass:

sin² θWeff (MS̄): 0.23153 ± 0.00016
αs(MZ): 0.1181 ± 0.0011
Δαhad(5): Hadronic vacuum polarization contribution

All observables consistent with SM at χ²/dof ≈ 1. No significant deviations!

2. W Boson Mass

The W boson mass is sensitive to radiative corrections from top quark and Higgs loops:

Measurements:

LEP-2 (1996-2000): MW = 80.376 ± 0.033 GeV
Tevatron (CDF/D0): MW = 80.387 ± 0.016 GeV
LHC (ATLAS): MW = 80.370 ± 0.019 GeV
World average: MW = 80.379 ± 0.012 GeV

CDF-II Anomaly (2022):

CDF-II reported MW = 80.433 ± 0.009 GeV, a 7σ deviation from SM!

If confirmed by other experiments, this would be evidence for new physics. ATLAS/CMS/LHCb are investigating. Current status: tension remains unresolved.

Radiative Corrections:

MW² / MZ² = 1 - sin² θW = ½(1 + √(1 - 4πα/√2 GFMZ²(1-Δr)))

where Δr contains radiative corrections: Δr ∝ mt² (dominant) + log(mH)

3. Top Quark Physics

Mass Measurements:

Tevatron (1995): Discovery at mt ~ 175 GeV
LHC combined: mt = 172.76 ± 0.30 GeV (direct reconstruction)
From cross sections: mtpole = 172.5 ± 0.7 GeV

The top mass is crucial for electroweak fits and Higgs vacuum stability!

Top Properties:

  • Width: Γt ≈ 1.4 GeV → lifetime τ ~ 5 × 10-25 s
    Decays before hadronization! Only quark with "bare" mass.
  • Decay: t → Wb with BR ≈ 100% (|Vtb| ≈ 0.999)
  • Charge: Confirmed Q = +2/3 (not exotic +4/3)
  • Spin correlations: Measured, agree with V-A structure

Top Yukawa Coupling:

From ttH production at LHC:

yt = 1.02 ± 0.09 (ATLAS+CMS combined)

Consistent with SM prediction yt = √2 mt/v ≈ 0.995!

4. QCD Precision Tests

Running of αs

The strong coupling runs with energy Q (asymptotic freedom):

αs(Q) = αs(MZ) / [1 + (αs(MZ)/2π) β0 log(Q²/MZ²)]

Measurements at different scales:

• τ decays (2 GeV): αs = 0.32 ± 0.02
• Z pole (91 GeV): αs = 0.1181 ± 0.0011
• Top production (170 GeV): αs = 0.108 ± 0.003
• Jets at LHC (1 TeV): αs ~ 0.09

Beautiful agreement with QCD prediction across 3 orders of magnitude!

Other QCD Tests:

Deep Inelastic Scattering (HERA):
Measured parton distribution functions (PDFs) with high precision. Confirmed DGLAP evolution.
Jet Production:
3-jet, 4-jet rates at LEP, Tevatron, LHC agree with NLO/NNLO QCD calculations.
Heavy Quark Production:
bb̄, cc̄ cross sections at hadron colliders consistent with QCD (within large theory uncertainties).

5. Higgs Boson Measurements

Mass:

mH = 125.25 ± 0.17 GeV (ATLAS+CMS combined)

Measured from H → γγ and H → ZZ* → 4ℓ channels. Precision: 0.1%!

Coupling Measurements:

Channelμ = σ×BR / (σ×BR)SMStatus
H → γγ1.10 ± 0.07✓ Consistent
H → ZZ*1.01 ± 0.08✓ Consistent
H → WW*1.09 ± 0.10✓ Consistent
H → τ+τ-1.04 ± 0.11✓ Consistent
H → bb̄1.02 ± 0.12✓ Consistent
ttH (yt)1.02 ± 0.09✓ Consistent

Spin and Parity:

Angular distributions in H → ZZ* → 4ℓ and H → γγ exclude JP = 0-, 1+, 2+.

Consistent with JP = 0+ (scalar) at 99.9% CL.

6. Rare Processes & Anomalies

Muon g-2 Anomaly:

Fermilab 2021: (g-2)μ differs from SM by 4.2σ

Δaμ = (251 ± 59) × 10-11

Possible new physics in loops (SUSY? Dark sector?) or hadronic vacuum polarization issue?

B Anomalies (RK, RK*):

LHCb observed hints of lepton flavor universality violation in b → sℓ+ℓ-:

RK = BR(B → Kμ+μ-) / BR(B → Ke+e-) = 0.846 ± 0.042 (expect 1.0)

~3σ tension. New measurements from Belle II, LHCb Run 3 ongoing. Status: intriguing but not conclusive.

Electric Dipole Moments:

EDMs probe CP violation beyond CKM. Current limits:

• Electron: |de| < 1.1 × 10-29 e·cm (ACME 2018)
• Neutron: |dn| < 1.8 × 10-26 e·cm
• Mercury: |dHg| < 7.4 × 10-30 e·cm

All consistent with zero. Constrain SUSY, extra dimensions, etc.

Summary

  • ✓ Z-pole: Precision at 10-3-10-5 level, Nν = 2.984 ± 0.008
  • ✓ W mass: MW = 80.379 ± 0.012 GeV (CDF-II anomaly under investigation)
  • ✓ Top mass: mt = 172.76 ± 0.30 GeV, crucial for EW/Higgs fits
  • ✓ QCD: αs running verified over 3 decades in energy
  • ✓ Higgs: mH = 125.25 ± 0.17 GeV, all couplings consistent with SM
  • ✓ Anomalies: (g-2)μ at 4.2σ, B-physics hints at ~3σ, but nothing conclusive
  • ✓ Overall verdict: SM passes every precision test to date! (with possible exceptions)

Further Resources

  • • PDG Review - "Electroweak Model and Constraints on New Physics"
  • • ATLAS+CMS - Higgs coupling measurements (various publications)
  • • Gfitter Group - Global electroweak fits (http://gfitter.desy.de)
  • • Langacker - The Standard Model and Beyond (2nd ed., 2017)