Experimental tests of the Standard Model • Discovery of the W and Z bosons • Precision tests of the Z sector • Precision tests of the W sector • Electro-weak unification at HERA • Radiative corrections and prediction of the top and Higgs mass • Top discovery at the Tevatron • Higgs searches at the LHC
1. Discovery of the W and Z boson 1983 at CERN SppS accelerator, √s≈540 GeV, UA-1/2 experiments 1.1 Boson production in pp interactions
− − p , q p ,q u W u Z ˆ ˆ d s ν u s +,q p , q p
→ → ν + → → + pp W X pp Z ff X σ (σ ) 10 nb W Z Similar to Drell-Yan: (photon instead of W)
1nb = ≈ sˆ xq xq s mit xq 12.0 2 1.0 nb = ≈ = 2 sˆ xq s .0 014 s 65( GeV )
→ Cross section is small ! sˆ M 1 10 100 W ,Z 1.2 UA-1 Detector
1.3 Event signature: pp → Z → ff + X
+
p p
−
High-energy lepton pair:
2 2 2 m = (p + + p − ) = M Z
≈ MZ 91 GeV
→ → ν + 1.4 Event signature: pp W X
Missing p T vector Undetected ν − ν Missing momentum
p p
High-energy lepton – Large transverse momentum p t
How can the W mass be reconstructed ?
W mass measurement
In the W rest frame: In the lab system: • = = MW p pν • W system boosted 2 only along z axis T ≤ MW • p • p distribution is conserved 2 T
−1 2 dN 2p M 2 Jacobian Peak: T ⋅ W − 2 ~ pT pT MW 4 dN dp T
• Trans. Movement of the W • Finite W decay width • W decay is not isotropic
T p MW ≈ MW 80 GeV 2 The Nobel Prize in Physics 1984
Carlo Rubbia Simon van der Meer
"for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction"
S. van der Meer One of the achievements to allow high-intensity p p collisions, is stochastic cooling of the p beams before inserting them into SPS.
1.5 Production of Z and W bosons in e+e– annihilation
W → qq
Precision tests of the Z sector Tests of the W sector 2. Precision tests of the Z sector (LEP and SLC)
+ − → γ → ~4.5M Z 2.1 Cross section for e e / Z ff decays / experiment 2 2 M = + γ Z
for e+ e− → µ + µ −
2 1 µ Mγ = −e (µγ µ µ) (eγ e) q2 2 2 g ν 1 µ µ gνρ − qν qρ M ρ 1 M = − µγ (g − g γ 5 )µ Z eγ (ge − geγ 5 )e Z 2 θ V A 2 − 2 + Γ V A cos W 2 (q MZ ) iM Z Z 2
Z propagator considering a finite Z width
+ − + − Differential cross section for e e → µ µ
σ πα 2 − 2 2 d s(s MZ ) s = Fγ (cos θ ) + Fγ (cos θ ) + F (cos θ ) θ Z − 2 2 + 2Γ2 Z − 2 2 + 2Γ2 d cos 2s (s MZ ) MZ Z (s MZ ) MZ Z γ γ /Z interference Z
√ ≈ Vanishes at s MZ
with
θ = 2 2 + 2 θ = + 2 θ Fγ (cos ) QeQµ 1( cos ) 1( cos )
Q Q F (cos θ ) = e µ [2g eg µ 1( + cos 2 θ ) + 4g eg µ cos θ ] γZ 2 θ 2 θ V V A A 4sin W cos W
1 2 2 µ 2 µ 2 µ µ F (cos θ ) = [(g e + g e )( g + g )( 1+ cos 2 θ) + 8g eg eg g cos θ ] Z 4 θ 4 θ V A V A V A V A 16 sin W cos W
√ ≈ → At the Z-pole s MZ Z contribution is dominant → interference vanishes
2 2 4π α µ µ s σ ≈ σ = ⋅ [][](ge )2 + (ge )2 (g )2 + (g )2 ⋅ tot Z 4 θ 4 θ V A V A − 2 2 + Γ 2 3s 16 sin w cos w (s MZ ) (MZ Z )
Γ Γµ s σ(s) = 12 π e ⋅ 2 − 2 2 + 2Γ2 MZ (s MZ ) MZ Z
12 π Γ Γµ σ ()s = M = e Z Z 2 Γ2 MZ Z
With partial and total widths: Cross sections and widths can be calculated within the αM Γ = Z ⋅ [](gf )2 + (g f )2 Standard Model if all f 2 θ 2 θ V A 12 sin w cos w parameters are known
Γ = Γ Z ∑ i i e+ e− → hadrons e+ e− → µ + µ −
Resonance looks the same, independent of final state: Propagator is the same
e+ e− → e+e− t channel contribution → forward peak
+ − − − e e e e k k′ k k′
+ p p′ p p′
+ + − + e e e e t channel s channel
Z line shape parameters (LEP average)
M = 91.1876 ± 0.0021 GeV Z = ± 23 ppm (*) Γ = 2.4952 ± 0.0023 GeV Z ±0.09 % Γ = 1.7458 ± 0.0027 GeV had Γ = 0.08392 ± 0.00012 GeV e 3 leptons are treated independently Γµ = 0.08399 ± 0.00018 GeV
Γτ = 0.08408 ± 0.00022 GeV test of lepton universality Γ = 2.4952 ± 0.0023 GeV Z Assuming lepton
Γ = 1.7444 ± 0.0022 GeV universality: Γ = Γµ=Γτ had e Γ = 0.083985 ± 0.000086 GeV e *) error of the LEP energy determination: ±1.7 MeV (19 ppm)
http://lepewwg.web.cern.ch/ (Summer 2005)
LEP energy calibration: Hunting for ppm effects
Changes of the circumference of the LEP ring changes the energy of the electrons: • tide effects Changes of LEP circumference ∆C=1…2 mm/27km (4…8x10 -8 ) • water level in lake Geneva
1992 Effect of moon 1993 Effect of lake
100 ppm
Effect of the French “Train a Grande Vitesse” (TGV)
Vagabonding currents (~1A) from trains
In conclusion: Measurements at the ppm level are difficult to perform. Many effects must be considered!
2.3 Number of light neutrino generations
In the Standard Model: + − → →ν ν e e Z e e 3 + − Z = had N e e → Z →ν µν µ + − → →ν ν Γ e e Z τ τ invisible : inv Γ = ± inv .0 4990 .0 0015 GeV
To determine the number of light neutrino generations: Γ Γ N = inv ⋅ ν Γ Γ exp ν SM
5.9431 ±0.0163 =1.991 ±0.001 (small theo.
uncertainties from mtop MH) N = 2.9840 ± 0.0082 ν
No room for new physics: Z → new Forward-backward asymmetry e+ e− → Z → µ +µ − dσ 8 ~ 1( + cos 2 θ ) + A cos θ d cos θ 3 FB σ − σ A = F B FB σ + σ F B with )0(1 dσ σ = d cos θ F(B) ∫ θ 0 (− )1 d cos
√ ≈ At the Z-pole s MZ → Z contribution is dominant → interference vanishes gege g µg µ A = 3 ⋅ V A ⋅ V A FB e 2 + e 2 µ 2 + µ 2 σ σ (gV ) (gA ) (gV ) (gA ) F F
Forward-backward asymmetry
• + − + − Away from the resonance AFB is large e e → Z → µ µ → interference term dominates s(s − M 2 ) A ~ geg f ⋅ Z FB A A − 2 2 + 2Γ2 (s MZ ) MZ Z • At the Z pole: Interference = 0
e e f f AFB ~ gAgV gAgV → l very small because g V small in SM
Fermion couplings Lowest order SM prediction: = − 2 θ = gV T3 2q sin W gA T3
• Away from the resonance AFB is large → interference term dominates s(s − M 2 ) A ~ geg f ⋅ Z FB A A − 2 2 + 2Γ2 (s MZ ) MZ Z • At the Z pole: Interference = 0
e e f f AFB ~ gAgV gAgV → l very small because g V small in SM
Asymmetries together with cross sections allow the determination of the fermion
couplings gA and gV Confirms lepton universality Higher order corrections seen −,q W decays W d ν ,qu
Lepton Neutrino
Jet
Jet W branching ratios
Br (W → qq) = 67( 77. ± 28.0 )%
Lepton universality tested to 2%
Invariant W mass recontruction
More difficult: pairing ambiguities indirect
4. Electro-weak unification, as visible at HERA d 1 1 1 NC ...... 2 ~ 2 2 2 2 2 2 2 2 d Q Q Q Q M Z Q M Z
γ γ /Z Z
d CC 1 2 ~ 2 2 2 d Q Q M W 4. Electro-weak unification, as visible at HERA d 1 1 1 NC ...... 2 ~ 2 2 2 2 2 2 2 2 d Q Q Q Q M Z Q M Z
d CC 1 2 ~ 2 2 2 d Q Q M W
5. Higher order corrections and the Higgs mass
Including radiative corrections
Lowest order SM predictions
Top mass prediction from radiative corrections
Direct measurement The measurement of the of m t radiative corrections: 1 sin 2 θ ≡ 1( − g g ) eff 4 V A 2 θ = + ∆κ 2 θ sin eff 1( )sin w allows an indirect determination of the unknown parameters
m t and M H. Prediction of m t by LEP before the discovery of the top at TEVATRON.
Good agreement between the indirect prediction of mt and the value obtained in direct measurements confirm the radiative corrections of the SM
Observation of the top quark at TEVATRON (1995)
pp @ 2 TeV
Top decay
q ν q q
Channel used for mass reconstruction: = − → + mt minv (b jet ,W jet jet ) Higgs mass prediction from radiative corrections
Status end of 2007
M > 114 GeV (from direct searches) Awaiting the discovery H
of the Higgs at the LHC MH < 144 GeV (from EW fits)