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StandardStandard ModelModel -- ElectroweakElectroweak InteractionsInteractions

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Weak Neutral Neutral Currents (NC) Electroweak Theory W± and Z0 and γ Discovery of W± and Z0 Experimental Tests LEP Z0 and Width Number of W± Boson W± Pair Production Mass and Width Mass, LHC SUSY Summary

Nuclear and Particle Franz Muheim 1 WeakWeak NeutralNeutral InteractionsInteractions Weak (NC) Z0 boson couples to all : neutrinos, charged , Weak NC is flavour conserving e.g µτZ0 vertex does not exist Coupling Strength

Proportional to weak neutral charge g’W 0 Î For each Z vertex add factor g’W to element

How are g’W and gW related? Z0 Boson Neutral Current mediated by exchange of virtual Z0 boson 2 2 Î Add propagator term 1/(q –MZ ) to matrix element/amplitude At small q2 NC masked by electromagnetic interactions Are weak and electromagnetic related? Discovery of Neutral Currents 1973 Bubble chamber at CERN 3 events in elastic νµ scattering e

− − ν µ + e →ν µ + e

Anti-νµ beam Very low background

Nuclear and Franz Muheim 2 StandardStandard ModelModel ElectroweakElectroweak InteractionsInteractions Electroweak Unification Developed in 1960s by Glashow Weinberg Salam Quantum Theory of weak charged (CC) and neutral currents (NC) and electromagnetic interactions (QED) Surprise - QED and weak interactions are a unified force Electroweak Gauge Bosons Initially four massless bosons W+, W0, W- and B0 Neutral bosons mix Î Physical bosons W± and Z0 and γ ⎛ Z 0 ⎞ ⎛cosθ − sinθ ⎞ ⎛W 0 ⎞ ⎜ ⎟ = ⎜ W W ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 0 ⎟ ⎝γ ⎠ ⎝ sinθ W cosθ W ⎠ ⎝ B ⎠

θW weak mixing (Weinberg) angle W± and Z0 acquire mass via Electroweak Coupling Constants

gW and g’W are related to e

e = gW sin θW = g’W cos θW

2 2 ElectroweakElectroElectroweakweak TheoryTTheoryheory e GF gW αem = , = 2 , sinθW 3 fundamental parameters, e.g. 4π 2 8MW ± 0 2 2 2 Mass of W and Z related M Z 0 = MW / cos θW Predicts coupling strengths of W± and Z0 to quarks and leptons, self couplings of W± and Z0 and γ

Nuclear and Particle Physics Franz Muheim 3 WW andand ZZ BosonsBosons

Virtual W± and Z0 Bosons Mediate in scattering and decay of weakly interacting fermions − − 0 − + e.g. or decay, µ → e ν eν µ D → K µ ν µ − − − − v-e scattering ν e + e →ν e + e ν µ + e →ν µ + e Real W± and Z0 Bosons Produced in collisions if sufficient available + + + u + d → W → e ν e , µ ν µ − − − u + d → W → e ν e , µ ν µ u + u⎫ ⎬ → Z 0 → e +e − , µ + µ − d + d ⎭ Discovery of W± and Z0 Bosons at p-pbar collider at CERN in 1983 Energy E(p) =E(pbar) = 270 GeV

W event UA1 experiment CERN

− − e- W → e ν e

Nuclear and Particle Physics Franz Muheim 4 ExperimentalExperimental TestsTests -- LEPLEP

LEP - Large Collider Largest e+e- collider, 27 km circumference Centre-of-mass energy √s = 90 – 200 GeV Operational from 1989 to 2000 Four experiments: Aleph, Delphi, L3, OPAL e +e − → Z 0 → qq → hadrons

Z0 Bosons at LEP

Resonance production at √s = MZ ~4 million e+ e- → Z0 events/expt W± Bosons at LEP

Production at √s ≥ 2 MW ~8000 e+ e- → W+ W- events/expt LEP Measurements Mass and width of Z0 and W± bosons Z0 and W± boson couplings to quarks and leptons Weak decays of heavy QCD measurements Precision tests of Standard Model of Particle Physics

Nuclear and Particle Physics Franz Muheim 5 ZZ0 ResonanceResonance e+ e- Annihilations → Hadrons at High √s < 50 GeV exchange of γ dominates At larger energies √s ≥ 50 GeV Z0 and γ exchange diagram, also Z0/γ interference

Z0 Boson Production 0 at energies √s ≈ MZ production of real Z boson diagram with Z0 boson dominates Z0 boson is Breit-Wigner Resonance Z0 boson decays very fast, lifetime τ ~ 10-25 s 0 Measure energy width of Z resonance ΓZ = ħ/τ

Nuclear and Particle Physics Franz Muheim 6 ZZ0 MassMass andand WidthWidth

Breit-Wigner Resonance Cross section for relativistic initial and final states 4π Γee Γ σ ()e +e − → Z 0 → f f = g ff s ⎡ 2 2 ⎤ ()s − M Z + ΓZ / 4 ⎣⎢ ⎦⎥ 0 Partial decay widths Γff = Γ(Z → f f ) : average initial states 2J + 1 g = Z & sum final states ()2se− + 1 (2se+ + 1)

Total Decay Width ΓZ

Sum over all partial decay widths Γff Γ = Γ + Γ + Γ + Γ + Γ + Γ + Γ Z qq ee µµ ττ ν eν e ν µν µ ντντ Cross section at peak of resonance √s = MZ

0 + − 0 12π Γee Γff σ ff = σ ()e e → Z → f f = 2 2 M Z ΓZ Z0 Resonance Measure e+ e- → Hadrons

at energies close to MZ QED corrections Shift: e+ e- → γ hadrons Mass and Width of Z0

MZ = 91.1876(21) GeV

ΓZ = 2.49529(23) GeV Peak cross section 0 σ qq = 41.5409(37) nb

Nuclear and Particle Physics Franz Muheim 7 ZZ0 PartialPartial DecayDecay WidthsWidths

Cross Sections σ (e +e − → Z 0 → f f ) Measurements for all visible fermions Obtain partial decay widths using 0 peak cross section σ qq and MZ, ΓZ

Note --- all resonance curves have width ΓZ

ΓZ = 2495.2 ± 2.3 MeV Γ = 1744.4 ± 2.0 MeV qq Evidence for Ncolour = 3

Γll = Γee = Γµµ = Γττ = 83.984 ± 0.086 MeV Invisible Z0 Width 0 Decays Z →ν eν e ,ν µν µ ,ν τν τ Comparison of total and partial decay widths

ΓZ = Γqq + Γee + Γµµ + Γττ + Nν Γνν Nν - number of Γ = Γ = Γ = Γ neutrino flavours νν ν eν e ν µν µ ντντ Number of Neutrino Flavours

Prediction Γνν = 167 MeV Measurement

NνΓνν = 499.0 ± 1.5 MeV Number of neutrinos

Nν = 2.994 ± 0.012

(with mass mν < MZ/2) Consistency also for e, µ, τ Lepton universality holds for Z0 →ee, µµ, ττ couplings Nuclear and Particle Physics Franz Muheim 8 WW+WW- PairPair ProductionProduction

Standard Model Diagrams

W± Boson Decays CC Universality for leptons and weak eigenstates

− − − − − − 1 ± Γ(W → e ν e )= Γ(W → µ ν µ ) = Γ(W → τ ν τ )= 3 Γ(W → lν ) − − − − − Γ()W → d'u = Γ()W → s'c = N cΓ()W → e ν e Γ()W → b't = 0 ⇒ Γ()W ± → q'q = 2Γ(W ± → lν ) e+ e- → W+ W- at LEP Example L3 experiment + − + − − e e → W W → qqe ν e

My 1st W± pair

Cross Section vs Energy Agrees with SM prediction Confirms existence of Mass and Width of W± Boson W+ W- Z0 vertex MW = 80.425 ± 0.038 GeV Nuclear and Particle Physics Franz Muheim 9 ΓW = 2.124 ±.0.041 GeV HiggsHiggs andand UnificationUnification

Electroweak Theory 2 Precise measurements of αem, GF, MZ, MW and sin θW Only 3 independent parameters Powerful constraints, corrections: higher order diagrams Higgs Mechanism Only missing particle in Standard Model Scalar, i.e Spin 0, Non-zero vacuum -> All particles acquire mass by Higgs interaction

Peter Higgs

Higgs coupling ∝ mass gHff = √(√2 GF ) mf Prof emeritus

Direct Mass Limit MH > 114 GeV Univ of Edinburgh Require (LHC) starts in 2007 Supersymmetry - SUSY SUSY Partners: ↔ Boson fermion ↔ sfermion Unification of electroweak boson ↔ …ino and

α1 = αem

α2 = αW

α3 = αS

Nuclear and Particle Physics Franz Muheim 10 StandardStandard ModelModel ofof ParticleParticle PhysicsPhysics

One-pageOne-page SummarySummary Fermions Gauge Bosons Quarks and Leptons Mediate interactions

3 Generations of Charge Inter- Gauge Charge Coupling action Goson Constant Leptons & Quarks [e] [e]

Strong g 0 αS ≈ 0.2 νe νµ ντ 0 µ τ e- - - -1 Electro γ 0 αem ≈ 0.008 u c t +2/3 magnetic 0 d s b -1/3 Weak Z 0 αW ≈ 0.03 W± ±1

Electromagnetic (QED) Strong (QCD) γ couples to charge e g couple to colour conserves q, l flavour quark flavour conserved

Weak (CC) Neutral Current (NC) ± 0 W couples to weak charge gW Z couples to g’W Flavour changing for quarks conserves q, l flavour

Nuclear and Particle Physics Franz Muheim 11 FeynmanFeynman DiagramsDiagrams

One-Page Tutorial One-pageOne-page TutorialTutorial Scattering, annihilation or decays Only Standard Model vertices Initial and final states Write //boson content for all initial and final state particles Interactions Try to find out which exchange bosons are responsible for reaction by checking conservation laws Conservation Laws For all interactions at each vertex Energy-momentum Electric charge, number For strong and electromagnetic interactions Quark and Lepton flavour, , , For weak charged interactions (CC) Quark flavour is not conserved, Lepton universality For weak neutral interaction (NC) Quark and lepton flavour are conserved Useful Hints only interacts electromagnetically Neutrinos and Z0 only interact weakly Only Quarks and interact strongly If more than 1 possibility, faster reaction wins Keep it as simple as possible

Nuclear and Particle Physics Franz Muheim 12