StandardStandard ModelModel -- ElectroweakElectroweak InteractionsInteractions OutlineOutline Weak Neutral Interactions Neutral Currents (NC) Electroweak Theory W± and Z0 and γ Discovery of W± and Z0 bosons Experimental Tests LEP Z0 Boson Mass and Width Number of Neutrinos W± Boson W± Pair Production Mass and Width Higgs Boson Mass, LHC Supersymmetry SUSY Unification Standard Model Summary Nuclear and Particle Physics Franz Muheim 1 WeakWeak NeutralNeutral InteractionsInteractions Weak Neutral Current (NC) Z0 boson couples to all fermions: neutrinos, charged leptons, quarks 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 matrix element How are g’W and weak charge gW related? Z0 Boson Propagator 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 force related? Discovery of Neutral Currents 1973 Bubble chamber Gargamelle at CERN 3 events in elastic νµ neutrino scattering e − − ν µ + e →ν µ + e Anti-νµ beam Very low background Nuclear and Particle Physics 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 Higgs Mechanism Electroweak Coupling Constants gW and g’W are related to electric charge 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 interaction couplings of W± and Z0 and γ Nuclear and Particle Physics Franz Muheim 3 WW andand ZZ BosonsBosons Virtual W± and Z0 Bosons Mediate weak interaction in scattering and decay of weakly interacting fermions − − 0 − + e.g. muon or meson 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 energy 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 Electron Positron 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 mesons 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 Energies √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 ) Spin: 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 light 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 quark 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 Large Hadron Collider (LHC) starts in 2007 Supersymmetry - SUSY SUSY Partners: Fermion ↔ Boson fermion ↔ sfermion Unification of electroweak boson ↔ …ino and strong interaction 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 Charged Current (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 down quark/lepton/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, Baryon number For strong and electromagnetic interactions Quark and Lepton flavour, Parity, Isospin, Strangeness 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 Photon only interacts electromagnetically Neutrinos and Z0 only interact weakly Only Quarks and Gluons interact strongly If more than 1 possibility, faster reaction wins Keep it as simple as possible Nuclear and Particle Physics Franz Muheim 12.