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SU(2)

SU(3). The Standard Model. SU(2). U(1). Forces. Electromagnetic. Particles. Strong. Weak. H. Gravity. The Higgs boson. Quarks – “the building blocks of the Universe”. The number of quarks increased with discoveries of new particles and have reached 6.

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SU(2)

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  1. SU(3) The Standard Model SU(2) U(1) Forces Electromagnetic Particles Strong Weak H Gravity The Higgs boson

  2. Quarks – “the building blocks of the Universe” The number of quarks increased with discoveries of new particles and have reached 6 Charm came as surprise but completed the picture For unknown reasons Nature created 3 copies (generations) of quarks and leptons

  3. ne nm nt c t u 1956 1963 1974 1995 e m t s b d 1895 1936 1975 1977 1947 six leptons six quarks Discovery History 2000 Now we have a beautiful pattern of three pairs of quarks and three pairs of leptons. They are shown here with their year of discovery.

  4. Matter and Antimatter Antimatter was created together with matter during the “Big bang” The first generation is what we are made of Antiparticles are created at accelerators in ensemble with particles but the visible Universe does not contain antimatter

  5. Quark’s Colour Baryons are “made” of quarks ? To avoid Pauli principle veto one can antisymmetrize the wave function introducing a new quantum number - “colour”, so that

  6. The Number of Colours • The x-section of electron-positron annihilation into hadrons is proportional to the number of quark colours. The fit to experimental data at various colliders at different energies gives Nc = 3.06  0.10

  7. The Number of Generations • Z-line shape obtained at LEP depends on the number of flavours and gives the number of (light) neutrinos or (generations) of the Standard Model Ng = 2.982  0.013

  8. Quantum Numbers of Matter SU(3)c SU(2)L UY(1) doublets • Quarks • Leptons triplets V-A currents in weak interactions singlets - Electric charge 0 0

  9. The group structure of the SM Casimir Operators For SU(N) QCD analysis definitely singles out the SU(3) group as the symmetry group of strong interactions

  10. Electro-weak sector of the SM SU(2) x U(1) versus O(3) • The heavy photon gives the neutral current without flavour violation 3 gauge bosons 1 gauge boson 3 gauge bosons After spontaneous symmetry breaking one has 2 massive gauge bosons (W+ , W- ) and 1 massless (γ) 3 massive gauge bosons (W+ , W- , Z0) and 1 massless (γ) • Discovery of neutral currentswas a crucial test of the gauge model of weak interactionsat CERN in 1973

  11. Gauge Invariance Gauge transformation matrix parameter matrix Fermion Kinetic term Covariant derivative Gauge field Gauge invariant kinetic term Gauge field kinetic term Field strength tensor

  12. Lagrangian of the SM α,β=1,2,3 - generation index

  13. Fermion Masses in the SM Direct mass terms are forbidden due to SU(2)L invariance ! Dirac Spinors left right Dirac conjugated Charge conjugated Lorenz invariant Mass terms SUL(2) Unless Q=0, Y=0 SU(2) doublet SU(2) singlet SUL(2) & UY(1) UY(1) Majorana mass term

  14. Spontaneous Symmetry Breaking Introduce a scalar field with quantum numbers: (1,2,1) With potential Unstable maximum At the minimum v.e.v. scalar Stable minimum pseudoscalar Gauge transformation Higgs boson h

  15. The Higgs Mechanism Q: What happens with missing d.o.f. (massless goldstone bosons P,H+ or ξ) ? A: They become longitudinal d.o.f. of the gauge bosons Wμi, i=1,2,3 Gauge transformation Longitudinal components Higgs field kinetic term

  16. The Higgs Boson and Fermion Masses α, β =1,2,3 - generation index Dirac fermion mass Dirac neutrino mass

  17. The Running Couplings Radiative Corrections ~α (log Λ2/p2 +fin.part) UV divergence Renormalization operation UV cutoff Renormalization scale Renormalization constant Subtraction of UV div Finite Running coupling

  18. Renormalization Group Observable RG Eq. Solution to RG eq. Effective coupling Solution to RG eq. sums up an infinite series of the leading Logs coming from Feynman diagrams

  19. Asymptotic Freedom and Infrared Slavery One-loop order 4/3 nf QED -11+2/3 nf QCD _ _ α α QED QCD UV Pole IR Pole

  20. Comparison with Experiment Global Fit to Data Higgs Mass Constraint Though the values of sin w extracted from different experiments are in good agreement, two most precise measurements from hadron and lepton asymmetries disagree by 3 Remarkable agreement of ALL the data with the SM predictions - precision tests of radiative corrections and the SM

  21. The SM and Beyond The problems of the SM: • Inconsistency at high energies due to Landau poles • Large number of free parameters • Still unclear mechanism of EW symmetry breaking • CP-violation is not understood • The origin of the mass spectrum in unclear • Flavour mixing and the number of generations is arbitrary • Formal unification of strong and electroweak interactions Where is the Dark matter? The way beyond the SM: • The SAME fields with NEW • interactions and NEW fields GUT, SUSY, String, ED • NEW fields with NEW • interactions Compositeness, Technicolour, preons

  22. We like elegant solutions

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