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

Discovery History u d tc sb six quarks e     e six leptons 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. 2000

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

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 ?

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 N c = 3.06  0.10

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 N g =  0.013

Quantum Numbers of Matter  Quarks  Leptons SU(3) c SU(2) L U Y (1) triplets doublets singlets Electric charge V-A currents in weak interactions

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

Electro-weak sector of the SM SU(2) x U(1) versus O(3)  The heavy photon gives the neutral current without flavour violation gauge  Discovery of neutral currents was a crucial test of the gauge model of weak interactions at CERN in gauge bosons1 gauge boson3 gauge bosons After spontaneous symmetry breaking one has 3 massive gauge bosons (W +, W -, Z 0 ) and 1 massless (γ) 2 massive gauge bosons (W +, W - ) and 1 massless (γ)

Gauge Invariance Gauge transformation parametermatrix Fermion Kinetic term Covariant derivative Gauge field matrix Gauge invariant kinetic term Gauge field kinetic term Field strength tensor

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

Fermion Masses in the SM Direct mass terms are forbidden due to SU(2) L invariance ! SU(2) doubletSU(2) singlet Dirac SpinorsleftrightDirac conjugatedCharge conjugated Lorenz invariant Mass terms SU L (2) SU L (2) & U Y (1)U Y (1) Unless Q=0, Y=0 Majorana mass term

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

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 W μ i, i=1,2,3 Gauge transformation Longitudinal components Higgs field kinetic term

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

The Running Couplings Radiative Corrections ~α (log Λ 2 /p 2 +fin.part) UV divergence Renormalization operation UV cutoffRenormalization scale Renormalization constant Subtraction of UV div Finite Running coupling

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

Asymptotic Freedom and Infrared Slavery One-loop order 4/3 n f QED -11+2/3 n f QCD QED QCD α _ α _ UV PoleIR Pole

Comparison with Experiment Global Fit to DataHiggs Mass Constraint Remarkable agreement of ALL the data with the SM predictions - precision tests of radiative corrections and the SM 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 

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

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