The Standard Model. Antonio Pich. IFIC, CSIC Univ. Valencia

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1 The Standard Mode Antonio Pich IFIC, CSIC Univ. Vaencia Gauge Invariance: QED, QCD Eectroweak Uniication: SU() Symmetry Breaking: Higgs Mechanism Eectroweak Phenomenoogy Favour Dynamics L U() Y Taer de Atas Energías (TAE) 00 Barceona, Spain, August September 00

2 Quarks Leptons Bosons up down eectron neutrino e e photon guon charm strange muon neutrino Z 0 ± τ top beauty tau neutrino τ Higgs The Standard Mode A. Pich - TAE 00

3 FREE Dirac ermion: = ψ ( iγ m) ψ Phase Invariance: ψ ψ = ψ ; ψ ψ = ψ e iqθ Absoute phases are not observabe in Quantum Mechanics GAUGE PRINCIPLE: θ = Phase Invariance shoud hod LOCALLY θ( x) e iqθ BUT e iq θ θ ψ ( + iq ) ψ SOLUTION: Covariant Derivative D ( i A ) e iq θ ψ + eq ψ D ψ One needs a spin- ied A satisying A A e θ The Standard Mode A. Pich - TAE 00

4 = ψ ( iγ D m) ψ = ψ ( iγ m) ψ e QA ( ψγ ψ) γ ψ e Q ψ Kinetic term: K = Fν F ν 4 Mass term: M = m A A γ = eq ( ψγ ψ) Maxwe F ν Not Gauge Invariant m γ = 0 ν 8 [exp: m < 0 ev ] γ Gauge Symmetry QED Dynamics The Standard Mode A. Pich - TAE 00

5 e Successu Theory γ e + + Anomaous Magnetic Moment g e m a ( g ) a e = ( ± 0.76) 0 α = ± th a = (65988 ± 0) [ Exp: ( ± 6.) 0 ] The Standard Mode A. Pich - TAE 00

6 FREE QUARKS: = q [ iγ m] q q q q q N C = SU() Coour Symmetry: q U q ; q q U ; det ; exp i λ = = = = θ a UU UU U U a Gauge Principe: Loca Symmetry θ = θ ( ) D μ q ( I + i G ) q U g s The Standard Mode A. Pich - TAE 00 μ Dq i D U D U ; G U G U + ( U) U g ( a α β λ ) α β Ga [ ] ( x ) a a x G 8 Guon Fieds s

7 Ininitesima SU() Transormation: a α λ q a β abc = i δθ q ; Ga ( ) = δθ s a δθ b G g δ δ αβ c Non Abeian Group: a b c λ λ abc λ, = i δ G a depends on Universa g s G a No Coour Charges The Standard Mode A. Pich - TAE 00

8 Kinetic Term: i G ν [ D, D ν ] = G ν ν G + igs[ G, G ν ] U G ν U g G s a ν ν ν ν ν c ν λ abc Ga ; Ga = Ga Ga gs Gb G K Tr ( G G ) 4 ν a ν Ga ν Gν = = Mass Term: M = mg Ga G a Not Gauge Invariant m G = 0 Massess Guons The Standard Mode A. Pich - TAE 00

9 QCD = Tr ( G ν G ) [ i m ] ν + q γ D q q a a ( a a ) ( ) = G ν ν G G G + q [ iγ mq ] q 4 q a a α αβ β g [ q ( λ ) γ q ] G s ν ν α α q + g g G G G G 4 a a d e s abc ( G G ) G b G ν ν ν ν c s abc ad e b c ν Guon Se interactions g s 4 G,G Universa Couping (No Coour Charges) The Standard Mode A. Pich - TAE 00

10 Three Famiies νe u ν c ντ t,, e d s τ b Famiy Structure ν qu ν q u,( ν ) R, R ;,( qu) R,( qd ) R q d q L d L Charged Currents Neutra currents ± γ, Z Let handed Fermions ony Favour Changing: ν, qu q Favour Conserving d Universaity (Famiy Independent Coupings) ( )? R ν The Standard Mode A. Pich - TAE 00

11 The Standard Mode A. Pich - TAE 00

12 SU() L U() Y Fieds ψ ( x) ψ ( x) ψ ( x) Quarks Leptons q q u d ν L L ( q ) ( q ) u R d ( ν ) ( ) R R R Free Lagrangian or Massess Fermions: 0 = i ψ j γ ψ j j SU () U () L { } Y Favour Symmetry: L exp i σ U α iy β iy β iy β e e e UL ; ; ψ ψ ψ ψ ψ ψ i y β i y β i y β e e e UL ; ; ψ ψ ψ ψ ψ ψ 4 Massess Gauge Bosons ± 0,, B The Standard Mode A. Pich - TAE 00

13 Gauge Principe: α = α ( x), β = β ( x) D ( ) e iy β x ψ + ig ( x) + ig y B ( x) ψ U () x D ψ L D i y k β ( x) ψk + ig yk B ( x) ψk e ψ k = D B ( x) B ( x) β ( x) g i ( x) UL( x) ( x) UL( x) + UL(x) UL( x) g ( k,) { } i ( ) exp ( ) ; ( ) ( ) ; i ijk j k x i σ α x x σ U x δ = ( δα ) ε δ α g 4 Massess Gauge Bosons ± 0,, B The Standard Mode A. Pich - TAE 00

14 CHARGED CURRENTS i ψ j γ D ψ j g ψγ ψ g B yj ψ j γ ψ j j j σ ; = i + ( ) = g q u γ ( γ ) qd + ν γ ( γ ) + h.c. CC 5 5 Quark / Lepton Universaity Let Handed Interaction The Standard Mode A. Pich - TAE 00

15 NEUTRAL CURRENTS NC σ = ψγ ψ j ψ jγ ψ j j g g B y Massess Fieds Arbitrary Combination cos θ sin θ Z B sin θ cos θ A A has the QED Interaction IF g sin θ = g cos θ = e y = Q u = d ; u ; Q + y = Q y = Q d NC Q = ea ψ j γ Q j ψ j + j Qu 0 = ; Q = Qu ; Q = 0 Q d Q d Z NC The Standard Mode A. Pich - TAE 00

16 Z NC = sinθ e cosθ Z σ ψγ ψ sin θ ψ j γ Q j ψ j j = sinθ cosθ e Z γ [ γ ] v a 5 qu qd ν v 8 sin θ 4 + s in θ + 4 sin θ a ν R IF do exist: yv ( R ) = Qv = 0 No R Sterie Neutrinos v Interactions The Standard Mode A. Pich - TAE 00

17 γ NEUTRAL Z CURRENTS eq a = T = ± ( sin ) v = T 4 Q θ e s c θ θ ( a γ 5) v CHARGED g ( γ ) / 5 ν CURRENTS qd g ( γ ) / 5 qu yv ( R ) = Qv = 0 No R v Interactions Sterie The Standard Mode A. Pich - TAE 00 Neutrinos

18 i, σ ; g D D U U L L ν B B B B ν ν ν ν ν ν ν i i i i jk j k ν = ν ν g ε ν K ν Tr( ν = B B ) B B ν ν ν = ν ν ν = kin = ν ν ν ν ν ν {( ) ν ν ν Z } ie cot θ Z ( ) Z + ( Z ) ν ν {( ) ( ) ( )} ν ν ν ν ν ν ν + ie A A + A A {( ) } ν e cot { ν Z Z Z ν ν θ ν ν Z } e = sin θ { ν ν ν } { ν ν ν ν ν ν ν } e cotθ Z A Z A A Z e A A A A The Standard Mode A. Pich - TAE 00

19 + GAUGE SELF-INTERACTIONS γ,z γ,z γ,z The Standard Mode A. Pich - TAE 00

20 Gauge Symmetry m γ = 0 M = M = Z 0 Good Bad! M M Z = = GeV 9.9 GeV Moreover m L R R L m = m ( + ) Aso Forbidden by Gauge Symmetry m 0 = A Partices Massess The Standard Mode A. Pich - TAE 00