Antonio Pich IFIC, CSIC Univ. alencia Antonio.Pich@cern.ch
Fermion Masses Fermion Generations Quark Mixing Lepton Mixing Standard Model Parameters CP iolation
Quarks Leptons Bosons up down electron neutrino e e photon µ gluon charm strange muon neutrino µ Z 0 W ± τ top beauty tau neutrino τ Higgs
FERMION MASSESS Scalar Fermion Couplings allowed by Gauge Symmetry 0 ( ) ( ) ( ) ( d ) φ ( u) φ ( l) φ LY = ( qu, qd) L c ( q ) ( ) (, ) h.c. ( 0) d R + c q ( ) u R vl l L c l + + ( 0) R + φ φ φ L + + SSB = H 1+ + + v d u { m q } d q d m q q m l l l Y q q u u Fermion Masses are New Free Parameters H m f v f mq, m,,, d q m u l = c c c Couplings Fixed: ( d) ( u) ( l) v g Hf f = m v 2 f f
FERMION GENERATIONS NG = 3 Identical Copies Q = 0 Q = 1 v j u j lj d j Q Q Masses are the only difference = + 23 = 13 ( j = ) 1,, N G WHY? L φ φ φ =, + +, + h.c. ( + ) (0) ( + ) ( d) ( u) ( l) Y ( u j d j) (0) kr ( ) kr ( j j) L cjk d cjk u v l c L jk l + (0) kr jk φ φ φ L SSB H = 1+ h.c. v d + + l + { d M d u M } u u l M l Y L R L R L R Arbitrary Non-Diagonal Complex Mass Matrices ( d) ( u) ( l),,,, v d u l = c jk jk c jk c jk M M M 2
DIAGONALIZATION OF MASS MATRICES = = M H U S M S U d d d d d d d = = M S M H U S U u u u u u u u = = M M H U S S U l l l l l l l H f = H f U U = U U = 1 f f f f S S = S S = f f f f 1 µ ( 1 ) + H { d d + u u + } d u l l l L Y = M M M v M = diag ( m, m, m ) ; M = diag( m, m, m ) ; M = diag( m, m, m ) u u c t d d s b l e µ τ d S d ; u S u ; l S l L d L L u L L l L d S U d ; u S U u ; l S U l R d d R R u u R R l l R Mass Eigenstates Weak Eigenstates f f = f f ; f f = f f L L L L R R R R u d = u d ; L = S S CC CC L L L L u d QUARK MIXING NC L L L NC
L e = [ v a γ ] Z N Z C µ f γ f f f 5 2sinθW cosθw f µ Flavour Conserving Neutral Currents L CC g W µ µ u ( 1 ) d v ( 1 ) l h.c. = µ iγ γ5 ij j + l γ γ5 + 2 2 ij l Flavour Changing Charged Currents u c t d s b
L ( l ) CC g µ = W (1 ) + h.c. 2 2 ( l ) µ νi γ γ5 ij lj ij IF mν = 0 i ν lj ν i () l ij L g = ( l ) µ CC Wµ νl γ (1 γ5 ) l + h. 2 2 l c. Separate Lepton Number Conservation ν ( Minimal SM without ) R IF BUT i ν exist R and m 0 ν i Le, Lµ, L τ ( Le + Lµ + Lτ Conserved ) Br ( µ eγ) < 1.2 10 ; Br ( τ µγ) < 6.8 10 11 8 (90 % CL)
Measurements of ij Γ( ) dj uie ν e ij 2 d j ij W u i e ν e We measure decays of hadrons (no free quarks) Important QCD Uncertainties
ij CKM entry alue Source tb ud us cd cs cb ub q 2 tq 0.9740 ± 0.0005 0.9745 ± 0.0019 0.9740 ± 0.0005 0.2233 ± 0.0028 0.2208 ± 0.0034 0.2219 ± 0.0025 0.2221± 0.0016 0.224 ± 0.012 0.97 ± 0.11 0. 974 ± 0.013 0.0413 ± 0.0021 0.0416 ± 0.0010 0.0415 ± 0.0010 0.0038 ± 0.0009 0.0044 ± 0.0005 0.0043 ± 0.0005 0.97 + 0.16 0.12 Nuclear n pe v β decay K π e ve τ decays K / π µν, Lattice W + vd cx e + W cs had,, uj B b cl v * D l vl B ρ l v b ul v t bw l l l / qw cd, cb 2 2 2 ud + us + ub = 0.9980 ± 0.0017 ( 2 2 ) uj + cj = 1.999 ± 0.025 (LEP) j
QUARK MIXING MATRIX Unitary N G 2 N G N Matrix: parameters G = = 1 2 N 1 arbitrary phases: G φ i i i j e i θ j i j u e u ; d d ij ( e i θ φ j i ) ij ij Physical Parameters: 1 ( 1) G G 2 N N Moduli ; 1 ( 1) ( 2) G G phases 2 N N
N f = 2 : 1 angle, 0 phases (Cabibbo) cos θ sin θ C C = sin θc cos θ C No CP N f = 3 : 3 angles, 1 phase (CKM) c cos θ ; s sin θ ij ij ij ij = c12 c13 s12 c13 s13 e iδ iδ s c c s s e c c s s s e s c iδ iδ s s c c s e c s s c s e c c iδ 13 13 12 23 12 23 13 12 23 12 23 13 23 13 13 13 12 23 12 23 13 12 23 12 23 13 23 13 13 2 3 1 λ /2 λ Aλ ( ρ iη ) 2 2 λ 1 λ /2 A λ + 3 2 Aλ (1 ρ iη) Aλ 1 O 4 ( λ ) λ θ ρ + η 2 2 sin C 0.222 ; A 0.84 ; 0.41 δ 13 0 (η 0) CP
Standard Model Parameters QCD: αs( M Z) 1 EW Gauge / Scalar Sector: 4 g g h M M M 2,, µ, α, θw, W, M H α, GF, Z, H Yukawa Sector: m, m, m e m, m, m d s m, m, m u c t θ, θ, θ, δ 1 2 3 µ τ b 13 18 Free Parameters TOO MANY! (+ Neutrino Masses / Mixings?)
C, P : iolated maximally in weak interactions CP : Symmetry of nearly all observed phenomena 0 Slight (~ 0.2 %) CP in K decays (1964) Sizeable CP in decays (2001) Huge Matter Antimatter Asymmetry in our Universe Baryogenesis B 0 CPT Theorem: CP T Thus, CP requires: Complex Phases Interferences
Meson Antimeson Mixing B 0 B 0 0 B f 2 Interfering Amplitudes 0 B CP Signal BABAR Γ Γ 0 0 ( B J/ ψ KS) ( B J/ ψ KS) 0 0 ( B J/ ψ KS) ( B J/ ψ KS) Γ +Γ 0
* * * ud ub cd cb td tb + + = 0 * * ud ub cd * * cb td tb cd cb UT fit 1 2 η η 1 λ = 0.342 ± 0.022 2 1 2 ρ ρ 1 λ = 0.216 ± 0.036 2 α = 98.2 ± 7.7 ; β = 23.7 ± 1.4 ; γ = 57.9 ± 7.3
Complex phases in Yukawa couplings only: L Y ( + ) (0) ( d) φ ( u) φ = ( u j, d j) L cjk d (0) kr + cjk u ( ) kr + h.c. + jk φ φ SSB ( d ) ( u ) { jl cjk kr jl cjk ukr.} L 1 v Y = H + d d u h.c v 2 + + φ (0) = v/ 2 c ( q) jk diagonalization H LY = 1+ d d + u u + h.c. j j v { } jl md jr jl mu jr g µ L = Wµ u γ (1 γ ) d + h.c. CC i 5 ij j 2 2 ij The CKM matrix ij is the only source of CP
Neutrino µ τ Oscillations ν e ν µ ν ν M. Maltoni Lepton Mixing ν R, CP? NEW PHYSICS
THE STANDARD THEORY OF FUNDAMENTAL INTERACTIONS ( ) ( ) ( ) SU 3 SU 2 U 1 C L Y Electroweak + Strong Forces Gauge Symmetry Dynamics 3 Gauge Parameters: 2 ( ) α, α, θ s M Z W All Known Experimental Facts Explained Problem with Mass Scales / Mixings: - 15 Additional Parameters - Why 3 Families? - Why Left Right? m > M -Why t Z? - Does the Higgs Exist? - Flavour Mixing - CP iolation - Neutrino Masses / Oscillations
e WANTED WANTED Higgs Higgs µ GREAT GREAT REWARD REWARD STOCKHOLM τ