http://arxiv.org/pd/0705.464 The Standard Model Antonio Pich IFIC, CSIC Univ. Valencia Gauge Invariance: QED, QCD Electroweak Uniication: Symmetry reaking: Higgs Mechanism Electroweak Phenomenology Flavour Dynamics SU() L U(1) Y 010 International School on Astroparticle Physics (ISAPP 010) Zaragoza, Spain, 13- July 010
Standard Model Parameters QCD: α ( M ) 1 S Z EW Gauge / Scalar Sector: 4 g, g, µ, λ α, θw, MW, MH α F, G, M, M Z H
G F α 1 ( ) = 1.166 371 ± 0.000 006 10 GeV M ( ) 5 = 137. 035 999 710 ± 0.000 000 096 Z = 91. 187 5 ± 0.001 GeV INPUTS ( M Z ) α = 18.93 ± 0.05 1 M W sin W sin θ = 1 W θ = M M πα W Z G F G ν µ µ g g e g F MW W ν e [ Exp: 80 ] M = 80. 94 GeV 79.96.399 ± 0.03 W sin θ = 0.1 W ( ) ( 0.31)
The Photon Couples to Virtual Pairs Vacuum Polarized Dielectric Medium α = α( m ) = 137.035999710 ( 9) ; α ( M ) = 18.93 ± 0.5 0 1 1 1 6 Z e + ( l l and qq contributions included )
W l,d i W e v, µ v, τ v, du, sc e µ τ ν l,u j uj = u, c ; d cosθc sinθc d s sinθc cosθ C s ( W l νl ) ( W all) Γ 1 r ( W l νl ) = = 11.1% Γ 3+ N C QCD: N C αs ( M ) 1 Z + 3.115 π ( ) r W l ν l 10.8% Experiment: ( W e νe ) = ( ± ) ( W µνµ ) = ( ± ) ( W τ ντ ) = ( ± ) Universal r 10.65 0.17 % r 10.59 0.15 % r 11.44 0. % W lν l Couplings
LEPTON UNIVERSALITY g g µ e g g µ τ
g µ / ge τ µ τ e π µ π e 1.0018 ± 0.0015 1.001± 0.0016 g / g τ µ K µ K e 1.004 ± 0.007 τ τ τ e µ τ 1.0006 ± 0.00 K πµ K πe W µ W e 1.00 ± 0.00 0.997 ± 0.010 g τ / ge Γ Γ Γ τ π π µ Γ τ K K µ W τ W µ 0.996 ± 0.005 0.979 ± 0.017 1.039 ± 0.013 τ τ τ µ µ τ 1.0005 ± 0.003 W τ W e 1.036 ± 0.014
Z Z l l +, v v l l ( ) ( Z ll v ) l a l Γ + ( Z ) Γ( Z νν l l) + + Z l l ( Z l l ) ( θ ) Γinv Γ invisible = N = N = 1.955 N Γll Γ 1 4sin + 1 ν ν ν W ( 1.989) Experiment: µ Γinv = 5.94 ± 0.016 Γ ll N ν = N =.9840 ± 0.008 v 3.04 (.99)
+ e e γ,z e γ, Z e θ e + e + dσ α = + + + + 8 { A (1 cos θ) cosθ - h } (1 cos θ) D cosθ dω s N C αs ( M Z ) Nl = 1 ; Nq = NC 1 + + ; h = ± 1 π A = 1+ vν Re( χ) + (v + a) (v + a) e e e χ = 4 a a Re( χ) + 8 v a v a e e e C = v a Re( χ) + (v + a ) v a e e e χ χ χ = G M F Z πα s s M + isγ / M Z Z Z D = 4 a v Re( χ) + 4 v a (v + a ) e e e χ
+ e e γ,z e γ, Z e θ e + e + dσ α = + + + + 8 { A (1 cos θ) cosθ - h } (1 cos θ) D cosθ dω s N C F Pol () s () s N N F F h + N N = 3 8 A =+ 1 h = 1 ( ) ( ) σ σ C 4πα = ; σ = ( h =+ 1) ( h = 1) σ + σ A 3s N A Pol F ( s) ( + 1) ( 1) ( + 1) ( 1) F F + ( + 1) ( 1) ( + 1) ( 1) F + NF + N + N N N N N N = 3 8 D A
Z Peak (s = M Z ) σ 1π Γ Γ = ; Γ Γ( Z M e Z ΓZ ) 3 3 () s = ; () s = ; () s = 4 4 Pol F e Pol F e σ σ 3 LR = = 4 L R LR () s e ; F () s σl + σr v a Final Polarization A = Only Available or =τ v + a 1 vl = 1+ 4sin θ 1 l Sensitive to Higher Order Corrections
Sensitive to Heavier Particles: TOP, HIGGS
Evidence o Electroweak Corrections August 009 LEPEWWG September 005 α 1 ( M Z ) = 18.93 ± 0.05 Low Values o M H Preerred
R Γ( Z bb ) Γ( Z hadrons) b LEPEWWG September 005 ernabéu-pich-santamaría 1988
LEPEWWG September 005 m = (17.7 ±.9) GeV t M H = (300 ) GeV + 700 186 α 1 ( M Z ) = 18.93 ± 0.05 Heavy Quarks (Leptons) Favour High (Low) M H
LEPEWWG August 009 m t = (173.1 ± 1.3) GeV (CDF + D0)
CDF / D0 (January 010) LEPEWWG (August 009) H W + W 114.4 GeV < < 157 (186) GeV (95% CL) M H M H [16,166] excluded (95% CL)
e W e + e W + W ν e e + W + e γ, Z W e + W + Evidence o Gauge Sel-Interactions
+ e e ZZ e Z e e + Z e γ, Z Z e +? Z No Evidence o γ ZZ or ZZZ couplings
Searching or the HIGGS ranching Ratios D. Denegri Total Decay Width Interaction proportional to mass ( M, M, m ) W Z The Higgs decays into the heaviest possible particles
The Large Hadron Collider ATLAS CMS
Quarks Leptons osons 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 Y = ( qu, qd ) L c ( q ) ( ) (, ) h.c. ( 0) d R + c q ( ) u R vl l L c l + ( 0) R + φ φ φ + + SS H = 1 + d v + + { m } q q q mq q u u qu m ll Y d d l Fermion Masses are New Free Parameters H m v m q, m,,, d q m u l = c c c Couplings Fixed: ( d) ( u) ( l) v g H = m v
FERMION GENERATIONS NG = 3 Identical Copies Q = 0 Q = 1 v j u j l j d j Q Q Masses are the only dierence = + 3 = 13 ( j = ) 1,, N G WHY? Y ( + ) (0) ( + ) ( d) φ ( u) φ () l φ = ( u j, d j) cjk d (0) kr cjk u ( ) kr ( vj, lj) c h.c. L + L j k l + (0) kr + j k φ φ φ SS H = 1+ d + + l + h.c. v { 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 =
DIAGONALIZATION OF MASS MATRICES = = = = M H U S S U d d d d d d d M H U S S U u u u u u u u = = M H U S S U l l l l l l l H = H U U = U U = 1 S S = S S = 1 µ ( 1 ) + H { d d + u u + } d u l l l Y = v = diag ( m, m, m ) ; = diag ( 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 = ; = L L L L R R R R u d = u d ; QUARK MIXING = V V S S CC CC L L L L u d NC NC
Z NC e = Zµ sin θ cos θ W W µ γ [ v a γ ] 5 Flavour Conserving Neutral Currents CC g µ µ = W µ uiγ ( 1 γ5) Vi j dj + vl γ ( 1 γ5) l + h.c. ij l Flavour Changing Charged Currents u c t d s b
L g µ = W µ ν γ (1 γ ) V l + h.c. ( l ) ( l ) CC i 5 ij j ij IF mν = 0 i ν lj Separate Lepton Number Conservation ν i V () l ij i IF ν R νi exist and m 0 g L = Wµ ν γ (1 γ ) l + h.c. ( l ) µ CC l 5 l ν ( Minimal SM without ) Le, Lµ, L τ ( Le + Lµ + Lτ Conserved ) R UT r ( µ eγ) < 1. 10 ; r ( τ µγ) < 4.4 10 11 8 (90 % CL)
Measurements o V ij Γ( ) V dj ueν i e ij d j V ij W u i e ν e We measure decays o hadrons (no ree quarks) Important QCD Uncertainties
V ij CKM entry Value Source V tb V V V V V V V ud us cd cs cb ub tb q V tq 0.9745 ± 0.000 Nuclear β decay 0.9746 ± 0.0019 0.9741± 0.006 pe ve + 0 + n π π e ν 0.46 ± 0.001 K π e ve 0.165 ± 0.0031 τ decays 0.59 ± 0.0015 K / π µν, Lattice 0.44 ± 0.001 0.30 ± 0.011 vd cx 0.9 ± 0. 06 D πν l, Lattice 0.985 ± 0.104 D Klν, Lattice 0.0386 ± 0.0011 0.0415 ± 0.0007 0.0407 ± 0.0007 0.0034 ± 0.0004 0.0041± 0.0003 0.0038 ± 0.0003 * D / Dl vl b clv π lv b ulv > 0.89 t bw / qw > 0.74 ; < 1 pp tb+ X l l l e ( ) V + V + V = 0.9995 ± 0.0010 V uj + V cj =. 00 ± 0.07 (LEP) ud us ub j
QUARK MIXING MATRIX Unitary N N Matrix: parameters G N 1 arbitrary phases: G G N G V V = V V = 1 φ e i ; e i i j u u d d i i j j θ V ij φ ( j i e i θ ) V ij V ij Physical Parameters: 1 ( 1) G G N N Moduli ; 1 ( 1) ( ) G G phases N N
N = : 1 angle, 0 phases (Cabibbo) V cos θ sin θ C C = sin θc cos θ C No N = 3 : 3 angles, 1 phase (CKM) c cos θ ; s sin θ ij ij ij ij V = s s c c s c s s c s iδ13 c1 c13 s1 c13 s13 e iδ13 iδ13 s1 c3 c1 s3 s13 e c1 c3 s1 s3 s13 e s3 c13 iδ13 iδ13 1 3 1 3 13 e 1 3 1 3 13 e c3 c13 3 1 λ / λ Aλ ( ρ iη ) λ 1 λ / A λ + 3 Aλ (1 ρ iη) Aλ 1 4 ( λ ) + δ13 0 (η 0) λ θ ρ η sin C 0.5 ; A 0.81 ; 0.37
Standard Model Parameters QCD: α ( M ) 1 S Z EW Gauge / Scalar Sector: 4 g g µ h α θ M M α G M M,,,, W, W, H, F, Z, H Yukawa Sector: m, m, m e m, m, m d s m, m, m u c t θ, θ, θ, δ 1 3 µ τ b 13 18 Free Parameters (+ Neutrino Masses / Mixings?) TOO MANY!
, : Violated maximally in weak interactions : Symmetry o nearly all observed phenomena 0 Slight (~ 0. %) in K decays (1964) Sizeable in decays (001) Huge Matter Antimatter Asymmetry in our Universe aryogenesis 0 Theorem: Thus, requires: Complex Phases Intererences
Meson Antimeson Mixing 0 0 0 Interering Amplitudes 0 Signal AAR Γ Γ 0 0 ( J/ ψ KS) ( J/ ψ KS) 0 0 ( J/ ψ KS) ( J/ ψ KS) Γ +Γ 0
* * * ud ub cd cb td tb V V + V V + V V = 0 * * Vud Vub Vcd V * * cb V V V V td tb cd cb UTit 1 η η 1 λ = 0.34 ± 0.014 1 ρ ρ 1 λ = 0.154 ± 0.0 α= 9.0 ± 3.4 ; β =.0 ± 0.8 ; γ = 65.6 ± 3.3
Neutrino Oscillations http://hitoshi.berkeley.edu/neutrino Lepton Mixing ν R,? NEW PHYSICS
Neutrino Oscillations González-García, Maltoni, Salvado, 010 5 1 (7.59 0.1) 10 ev m = ± 3 3 (.43 0.13) 10 ev m = ± sin ( θ ) = 0.87 ± 0.04 1 sin ( θ ) > 0.9 3 sin ( θ ) < 0.19 13
LEPTON FLAVOUR VIOLATION 90% CL Upper Limits on r(l X ) [AAR / ELLE] Decay U.L. Decay U.L. Decay U.L. µ e γ 1. 10 11 µ e e + e 1.0 10 1 µ e γγ 7. 10 11 τ e γ 3.3 10 8 τ e e + e 3.6 10 8 τ e e + µ.7 10 8 τ µ γ 4.4 10 8 τ e µ + µ 3.7 10 8 τ µ e + µ.3 10 8 τ e e µ +.0 10 8 τ µ µ + µ 3. 10 8 τ e π 0 8.0 10 8 τ µ π 0 1.1 10 7 τ e η 1.6 10 7 τ µ η 1.3 10 7 τ e η 9. 10 8 τ µ η 6.5 10 8 τ e Κ * 0 5.9 10 8 τ e Κ S 3.3 10 8 τ µ Κ S 4.0 10 8 τ µ ρ 0.6 10 8 τ e K + K 1.4 10 7 τ e K + π 1.6 10 7 τ e π + K 3. 10 7 τ µ K + K.5 10 7 τ µ K + π 3. 10 7 τ µ π + K.6 10 7 τ e π + π 1. 10 7 τ µ π + π.9 10 7 τ Λπ 7. 10 8 τ e + K K 1.5 10 7 τ e + K π 1.8 10 7 τ e + π π.0 10 7 τ µ Κ * 0 5.9 10 8 τ e φ 3.1 10 8 τ µ ω 8.9 10 8 τ µ + K K 4.4 10 7 τ µ + K π. 10 7 τ µ + π π 0.7 10 7
THE STANDARD THEORY OF FUNDAMENTAL INTERACTIONS ( ) ( ) ( ) SU 3 SU U 1 C L Y Electroweak + Strong Forces Gauge Symmetry Dynamics 3 Gauge Parameters: ( ) α, α, θ s M Z W All Known Experimental Facts Explained Problem with Mass Scales / Mixings: - 15 Additional Parameters - Why 3 Families? - Why Let Right? m > M - Why t Z? - Does the Higgs Exist? - Flavour Mixing - Violation - Neutrino Masses / Oscillations
e µ τ