Electroweak interactions of quarks Benoit Clément, Université Joseph Fourier/LPSC Grenoble HASCO School, Göttingen, July 15-27 2012 1
PART 1 : Hadron decay, history of flavour mixing PART 2 : Oscillations and CP Violation PART 3 : Top quark and electroweak physics 2
PART 1 Hadron decays History of flavour mixing 3
Hadron spectroscopy 1950/1960 : lots of «hadronic states» observed resonances in inelastic diffusion of nucleons or pions (pp, pπ, np, ) Interpreted as bound states of strong force Several particles - almost same mass - same spin - same behavior wrt. strong interaction - different electric charge Multiplet structure associated with SU(2) group symmetry. 4
Strange hadrons A few particles does not fit into this scheme : Name Mass (MeV) Decay Lifetime Λ 1116 Nπ 1.10-10 s Ξ 0, Ξ -, 1320 Λπ 3.10-10 s Σ +,Σ - 1190 Nπ 8.10-11 s Σ 0 1200 Λ 1.10-20 s (EM) Decay time characteristic from weak interaction Particles stable wrt. strong/em coupling Conserved quantum number : strangeness 5
Quark model Gell-Mann (Nobel 69) and Zweig, 1963 : hadrons are build from 3 quarks u, d and s. Strangeness : content in strange quarks Only weak interaction can induce change of flavour BR(K s Wu or s Zd eg. + π + vv) BR(K + π 0 μ + v) <10-5 No Flavor Changing Neutral Currents (FCNC) in SM 6
Electroweak lagrangian OK for leptons What happens for quarks? 7
SU(2) L symetry : SU(2) L and quarks doublets of left handed fermions with u u and s d L or and d L s L L ΔQ=1: singlets for right handed fermions : u R, d R, s R But both Wud and Wus vertices happen! Eg. Leptonic pion and kaon decays : u W + μ + u W + μ + d + ν μ s K + ν μ 8
Flavour mixing strong interaction eigenstates (mass eigenstates) may be different from weak interaction eigenstates Some mixing of d and s : d C s C =U d s universality of weak interaction : conserve the overall coupling : U + U =1 U is 2x2 rotation matrix, 1 parameter U = cosθ C sinθ C θ sinθ C cosθ C is the Cabibbo angle (1963) C 9
Back to lagrangian 1 doublet u d C Charged currents : Vertices : L and 4 singlets u R, d CR, s CR, s CL L CC = ig 2 2 ψ uγ μ 1 γ 5 ψ dc W μ + + h. c. = igcosθ C 2 2 ψ u γ μ 1 γ 5 ψ d W μ + + igsinθ C 2 2 ψ uγ μ 1 γ 5 ψ s W μ + + h. c. Wud : Wus : igcosθ C 2 2 γμ (1 γ 5 ) igsinθ C 2 2 γμ (1 γ 5 ) 10
Naive estimation of C From pion and kaon lifetimes τ π = 2.603 10 8 s τ K = 1.23 10 8 s u d u s + K + gcos gsin W + W + tan 2 θ C = 0. 63 τ 3 π m K τ K m π 3 μ + ν μ μ + ν μ Γ π μν BR ~ 100% Γ K μν BR ~ 63% g 4 cos 2 θ C Feynman amplitude g 4 sin 2 θ C 2 m π 2 m μ 2 2 m π 3 Phase space m 2 2 K m 2 μ m K 3 m 2 2 π m μ m 2 K m2 2 sinθ C= 0.265 cosθ C = 0.964 μ 11
FCNC troubles Neutral currents (d and s quark only) L NC = ig 2cosθ W ψ dc γ μ c V c A γ 5 ψ dc Z μ + ψ sc γ μ c V c A γ 5 ψ sc Z μ c V = T 3 2sin 2 θ W Q : c V ψ dc = 1 2 + 2 3 sin2 θ W ψ dc ; c V ψ sc = 2 3 sin2 θ W ψ sc c A = T 3 : c A ψ dc = 1 2 ψ d C ; c V ψ sc = 0 Introducing mass eigenstates : L NC = ig 2cosθ W ψ dc γ μ c Z 1 ψ dc Z μ + ψ sc γ μ c Z 2 ψ sc Z μ = ig 2cosθ W ψ d γ μ cos 2 θ C c Z 1 + sin 2 θ C c Z 2 ψ d Z μ + ψ s γ μ sin 2 θ C c Z 1 + cos 2 θ C c Z 2 ψ s Z μ + igcosθ Csinθ C 2cosθ W ψ d γ μ c Z 1 c Z 2 ψ s Z μ + ψ s γ μ c Z 1 c Z 2 ψ d Z μ FCNC inducing term 12
GIM and charm Natural solution proposed by Glashow, Iliopoulos, Maiani in 1970(GIM mechanism) Add a 4th quark to restore the symmetry : charm 2 SU(2) L doublets + right singlets u d, c C L s, u R, d CR, c R, s CR C L Then the coupling to the Z becomes : c Z 1 = c Z 2 = 1 2 + 2 3 sin2 θ W 1 2 γ5 And the FCNC terms cancel out : igcosθ C sinθ C ψ 2cosθ d γ μ c 1 =0 Z c 2 Z ψ s Z μ + ψ s γ μ c 1 =0 Z c 2 Z ψ d Z μ W 13
Top and bottom Generalization to 6 quarks : u d, c Complex 3x3 unitary matrix : s, t b Kobayashi & Maskawa in 1973 (Nobel in 2008) Cabibbo-Kobayashi-Maskawa or CKM Matrix V CKM = V ud V us V ub V cd V cs V cb, V td V ts V tb d s b = V CKM d s b Lepton vertex : ig 2 2 γμ (1 γ 5 ) W + q u q d vertex : igv quq d 2 2 W - q u q d vertex : igv quq d 2 2 γ μ (1 γ 5 ) γ μ (1 γ 5 ) 14
V CKM = V ud V us V ub V cd V cs V cb = V td V ts V tb CKM matrix 0.97428 ± 0.00015 0.2253 ± 0.0007 +0.00016 0.00347 0.00012 0.2252 ± 0.0007 +0.00015 0.97345 0.00016 +0.0011 0.0410 0.0007 +0.00026 +0.0011 +0.000030 0.00862 0.00020 0.0403 0.0007 0.999152 0.000045 1 0 0 First approximation : Diagonal matrix V CKM = 0 1 0 0 0 1 no family change : Wud, Wcs and Wtb vertices Second approximation : Block matrix V CKM = submatrix is almost the Cabibbo matrix V ud V us 0 V cd V cs 0 0 0 1 V ud V cs cos C and V us V cd sin C Top quark only decays to bottom quark Charm quark mostly decays to strange quark Bottom and Strange decays are CKM suppressed 15
PART 2 Oscillations and CP Violation 16
Discrete symmetries 3 discrete symmetries, such as S ²=1 Affects : coordinates, operators, particles fields P = Parity : space coordinates reversal : x x C = Charge conjugaison : particle to antiparticle transformation (i.e. inversion of all conserved charges, lepton and baryon numbers) eg. e C e +, u C u, π (du) C π + (ud),k 0 (ds) C K 0 (sd) T = Time : time coordinate reversal : t t 17
Parity Weak interaction is not invariant under parity : maximum violation of parity (C.S.Wu experiment on 60 Co beta decay) Strong and EM interaction are OK. Parity does not change the nature of particles parity eigenstates : P p = p : Intrinsic partity since P²=1, = 1 Under P : E E, vector; B B, pseudovector 4 -potential : φ, A φ, A so : η photon = 1 Strong and EM interaction conserves parity. 18
2 photons, helicity=+1 2 photons, e + helicity= -1 Parity of the pion 1 2 J=0 e - e - 0 e + EM decay : 0, conserves parity Parity eigenstates for photon pair : Pions can only decay in one of these states Measure angular distribution of e + e - pairs : + 1 + cos2φ 1 cos2φ Experimentally : η π 0 = 1 + = 1 + 2 2 = 1 2 2, η = 1, η = 1 19
CP symmetry : pion decay J=1/2 J 3 =-1/2 k μ + C J=1/2 J 3 =-1/2 k μ - J=0, J 3 = 0 π + scalar J=0,J 3 = 0 π - scalar J=1/2 J 3 =+1/2 -k ν μ left-handed, massless chirality = helicity J=1/2 J 3 =+1/2 -k ν μ right-handed P CP P J=1/2 J 3 =+1/2 k ν μ left-handed C J=1/2 J 3 =+1/2 k ν μ right-handed J=0, J 3 = 0 π + scalar J=0, J 3 = 0 π - scalar J=1/2 J 3 =-1/2 -k μ + J=1/2 J 3 =-1/2 -k μ - 20
CP symmetry : neutral kaons Kaons are similar to pions : same SU(3) octet pseudoscalar mesons P K O = K O and P K O = K O K 0 (=us) and K 0 (=us) are antiparticle of each other C K O = K O and C K O = K O So: CP K O = K O and CP K O = K O Then CP-eigenstates are : K 1 0 = K0 K 0 2, η CP = 1 K 2 0 = K0 + K 0 Does weak currents conserve CP? 2, η CP = 1 21
CP violation in Kaon decays If CP is conserved by weak interactions then only K 1 0 ππ, (η CP = 1) and K 2 0 πππ, With a longer lifetime for K 2 0 (more vertices) Experimentally : 1 =0.9x10-10 s 2 =5.2x10-8 s η CP = 1 After t>> 1 only the long-lived components remains but a few 2 pions decays are still observed! Cronin & Fitch, 1964, Nobel 1980 Conclusion : the long lived component isn t a pure CP eigenstate : small CP violation! 0 Physical states : K L = K 1 0 ε K 0 2 0, K 1+ε 2 S = ε K 1 0 + K 0 2 1+ε 2 ε = 2.3 10 3 22
Meson oscillations Neutral pseudoscalar mesons P and P (K 0, D 0, B 0, B S ) Propagation/strong interaction Hamiltonian : H 0 H 0 P = m P P, H 0 P = m P P (in rest frame) Interaction (weak) states propagation states. Decay is allowed : effective hamiltonian H W is not hermitian H W = M i Γ 2 with M = H W+H w 2 Γ = H W H w For eigen states : M = m 1 0 0 m 2 Γ = γ 1 0 0 γ 2 And the time evolution of state 1 is : hermitian P 1 (t) = e im 1t e γ 1t 2 P 1 (0) I t = P 1 0 P 1 t 2 = e γ 1t Exponential decay : M mass matrix, Γ decay width 23
Interaction eigenstates In the basis P, P, the 2 states have the same properties (CPT symmetry) : M 11 = M 22 M 0 and Γ 11 = Γ 22 Γ 0 If we assume M, Γ to be real : M 12 = M 21 M and Γ 12 = Γ 21 Γ Then : H W = M 0 i Γ 0 2 M i Γ 2 In new basis : P L = P S = P + P 2 P P 2 H W = M i Γ 2 M 0 i Γ 0 2 M 0 + M i Γ 0 + Γ 2 P L : long lived, mass M L = M 0 + M and width Γ L = Γ 0 + Γ Γ 0 P S : short lived, mass M S = M 0 M and width Γ S = Γ 0 Γ Γ 0 0 From perturbation theory : Γ Γ 0 0 M 0 M i Γ 0 Γ 2 24
Time evolution General state : mixing of P L and P S : P(t) = c L t P L + c S t P S Coefficients c L and c S satisfy the Schrödinger eq. : i d dt c L t c S t = M L i 1 2 Γ L 0 0 M S i 1 2 Γ S c L t c S t Then time evolution is : P(t) = e im 0t c L 0 e imt Γ Lt 2 P L + c S 0 e imt Γ St 2 P S 25
Time evolution For a pure P initial state : c L 0 = c S 0 = 1 2. And the intensity after a given time is : I t = P P t 2 = 1 4 e ΓLt + e ΓSt + 2e Γ L+Γ S 2 t cos (2Mt) Oscillations P L P S in time, with a frequency equal to the mass difference : Δm = M L M S = 2M For the Kaon system : m = 3.48x10-12 MeV = 5.29 ns -1 S = 89.6 ps L = 51.2 ns 26
CP violation Previously we assumed M and Γ to be real Interaction eigenstates = CP-eigenstates But if complex M 12 = M 21 and Γ 12 = Γ 21 Then the eigenstates ares : P L = N P + ε P P S = N P ε P ε = M 12 N 2 = 1 + M 12 i 2 Γ 12 M 12 i 2 Γ 12 2 1 + 4 Γ 12 2 1 M 12 + 4 Γ 12 2 +Im(Γ12 M 12 ) 2 Im(Γ12 M 12 ) Complex mass matrix induces CP-violation 27
Parametrization of CKM 3x3 complex unitary matrix has 4 parameters 3 angles : α = φ 13 = arg V tdv tb V ud V ub 1 complex phase : V CKM =, β = φ 23 = arg V cdv cb V td V, γ = φ 12 = arg V udv ub tb c 12 c 13 s 12 c 13 s 13 e iδ s 12 c 23 c 12 s 23 s 13 e iδ c 12 c 23 s 12 s 23 s 13 e iδ s 23 c 13 s 12 s 23 c 12 c 23 s 13 e iδ c 12 s 23 s 12 c 23 s 13 e iδ c 23 c 13 V cd V cb Complex phase u V us W + μ + allows CP violation d + V * cd V cs ν μ 28
Oscillation and boxes Quark interpretation : box diagram The mass matrix off-diagonal elements becomes: M 12 = C V us V ud m u + V cs V cd m c + V ts V td m 2 t = C V us V ud (m u m c ) + V ts V td (m t m c ) 2 Complex because of phase in CKM matrix : CP violation : can only happen if at least 3 families. only happens in loop diagrams : rare decays and oscillations. 29
Unitarity triangles Unitarity of CKM matrix : V CKM =1 V CKM V ud V ud + V us V us + V ub V ub = 1 V cd V cd + V cs V cs + V cb V cb = 1 V td V tb + V ts V ts + V tb V tb = 1 V ud V us + V cd V cs + V td V ts = 0 V ud V ub + V cd V cb + V td V tb = 0 V us V ud + V cs V cd + V ts V td = 0 V us V ub + V cs V cb + V ts V tb = 0 V ub V ud + V cb V cd + V tb V td = 0 V ub V us + V cb V cs + V tb V ts = 0 Sum of 3 complex numbers : triangle in complex plane Complex only if CP violating phase is large Most triangle are almost flat, except one. 30
Unitarity triangles Many decay processes, including rare decays of strange/charmed/beauty hadrons - Some sensitive to matrix elements V xy - Some sensitive mass differences (oscillations) - Some sensitive to angles (CP-violation) 31
PAST : e + e -, at (4S) resonnance (bb state) BELLE (KEK, Japan) BaBAR (SLAC, US) pp : CDF and D0 Experiments PRESENT pp : LHCb (+ ATLAS/CMS) FUTURE : e + e - SuperBELLE (Japan) SuperB (Italy) 32
PART 3 Top quark and electroweak physics 33
Top quark decays Top quark only decays through weak interaction V tb ~1 : t Wb at 100% m t > m W +m b : only quark that decays with a real W Coupling not «weak» : top ~10-25 s >> hadronization No loss of polarization. Top quark signature : 1 central b-quark jet, with high p T (~70 GeV) 1 on-shell W boson : 1 isolated lepton and E T (~35 GeV) or 2 jets (~35 GeV) 34
Top quark production s=7tev σ NLO 160 pb σ NLO 3 pb σ NLO 15 pb Strong interaction top/antitop pairs σ NLO 65 pb Weak interaction tb, tq(b) Weak interaction tw 35
Top quark and electroweak Top quark decays through Wtb vertex - Use pair production (largest cross-section) - Probe V-A theory in top coupling - Measure V tb assuming 3 generations Electroweak production of the top quark - lower cross-section, more background - cross-section gives access to V tb without assumptions on unitarity - sensitivity to new physics (W, 4th generation ) Precision measurement of mass and coupling - all electroweak quantities are linked at higher order - Sensitivity to the Higgs sector (high mass) 36
W helicity in top decays (1) Longitudinal W F 0 0.7 Left-handed W F L 0.3 Right-handed W F R 0 +1/2 W t b 0 +1/2 +1/2-1/2 b t W +1 +1/2 W t b +1-1/2 Like for muon decays : m b << m t, m W chirality = helicity right-handed W is strongly suppressed 37
W helicity in top decays (2) Angle between top and lepton in W rest frame In theory : Nice and easy In practice : Expected shapes for ATLAS experiment Also possible : unfolding 38
ATLAS results 1fb -1 The Model stays boringly Standard 39
Top decays and V tb B-jets can be identified : long lifetime of b-hadrons, larger mass, fragmentation ε btag ~60%, mistag~0.1% Use events with 0 b-tag, 1 b-tag and 2 b-tag Simutaneous measurment of σ tt and R R B(t B(t Wb) Wq) V ts 2 V V Very old D0 result Lepton+jets (~230 pb -1 ) 2 tb 2 V 2 2 tb td Vtb Likelihood discriminant R R 1.03 0.19 0.17 0.64 @ 95% CL 40
Single top Only t-channel has been clearly (>5σ) seen at Tevatron and LHC. First 3σ evidence for tw (ATLAS) 41
Direct V tb measurement All 3 diagrams feature 1Wtb vertex σ V tb ² 42
Standard Model consistancy Top mass is one of the ingredients of the electroweak fit indirect contraints on the Higgs mass Radiative corrections (1 loop) to the W mass 43