Electroweak interactions of quarks. Benoit Clément, Université Joseph Fourier/LPSC Grenoble

Transcription

1 Electroweak interactions of quarks Benoit Clément, Université Joseph Fourier/LPSC Grenoble HASCO School, Göttingen, July

2 PART 1 : Hadron decay, history of flavour mixing PART 2 : Oscillations and CP Violation PART 3 : Top quark and electroweak physics 2

3 PART 1 Hadron decays History of flavour mixing 3

4 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

5 Strange hadrons A few particles does not fit into this scheme : Name Mass (MeV) Decay Lifetime Λ 1116 Nπ s Ξ 0, Ξ -, 1320 Λπ s Σ +,Σ Nπ s Σ Λ s (EM) Decay time characteristic from weak interaction Particles stable wrt. strong/em coupling Conserved quantum number : strangeness 5

6 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

7 Electroweak lagrangian OK for leptons What happens for quarks? 7

8 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

9 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

10 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

11 Naive estimation of C From pion and kaon lifetimes τ π = s τ K = s u d u s + K + gcos gsin W + W + tan 2 θ C = 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= cosθ C = μ 11

12 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 = 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

13 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 = 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

14 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

15 V CKM = V ud V us V ub V cd V cs V cb = V td V ts V tb CKM matrix ± ± ± First approximation : Diagonal matrix V CKM = 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 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

16 PART 2 Oscillations and CP Violation 16

17 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

18 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

19 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 : cos2φ 1 cos2φ Experimentally : η π 0 = 1 + = = 1 2 2, η = 1, η = 1 19

20 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

21 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

22 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 K ε 2 ε =

23 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 m 2 Γ = γ 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

24 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

25 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

26 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

27 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 Γ M Γ Im(Γ12 M 12 ) 2 Im(Γ12 M 12 ) Complex mass matrix induces CP-violation 27

28 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

29 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

30 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

31 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

32 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

33 PART 3 Top quark and electroweak physics 33

34 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

35 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

36 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

37 W helicity in top decays (1) Longitudinal W F 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

38 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

39 ATLAS results 1fb -1 The Model stays boringly Standard 39

40 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 % CL 40

41 Single top Only t-channel has been clearly (>5σ) seen at Tevatron and LHC. First 3σ evidence for tw (ATLAS) 41

42 Direct V tb measurement All 3 diagrams feature 1Wtb vertex σ V tb ² 42

43 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