Elementary Particles I. 4 Weak Interaction

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1 Elementary Particles I 4 Weak Interaction

2 Electroweak Interaction Standard Model: Electromagnetic and Weak Interaction unified into Electroweak Energy scale where unification is evident: E ~ M W, M Z ~ 100 GeV At lower energies: Can still find tiny traces of the unification (Electroweak interference, Parity violation in atomic processes,...) Electroweak interaction split into two, almost not interfering, effective interactions: Electromagnetic Non fundamental, useful low energy approximations Weak Spring 01 E.Menichetti - Universita' di Torino

3 The Weak Interaction Compare: Strong interaction All quarks Electromagnetic interaction All quarks + Charged Leptons Weak interaction All quarks + All leptons Large variety of phenomena Classify weak processes into 3 types: Leptonic Semileptonic Nonleptonic + + µ e + ν + ν, ν + e ν + e µ e e e π µ + ν, τ ρ + ν K µ τ π + π, Λ n+ π Spring 01 E.Menichetti - Universita' di Torino 3

4 Lost Symmetries Many violations in weak processes: Space Parity (large) Charge Parity (large) CP (very small) T (very small) Flavor conservation (Isospin, S,C,B,T) (larger + smaller) Lepton numbers (?) (neutrino oscillations) Spring 01 E.Menichetti - Universita' di Torino 4

5 Fall of Parity - I Discovery of parity non conservation: Originated by the so-called τ θ puzzle Take K decays: Weak process (S violation) Observed decay modes (among many): K K ± ± 0 π π BR = π π π BR = ± ± ± Observe: 1. % 5.6 % P K =-1, as measured in strong processes P K =?, as measured by its decays Spring 01 E.Menichetti - Universita' di Torino 5

6 Fall of Parity - II Consider parity of the final states: l ( )( )( ) ( 1)( 1)( 1) ( 1) Pππ = =+ 1 l= 0 because J = 0, J = 0 Pπππ = P = P J = 0= L L L = L K orb Lππ ( ) ( ) Pπππ = 1 orb ππ π ππ π P = =+ 1 π L??? different particles, same mass, opposite parity? orb K π Lee & Yang suggestion: Parity is violated in weak processes Spring 01 E.Menichetti - Universita' di Torino 6

7 Fall of Parity - III Parity violation discovered almost simultaneously in 3 experiments First : Beta decay (Wu et al.) Others: π µ decay (Garwin et al., Friedman et al.) (see before) Interesting question: How does parity violation manifest itself? Breaking of parity selection rules Interference between even/odd amplitudes Asymmetries Non-zero value of parity-odd observables Spring 01 E.Menichetti - Universita' di Torino 7

8 Fall of Parity IV Co Ni + e + ν β * - e If weak interaction is parity invariant, Otherwise: ( θ) Ampl( π θ) Ampl = - Expect direction β anisotropy decay: Weak process P Require nuclear polarization: For an unpolarized sample, by averaging over J z-projections any possible anisotropy is washed out Spring 01 E.Menichetti - Universita' di Torino 8

9 Fall of Parity V Cold finger Spring 01 E.Menichetti - Universita' di Torino 9

10 Fall of Parity VI To measure nuclear polarization: γ counter Electric quadrupole transition γ counter Spring 01 E.Menichetti - Universita' di Torino 10

11 Fall of Parity VII Spring 01 E.Menichetti - Universita' di Torino 11

12 Fall of Parity - VIII + π µ + + ν P ( ) µ µ µ µ µ µ U long σµ pµ Pµ = = 0 if parity is a good symmetry p µ + + e + ν + ν P ( ) µ e µ e µ e U σµ pe = 0 if parity is a good symmetry pe If parity is violated: + + π µ + ν µ Expect µ polarization along p µ µ e + ν + νe Expect e direction correlated with s + In order to detect e correlation: µ spin precession in B µ σ p σ p = σ p µ σ p σ p = σ p µ e Pseudoscalar observable Pseudoscalar observable µ µ Spring 01 E.Menichetti - Universita' di Torino 1

13 Fall of Parity - IX Immediate conclusion: C-parity is also violated Indeed, it can be shown: i( β+ π ) ( ) * iα iβ iα iβ i( β+ π ) iβ iπ * ( SP) * A= Scalar+ Pseudoscalar A = S+ P = S + P + Re SP i CPT OK α If S S e iα, by taking e = e iβ C OK P P e SP = S e P e = S P e e = S P e e = S P e Re = 0 Interference term = 0 Asymmetry=0 Since asymmetries are observed, C must be KO Spring 01 E.Menichetti - Universita' di Torino 13

14 Beta Decay - I Most common weak process in ordinary matter 3 nucleon decays : n p+ e + v + p n+ e + v e + p n+ v e e e Allowed for free neutrons Energetically forbidden for free protons Atomic electron capture, usually from a K-shell (K-capture) Both β - and β + are observed for nucleons bound in a nucleus (, ) (, 1) A Z A Z+ + e + v (, ) (, 1) + A Z A Z + e + v ( ) ( ) e + A, Z A, Z 1+ v K - Capture e e e Reminder: When found in a bound state, particles are off-mass shell β β + Spring 01 E.Menichetti - Universita' di Torino 14

15 Beta Decay - II Energy scale ~ few MeV Small energy released to the pair eν eν orbital angular momentum = 0 Allowed Most frequent = 1,,.. Forbidden Rare (long lifetime) Allowed transitions: J eν 0 singlet = 1 1 = 1 triplet 0, J 0 Fermi J = 1, 0, 1 Gamow-Teller 3 nucleus= J3= ± Spring 01 E.Menichetti - Universita' di Torino 15

16 Beta Decay - III Examples: O N + e + ν e J= 0 J= 0 J= He Li + e + ν e J = 0 J= 1 J = n p+ e + ν e J= 1 J= 1 J= 0,1 pure Fermi pure Gamow-Teller mixed Fermi/Gamow-Teller Spring 01 E.Menichetti - Universita' di Torino 16

17 Beta Decay - IV Take EM interaction as a model: EM µ µ 1 Hint = j Aµ j( ) j ( ) for interacting currents a bµ q Fermi guess: Without introducing any intermediate particle, current-current interaction: H j j W int ( a) ( b) j (a), j (b) transition currents for leptons, nucleons Spring 01 E.Menichetti - Universita' di Torino 17

18 Beta Decay - V Observe: Sticking for a moment to parity conservation, any current*current product which is a Lorentz scalar is acceptable for H I. So we are free to guess different forms for the weak current j( ) ψ finγψin Operator Γ fixes the Lorentz structure of the current a Transitions involve charge variation Charged currents Spring 01 E.Menichetti - Universita' di Torino 18

19 Beta Decay - VI Fermi s original model: Γ=γ µ Pure vector current 1 γ σ γγ γ In general, Γ can be any of the set: Γ Γ Γ Γ Γ ψψ µ ψγψ µν ψσ ψ 5 µ ψγγψ 5 ψγψ scalar S vector V tensor T axial vector A pseudoscalar P µ µν 5 µ Most general form: i i Hint= Ci ( ψpγiψn)( ψeγ ψν) + ( ψnγiψp)( ψνγψe) i= S, V, T, A, P = herm. conj. Hermitian conjugate required in order to account for processes involving antiparticles Rely on experiment to investigate the Lorentz structure Spring 01 E.Menichetti - Universita' di Torino 19

20 Beta Decay - VII Non-relativistic limit of the different nucleon currents S 1 µ =0 χχ p n V γ µ µ = 1,,3 0 µ =0, ν 0 T σ, 0 0 µν µν= µν, = 1,,3 χpσχ µ =0 0 A γγ µ 5 µ = 1,,3 χ pσχn P γ 0 5 Conclude: χχ p n P not relevant for β-decay S,V do not change nucleon spin OK for Fermi T,A do change nucleon spin OK for Gamow-Teller n Spring 01 E.Menichetti - Universita' di Torino 0

21 Beta Decay - VIII Attempts to understand which terms are present in the interaction Pure Fermi : S and/or V Pure Gamow-Teller: T and/or A In both cases: If both terms are present, expect a distortion of the electron energy spectrum (Fierz interference) Not observed Fermi: Either S or V, Gamow-Teller: Either T or A Look for more indicators Spring 01 E.Menichetti - Universita' di Torino 1

22 Beta Decay IX Spring 01 E.Menichetti - Universita' di Torino

23 Beta Decay - X Angular correlation electron-neutrino. Expect: dn d cosθ = const( 1+ λβ cos θ), λ = S V T A Cannot observe neutrino Observe recoiling nucleus instead Many experiments made : Difficult, inconclusive, sometimes wrong, leading to mistakenly guess S & T Solution finally found after the discovery of parity non conservation, by ignoring (wrong) experimental data Spring 01 E.Menichetti - Universita' di Torino 3

24 Beta Decay - XI To yield parity violation, H must include both scalar and pseudo-scalar terms. Indeed, for any matrix element between initial and final states: f S+ P i = f S i + f P i + Parity f S i f P i ( ) ( ) f S+ P i f S i + f P i + f S i f P i = f S i + f P i f S i f P i * * * By allowing for parity non conservation, can write down: i i 5 Hint= Ci( ψpγiψn)( ψeγ ψν) + Ci '( ψpγiψn)( ψeγγψν) Ci, Ci ' 'constants' i= S, V, T, A S P + Hermitian conjugate always understood Spring 01 E.Menichetti - Universita' di Torino 4

25 Beta Decay - XII ( ) ( ) Actually C= C q, C ' = C ' q Weak form factors q i i i i But: 0 for β decay Constants γ 5 equivalently inserted in the nucleon current No difference in full operator: Just a re-labeling of C,C Taking as an example V,A terms, either: V µ µ 5 ( γ )( γ µ ν ) A ( γ γ )( γ µ γ 5ν ) C p n e + C p n e + µ µ 5 + CV '( pγ n)( eγ µ γ 5ν ) + CA '( pγ γ n) eγ µ γ 5 γ 5ν = 1 Or: V µ µ 5 ( γ )( γ µ ν ) A ( γ γ )( γ µ γ 5ν ) = C p n e + C p n e + + CV ' p n e + C p n e = 1 µ µ 5 5 ( γ γ 5 )( γ µ ν ) A ' γ γ γ ( γ µ γ 5ν ) Spring 01 E.Menichetti - Universita' di Torino 5

26 Beta Decay - XIII Redefine constants by extracting (G F : Fermi constant) G F i C ' i 5 H int= Ci( ψp iψ n) ψ e 1 γ ψ Γ ν Γ + =,,, C Time reversal invariance: C i, C i real In order to investigate the form of lepton current: Measurement of the lepton longitudinal polarization Reminder: ( ) = σ p ( ) = 0, T non-invariant: ( ) ( ) = ( ) P lept lept ˆ lept Long. Polarization = Average Helicity L l l P lept T σ p p σ p p σ p p e e ν e e ν e e ν T G F i S V T A i Spring 01 E.Menichetti - Universita' di Torino 6

27 Helicity/Chirality - I With reference to Dirac equation: γ , σ =, γ Dirac representation 0 1 γ= = σ Σ 0 σ S= Σ= = γ γ = γ 0 γ α σ α 0 5 5, Spin operator Σ p Λ= Helicity operator p ( + ) ( + ) Λ u =+ u Helicity eigenstates ( ) ( ) Λ u = u 1±Λ P ± = Projection operators onto helicity eigenstates Spring 01 E.Menichetti - Universita' di Torino 7

28 Helicity/Chirality - II Projectors, indeed: P P Λ 1+Λ 1 = = 1 +Λ+Λ+Λ 4 ( Σ p) ( ) 1 1+Λ Λ = = 1 P P + + = ( 1+ Λ+ 1 ) = = P+, P P = P P P p 4 1+Λ 1 Λ 1 = = ( 1 +Λ Λ Λ ) = 0 = P P Λ 1+Λ 1= + = P+ P 1u= ( P + P) u= u 5 Σ p 0 5 p α p 5 1± α pˆ γ Λ= = γ γγ = γ P± = p α p p u Spring 01 E.Menichetti - Universita' di Torino 8

29 Helicity/Chirality - III γ 5 α p= E βm E 1 m β Λ= γ γ p E m P ± Chirality operator γ 1+ γ PL=, PR= Projectors onto chirality eigenstates PL u= ul 1u= ( PL+ PR) u= ul+ ur PR u= ur A very important limit: ±Λ 1± γ = = P E m R, L For high energy, or massless, particles: Helicity projectors Chirality projectors Spring 01 E.Menichetti - Universita' di Torino 9

30 Helicity/Chirality - IV ( α p β ) Eu= + m u φ u =, φχ, components spinors χ σ α=, β= Dirac matrices in chiral representation 0 σ 1 0 ( σ p) ( σ p) Eφ= φ+ mχ Eχ= χ+ mφ ( σ p) ( σ p) φ E p, m= 0 ( σ p ) χ ( σ p) φ= φ Eφ= = φχ, Helicity eigenstates Eχ= χ= χ E = p Spring 01 E.Menichetti - Universita' di Torino 30

31 Helicity/Chirality - V States with definite value of chirality, massive or massless particles u u u u L R L R Particle Antiparticle = ( 1 γ) u vl= ( 1+ γ) v ( 1 5 = + γ) u vr= ( 1 γ) v = u ( 1 + γ) vl= v ( 1 γ) = u ( 1 γ) vr= v ( 1+ γ) Is it true? Try one example: γ ul= γ ( 1 γ) u= ( γ 1) u= ( 1 γ) u= u L OK Spring 01 E.Menichetti - Universita' di Torino 31

32 Helicity/Chirality - VI For chiral states: 1 Massless particle: ul H = ur H =+ 1 Helicity defined Full longitudinal polarization ul H β Massive particle: = ur H =+ β Helicity undefined, superposition of ±1 eigenstates Massless particles: Helicity is Lorentz invariant Massive particles: Helicity is frame dependent Spring 01 E.Menichetti - Universita' di Torino 3

33 Lepton Helicity - I Neutrino can be be either R or L: Must rely on experiment to decide Goldhaber experiment: -steps decay * Eu + e Sm + ν e K J = 0 J = 1 J = 1 J = 1 capture 15 * 15 Sm Sm + γ J = 1 J = 0 15 * v e 15 Sm γ Spin Sm 15 Eu 15 * ( ) ( ) H Sm = H ν e Spring 01 E.Menichetti - Universita' di Torino 33

34 Lepton Helicity - II γ emitted along momentum do not contribute orbital angular momentum: 15 Sm* with s z = 0 cannot yield a collinear γ: ( γ) Would yield a non existing γ with H = 0 =± 15 * Collinear γ only from Sm with sz 1 For collinear photons: 15 * ( γ) = ( ) = ( ν) H H Sm H e Spring 01 E.Menichetti - Universita' di Torino 34

35 Lepton Helicity - III How to select collinear photons? 15 Choose a Sm target: γ Sm Sm Sm * Resonant scattering: γ energy must be just larger than E in order to account for nuclear recoil Only available from collinear photons because includes a fraction of the decaying nucleus kinetic energy γ ( ) Measure H γ by absorbing γ in magnetized iron ( ) Result : H ν = 1 e Spring 01 E.Menichetti - Universita' di Torino 35

36 Lepton Helicity - IV Electron helicity: Method: Rotate e momentum by 90 0 by means of an electrostatic field Spin undeflected for non-relativistic e Longitudinal polarization becomes transverse Mott scattering sensitive to P H = β Average helicity Longitudinal polarization Spring 01 E.Menichetti - Universita' di Torino 36

37 V A - I Now closing on the analysis: H int G F i Ci ' 5 = C( ψ ψ ) ψ 1 γ ψ Γ Γ + ν i p i n e i= V, A Ci Neutrino helicity = - 1 yields lepton current = V - A C ' + = = C ( ) i γ ν 1 ν Ci ' C ψ γ ψ i G H = C ( ψγψ) ψγ ( γ) ψ + C GF C µ 5 5 V( p n) ( e ( 1 ) ) C µ = ψγψ µ ψγ γ ψν A( ψγγψ p µ 5 n) ( ψγ e ( 1 γ) ψ ν) GF C 5 V( p n) C µ = ψγψ µ A( ψγγψ p µ 5 n) ( ψγ e ( 1 γ) ψν) i ( 1 5 ) = µ γ γ µ 5 µ 5 5 ( 1 ) ( ψγγψ) ( ψγ γ ( 1 γ) ψ) F int V p µ n e ν A p µ 5 n e ν Spring 01 E.Menichetti - Universita' di Torino 37

38 V A - II Therefore: G µ 5 H = C ( ψγψ) C ( ψγγψ) ( 1 ) ψγ γ ψ G C H = C ψγ 1 γ ψ ψγ 1 γ ψ ( ) F int V p µ n A p µ 5 n e ν µ 5 ( ( ) ) F A int V p 5 n e µ ν C V Fermi s theory confirmed, only adding parity violation Parity violation is maximal: Vector = Axial vector Parity violation originating from V/A interference ( Strictly quantum effect: No classical counterpart!) Spring 01 E.Menichetti - Universita' di Torino 38

39 V A - III Observe: H 5 ( 1 γ) 5 ( 1 γ) G C = ψγ 1 γ ψ ψγ ψ F A µ int p 5 n e µ ν C V γ 1 γ Projection operator = 5 G ( 1 ) F C γ A µ H int ψγ p µ 1 γ 5 ψ = n ψγ e ψ C ν V 5 5 C A 1+ γ µ 1 γ Hint= GF ψγ p µ 1 γ 5 ψ n ψ e γ ψ ν C V Lepton current written as pure vector between chiral parts of ν,e states The (charged current) weak interaction is just the same as the e.m. current, except operates between chiral states with different charge Spring 01 E.Menichetti - Universita' di Torino 39

40 V A - IV V-A Theory: Neutrino has very peculiar properties 1) Only left-handed neutrinos (and right- handed antineutrinos) exist 4 component Dirac spinor not required «Two component» neutrino theory ) Consider P and C operations on neutrino states: U P L P R But: ν do not exist U R C L C L But: ν do not exist U U ν = η ν ν = η ν L ν = ηη ν P C L P C R OK CP symmetry apparently good for weak interactions (??) Spring 01 E.Menichetti - Universita' di Torino 40

41 V A - V Recent, indirect yet convincing evidence that neutrinos have mass (More and more direct, indeed ) What about V-A? Not so many changes in the Standard Model: If neutrino have mass, they are no longer pure left-handed particles Right-handed neutrinos exist Separation into +1 and -1 helicity states is frame dependent Separation into +1 and -1 chirality states is frame independent Only the L-chirality states (R- for antineutrinos) contribute to charged current Spring 01 E.Menichetti - Universita' di Torino 41

42 Muon Decay - I Consider muon weak interactions: + + µ e + ν + ν, µ e + ν + ν µ decay µ + p n+ ν µ µ e µ µ decay purely leptonic: Guess current-current, V-A µ capture, involves nucleon current for both electron and muon charged currents Compute: µ Lifetime Electron energy spectrum Electron longitudinal polarization e Spring 01 E.Menichetti - Universita' di Torino 4

43 Muon Decay - II + + Consider decay of a polarized muon: µ e + ν + ν, µ e + ν + ν P conservation: Predict dγ d ( cosθ) d( cosθ) 1 ξ 1 ξ ± ± Γ± 1 cosθ = Γ ± 1+ cosθ 3 3 ξ = 0 ± Experiment: ξ = ξ = 1 + P is violated θ = dγ ± ± π θ µ e µ e Spring E.Menichetti - Universita' di Torino 43

44 Muon Decay - III ± C : µ etc µ etc dγ 1 ξ ± ± = Γ± 1 cosθ d( cosθ) 3 1 Γ ± =, Γ + =Γ τ ± C conservation: Predict ξ = ξ Experiment: ξ = ξ = 1 + C is violated CP : d dγ dγ + ( cosθ) d( cosθ) θ = ξ = ξ + Experiment: OK CP is conserved π θ + Spring E.Menichetti - Universita' di Torino 44

45 Muon Decay - IV Spring 01 E.Menichetti - Universita' di Torino 45

46 Muon Decay - V Spring 01 E.Menichetti - Universita' di Torino 46

47 Muon Decay - VI Spring 01 E.Menichetti - Universita' di Torino 47

48 Muon Decay - VII Spring 01 E.Menichetti - Universita' di Torino 48

49 Muon Decay - VIII τ 1 = Lifetime and total rate Γ E max dγ 3G m 19 Γ= de = = de 1 8 E min 5 3 F µ π τ 3 5 GFmµ ( π) Extract G F from measured lifetime: G ( β ) ( µ ) F = 0.98 G Almost identical! % difference?? F Spring 01 E.Menichetti - Universita' di Torino 49

50 Muon Decay - IX Electron spectrum from µ decay used as calibration at SuperKamiokande Allows for absolute calibration of Cerenkov light signal vs. energy 41 m 39 m Water Cerenkov t pure water ( ) 1100 photomultipliers 50 cm! Spring 01 E.Menichetti - Universita' di Torino 50

51 Michel Parameter - I Detailed analysis: Differential decay rate depending on several parameters Alternative structures of charged current cast into different parameter sets Most important: Michel parameter ρ Electron differential spectrum determined by ρ for unpolarized muon G m 5 µ x 3( 1 x) ρ( 4x 3 ), x E e 4 π µ dp = + = dωdx 19 3 m V-A theory predicts ρ = ¾ Experimental result: ± Electron angular distribution for polarized muon decay: dp 1 1 = 1 ξp cos θ, P muon polarization dω 4π 3 V - A: ξ=+ 1 Experiment OK Spring 01 E.Menichetti - Universita' di Torino 51

52 Michel Parameter - II Extend to τ leptonic decays: + + τ e + ν + ν, τ e + ν + ν τ e + + τ µ + ν + ν, τ µ + ν + ν τ µ τ µ τ has many more decay channels open into quark-antiquark pairs τ e Leptonic decays: Similar to muon Allow for checking of: V A Lorentz structure Universality of lepton coupling Spring 01 E.Menichetti - Universita' di Torino 5

53 Michel Parameter - III Consider τ decays: Many modes, including Leptonic Semileptonic ± ± ± τ µ + ν / ν + ν / ν τ Hadrons+ ν / ν τ e + ν / ν + ν / ν ± ± e µ µ τ τ τ τ e τ τ A simple question: What is the τ charged current? Investigations at LEP: e + e Z τ + τ Conclusion: Current is V A ρ τ 0.747± 0.04 e mode = 0.776± µ mode Spring 01 E.Menichetti - Universita' di Torino 53

54 Neutrino Beams & Detectors - I Derived from -body π,k decay ± ± π µ + ν, ν K µ µ µ + ν, ν ± ± µ µ Spring 01 E.Menichetti - Universita' di Torino 54

55 Neutrino Beams & Detectors - II Gargamelle - Muonless BEBC Muon + Hadronic shower Spring 01 E.Menichetti - Universita' di Torino 55

56 Neutrino Beams & Detectors - III CDHS at CERN SPS Scintillator Drift chamber Iron toroid Spring 01 E.Menichetti - Universita' di Torino 56

57 Neutrino Interactions - I Inverse muon decay: Charged current process ν µ + e µ + ν e * * F 5 TfiT µ fi u() 3γ ( 1 γ) u() 1 u() 3γν( 1 γ5) u() 1 spin spin * ν 5 u( 4) γµ ( 1 γ5) u( ) u( 4) γ ( 1 γ) u( ) * ( ) Γ ( ) ( ) Γ ( ) = Γ ( + ) Γ ( + ) 1 1 b b a a spin spin spin F ( )( ) T = 64G p p p p fi fi G = u a u b u a u b Tr p m p m T m 4 = 56GF E µ 1 E Spring 01 E.Menichetti - Universita' di Torino 57

58 Neutrino Interactions - II dσ G m F * µ = E 1 * dω π E σ= m GF E * µ * 1,, * E CM energy of e v 4 π E * E meν σ Eν at high energy Spring 01 E.Menichetti - Universita' di Torino 58

59 Neutrino Interactions - III Spring 01 E.Menichetti - Universita' di Torino 59

60 Neutrino Interactions - IV NB These cross sections are only approximate, in that neutral current contribution in neglected Spring 01 E.Menichetti - Universita' di Torino 60

61 Hadronic Charged Currents - I As observed in β-decay of several baryons: Nucleon current # V A, rather V - αa Found ~ the same structure for lepton and nucleon current ( 5 ) µ ψγ 1 γ ψ Pure V-A e ψγ p µ C 1 C A V ν γ 5 ψ n V: identical coupling, A: modified by strong interaction Consider β decay of O 14 pure Fermi Call this the β-decay Fermi constant 0 Λ - Σ + G F = 1 10 M 5 p CA Measured value of for β decay of various baryons: C n Ξ 0.5 V Spring 01 E.Menichetti - Universita' di Torino 61

62 Hadronic Charged Currents - II Extend V-A to neutrino-nucleon scattering ν + N µ + µ + ν + N µ + µ X X Somewhat similar to e-n, µ-n deep inelastic scattering Modeling similar to DIS: Parton elastic scattering Deep ineastic neutrino scattering reveals the same structure as charged lepton DIS More information: Charged current sensitive to parton charge sign Can separate quark/antiquark contribution Spring 01 E.Menichetti - Universita' di Torino 6

63 Hadronic Charged Currents - III Spring 01 E.Menichetti - Universita' di Torino 63

64 Hadronic Charged Currents - IV As for leptonic charged currents: Cross section cannot be strictly proportional to E n Divergence at high energy! Indeed, unitarity bound is violated around E n ~ 300 GeV 4π 4π σ = * k E Unitarity bound for S-Wave scattering Radiative corrections to Fermi s theory divergent: No renormalization procedure available Fermi theory is non renormalizable Radical fix to the current*current model required: For both lepton and nucleon currents, exchange of a (heavy, charged) boson W ± Spring 01 E.Menichetti - Universita' di Torino 64

65 Semileptonic Decays: π, K - I π µ + ν π + ν µ, e e GF µ 5 Tfi= u() 3γ ( 1 γ) v( ) Fµ F : equivalent of 'current' for the qq bound state F µ = f p µ π µ 4-momentum is the only 4-vector available Spring 01 E.Menichetti - Universita' di Torino 65

66 Semileptonic Decays : π, K - II Obtain: Γ Γ π l G 3 Fml m ml 8mπ Γ = () e ( µ ) f ( π e) ( ) me m m = = m m m µ π µ ( π ) Quite surprising: Phase space factor is much larger for e! But: -4 _ µ - ν µ e - _ ν e Spring 01 E.Menichetti - Universita' di Torino 66

67 Semileptonic Decays : π, K - III Chirality rule: ν is only L, ν is only R - µ, e from π, K decay forced to R + + µ, e from π, K decay forced to L by angular momentum conservation: - ( µ e ) + ( µ + e ) H, = + 1 'Wrong' helicity H, = 1 e: Fully relativistic A( wrong H ) 0 µ : Not fully relativistic A( wrong H ) substantial Spring 01 E.Menichetti - Universita' di Torino 67

68 Universality: Quarks Semileptonic and non leptonic processes understood in terms of quarks Basically similar coupling to leptonic charged currents: Picture is slightly more complicated, however Fundamental question: Is the quark coupling identical to the lepton one? Spring 01 E.Menichetti - Universita' di Torino 68

69 Cabibbo Angle - I Consider charged current of leptons: Very natural to group charged and neutral leptons into doublets, or families ν e ν µ ν τ e µ τ Within each doublet, charged current transitions can be thought as due to emission/absorption of W ± bosons, similar to (neutral) e.m. current transitions W W ν W + e + e W Similar for nd, 3rd family Charged intermediate bosons W ± analog to photon Spring 01 E.Menichetti - Universita' di Torino 69

70 Cabibbo Angle - II Would seem natural to extend this scheme to quarks u W u W d s W d W + + Unfortunately, our scheme cannot work: a) Parallelism quark-lepton is incomplete with 4 leptons and only 3 quarks b) Does not account for strangeness violating processes Spring 01 E.Menichetti - Universita' di Torino 70

71 Cabibbo Angle - III Cabibbo s very ingenious idea: Quark flavor eigenstates (i.e., quark model eigenstates) are not to be identified with quark weak currents Weak currents are mixtures of different flavors By universal convention, mixing is assumed between d and s quarks: d ' = αd + β s s ' = γ d + δ s d ' = cosθcd + sinθcs By unitarity: s ' = sinθcd + cosθcs Spring 01 E.Menichetti - Universita' di Torino 71

72 Cabibbo Angle - IV Mixing matrix: d ' cosθc sinθ = s ' sinθ cosθ C C C d s θ c Cabibbo's angle This explain many things. Just one example: Get the angle from β decay (Remember that % difference..) G ( β ) ( ) F = 0.975G µ F θ 13 c 0 Spring 01 E.Menichetti - Universita' di Torino 7

73 Cabibbo Angle - V Now assume for leptonic π, K decays (very simply!) f f K π = f sinθ C = f cosθ C ( K l νl) ( π ν) ( ) ( ) ( K l) ( π l) Γ + m m m = tan θc Γ l+ l m m m 3 π 3 K Γ( K l+ νl) teo l= µ = Γ( π l+ νl) teo l= e Compare to experiment: ( ) ( ) exp l= µ exp l= e Amazingly close! Spring 01 E.Menichetti - Universita' di Torino 73

74 GIM - I Besides the many puzzles finally explained by Cabibbo, a few are left unexplained Most relevant: 0 K µµ + strongly suppressed nd order weak process, still quite easy to compute Expect rate higher by orders of magnitude BR meas (K 0 µµ)=(6.87±0.11)10-9 Compare charged decay: BR ( µν ) = 63.5 % meas K µ Spring 01 E.Menichetti - Universita' di Torino 74

75 Spring 01 E.Menichetti - Universita' di Torino 75 GIM - II cos sin ' sin cos ' C C C C u u u d s d d c c c d s s s θ θ θ θ + + Glashow, Iliopoulos and Maiani: There exists a fourth quark, call it c like charm Full symmetry restored between lepton-quark families Two weak doublets:

76 GIM - III Then expect a second amplitude for K 0 decay Total amplitude: Sum of two A A 1 sinθc cosθ c A + A sinθc cosθ c 1 0 Total amplitude not exactly 0 because From observed rate predict m 1 c m c mu GeV Leading to November Revolution: J/ψ discovery Spring 01 E.Menichetti - Universita' di Torino 76

77 CKM Extend the idea to 3 families: From Cabibbo s angle to Cabibbo-Kobayashi-Maskawa matrix From unitarity: 3 mixing angles 1 complex phase This can account for CP violation Experimental values: Almost diagonal Heavy quarks even more diagonal Spring 01 E.Menichetti - Universita' di Torino 77

78 Beyond Fermi s Theory As anticipated: Current-Current must be a low energy effective theory: Low energy approximation of a more general theory Replace contact interaction (current-current) by boson exchange: Modeled after the electromagnetic interaction Exchanged particle must be Charged (Charged current ±) Chiral (Only coupled to left chiral parts: Parity violation) Heavy (Fermi s point-like interaction OK at low energy) Spring 01 E.Menichetti - Universita' di Torino 78

79 Remark Spring 01 E.Menichetti - Universita' di Torino 79

80 Weak Interaction - I Just listing some important properties A) Quarks and leptons both interact through the exchange of vector particles Spring 01 E.Menichetti - Universita' di Torino 80

81 Weak Interaction - II B) Exchanged vector bosons are (very) massive C) Interaction form derived by a non-abelian gauge symmetry + Special mechanism giving mass to some of the gauge fields D) Non-Abelian vertexes Spring 01 E.Menichetti - Universita' di Torino 81

82 Weak Interaction - III Weak charged current: ( 1 γ 5 ) µ µ j = u fγ ui µ 1 µ jv= u fγ ui Vector µ 1 µ 5 ja= u fγ γ ui Axial Compare to electromagnetic current: µ µ j = uγ u Spring 01 E.Menichetti - Universita' di Torino 8

83 Weak Interaction - IV Apparently, totally different. But, as anticipated: ( 1 γ 5 ) = ( 1 γ 5 + 1) = ( γ 5 ) = ( 1 γ 5 ) ( 1 γ 5 ) ( 1 γ 5 ) ( 1 γ 5 ) = = 4 ( 1 γ 5 ) ( 1 γ 5 ) ( 1+ γ 5 ) ( 1 γ 5 ) µ µ µ u fγ ui = u fγ ui= u f γ ui 5 ( 1 γ) µ uγ u= u f i fl µ uil Same form, but involving only LEFT chiral states γ u fl u il Spring 01 E.Menichetti - Universita' di Torino 83

84 Weak Interaction - V em jµ = eγµ e 1 γ 1 γ e e+ e= el+ er Therefore: Because: ( ) ( ) = γ = + γ + = γ + γ em jµ e µ e el er µ el er el µ el er µ er 1+ γ 1+ γ 1 γ 1+ γ γ = γ = γ = el µ er e µ e e µ e 1 γ5 1+ γ 5 = 0 Projectors 'orthogonal' The bottom line: Weak (charged) and Electromagnetic currents: Same Lorentz structure (vector), but LL vs. LL+RR Spring 01 E.Menichetti - Universita' di Torino 84

85 Weak Interaction - VI W propagator: µν µ ν q MW µν µ ν W µν W q MW MW 1 () g µ µν 1 fi W f γ 1 γ i 1 f γν γ5 i M W 1 µ () 1 ( 4 ) Tfi i GF j jµ 8 g α Charged current coupling constant W W g q q M i g q q M g q M i i q W -independent T g u ( ) u () i u ( ) ( ) u ( ) G F g W = 8 M W Fermi constant Spring 01 E.Menichetti - Universita' di Torino 85

86 Weak Interaction - VII Spring 01 E.Menichetti - Universita' di Torino 86

87 Neutral Currents - I Charged intermediate boson W ± does not fix everything.. Typical issue left unsolved: ν+ ν W + W + Amplitude still divergent due to longitudinal W contribution.. Similar to QED process + e + e γ+ γ In QED: Renormalization possible due to gauge invariance Would like to upgrade charged current interaction model to a gauge theory to get finite, renormalized amplitudes Charged current weak interaction to be understood as a gauge interaction W ± as gauge fields Spring 01 E.Menichetti - Universita' di Torino 87

88 Neutral Currents - II fields: Gauge group must be non-abelian Massive field: Gauge invariance apparently impossible Nevertheless: Assume some funny mechanism can preserve gauge invariance with a massive field ( Bold, but true) Try SU() as gauge group: Predict a triplet of gauge fields) Neutral current should exist Neutral gauge field must be massive Spring 01 E.Menichetti - Universita' di Torino 88

89 Neutral Currents - III Spring 01 E.Menichetti - Universita' di Torino 89

90 Neutral Currents - IV As a result of the weak-electromagnetic unification, neutral currents are different from charged Lorentz structure not V A i ig g Z W γ µ γ µ 5 ( 1 γ) f f 5 ( CV CAγ) Charged Neutral Coupling Fermion V ν, ν, ν e µ τ C e, µτ, 1 + sin θ 1 u, c, t sin θ + 1 W,, 1 + 3sin θw 1 d s b W C A θ W new fundamental constant What about interaction strength? Spring 01 E.Menichetti - Universita' di Torino 90

91 Neutral Currents - V Tight relationship between weak and electromagnetic interactions Coupling constants: g g w z α= e e = sinθ W e = sinθ cosθ W W Charged, neutral and electromagnetic couplings fixed by universal constants: e : Elementary charge θ W : Weinberg angle, new fundamental constant Spring 01 E.Menichetti - Universita' di Torino 91

92 Neutral Currents - VI Expect to observe typical processes like: ( ν ν) e ( ν ν), +, + e Contributing to elastic scattering e e e e ( νµ, νµ ) e ( νµ, νµ ) + + e, +, + hadron shower New + + hadron shower ( ν ν) N ( ν ν) e e e e ( νµ, νµ ) N ( νµ, νµ ) Spring 01 E.Menichetti - Universita' di Torino 9

93 Discovery of NC: Gargamelle Main problem: Neutron background Observe vertex position along the chamber Exponential: Neutron background λ n int ν int 90 cm Flat: Neutrino signal λ Estimated n background: 9 6 Spring 01 E.Menichetti - Universita' di Torino 93