The weak interaction Part II

The weak interaction Part II Marie-Hélène Schune Achille Stocchi LAL-Orsay IN2P3/CNRS Weak Interaction, An-Najah National University, Nablus, Palestine 1

The K -K system The CKM mechanism Measurements of the unitarity triangle parameters : some examples Weak Interaction, An-Najah National University, Nablus, Palestine 2

The K -K system Remember the strange particles? V Two states : K 1 ππ K 2 πππ Same mass (~ 5 MeV) Very different lifetimes 3 Brookhaven, 1956 M(π) ~ 14 MeV M(K) ~ 5 MeV K 2 lifetime ~ 1 K 1 lifetime due to phase space Weak Interaction, An-Najah National University, Nablus, Palestine 3

CP violation in the K system NB : K 1 = K S and K 2 = K L K = sd CP K = K K = sd not CP eigenstates K = ds K = ds One can build : K K K 1 = 1 ( + ) 2 K 2 = 1 ( K - K ) 2 CP eigenstates K 1 ππ K 2 πππ CP(ππ) = +1 and CP(πππ) = -1 if CP is a good symmetry for the weak interaction : K 2 à ππ Weak Interaction, An-Najah National University, Nablus, Palestine 4

K 1 ππ After some time, pure K 2 beam initial beam K 1 and K 2 Search for the signal of the decay K 2 ππ à far (2 meters) from the production point of the K 1 and K 2? Weak Interaction, An-Najah National University, Nablus, Palestine 5

Cronin& Fitch experiment 1964 charged tracks detector initial beam K 1 and K 2 Weak Interaction, An-Najah National University, Nablus, Palestine 6

signal cosθ = 1 π - background cosθ < 1 π - Two informations : The π + π - invariant mass (m) The opening angle between the two pions in the K center of mass frame θ θ π + π + π not detected signal N(signal) = 45±1 m(π + π - ) HCPSS 217 Heavy Flavours Marie-Hélène Schune 7

1964 R. Turlay was a PhD student J Christenson was a graduate student «The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments.» Today : K 2 ππ A( à ) A( ) K 1 ππ = ( 2.271±.17)1 3.7 % precision! Weak Interaction, An-Najah National University, Nablus, Palestine 8

Experimental observation of CP violation in K decays + Cabibbo angle V CKM Cabibbo-Kobayashi-Maskawa matrix Weak Interaction, An-Najah National University, Nablus, Palestine 9

V CKM Cabibbo-Kobayashi-Maskawa matrix Two different way of seeing the charged interactions among quarks In the basis dealing with mass eigenstates : W W gv ud gv us u d u s Weak interaction eigenstates In the basis where : charged interactions are just between members of the same family and «CKM» is diagonal u W g d Mass eigenstates (flavour or strong interaction eigenstates) W gv ub u b d' Vud Vus Vub d s' = Vcd Vcs Vcb s b' Vtd Vts Vtb b 1

1973 Before the discovery of the 4 th quark Prediction of the 3 rd family # families # angles # reducible phases # irreducible phases n n(n-1)/2 2n-1 n(n+1)/2 (2n-1)=(n-1)(n-2)/2 2 1 3 3 1 4 6 3 V CKM Cabibbo-Kobayashi-Maskawa HCPSS 217 Heavy Flavours Marie-Hélène Schune matrix 11

V ub V ub à CP violation CP One amplitude : no sensitivity on phase ( V ij 2 = V ij 2 ) A 1 source A 1 A 2 B f A 2 12

No prediction on the V ij à they need to be measured à Experimental observations : = HCPSS 217 Heavy Flavours Marie-Hélène Schune 13

3 families 3 angles (θ ij ) and one phase (δ) V ub = 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 c s ij ij = = cosθ sinθ ij ij 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 à Parametrization in power of λ (=sinϑ c ) = s 12 = V us ~.22 ( i ) 2 3 1 λ /2 λ Aλ ρ η 2 2 4 λ 1 λ /2 Aλ + ϑ λ 3 2 Aλ ( 1 ρ iη) Aλ 1 ( ) λ = sinθ c ~.22 A ~.8 ρ ~.2 η ~.35 Weak Interaction, An-Najah National University, Nablus, Palestine 14

Measuring triangles Stay within the 3 families Unitarity of V CKM VV = = 1 à9 relations HCPSS 217 Heavy Flavours Marie-Hélène Schune 15

The non-diagonal elements of the matrix products correspond to 6 triangle equations They all have the same area, proportionnal to the amount of CP violation in the SM HCPSS 217 Heavy Flavours Marie-Hélène Schune 16

the unitarity triangle : = Aλ (1 ρ iη) + Aλ ( ρ + iη) td 2 λ V 3 ud Vub = Aλ ( ρ + iη) (1 ) 2 3 = Aλ cd 3 5 tb cb + + = ub ud cb cd tb td at order λ 5 Basis of the triangle aligned on the real axis, normalized to 1 2 arg VV atan td tb (1 λ / 2) η β = = 1 (1 2 V /2) cdv λ ρ cb 2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd VudV ub η γ = arg = atan VcdV ρ cb α+β+γ= π γ β 2 (1 λ / 2) ρ 1 2 sides ; 3 angles aim : to overconstrain this unitarity triangle precision test of the Standard Model Weak Interaction, An-Najah National University, Nablus, Palestine 17

Measurements of the unitarity triangle parameters : some examples Weak Interaction, An-Najah National University, Nablus, Palestine 18

2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd -1 1 γ β 2 (1 λ / 2) ρ 1 Rates of semileptonic B decays 2 2 ν ν l l b c b u Vcb Vub Conceptually simple, complicated by QCD Weak Interaction, An-Najah National University, Nablus, Palestine 19

The other side : B -B oscillations 2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd γ β 2 (1 λ / 2) ρ 1 Diagrams involving V td or V ts

( The mixing phenomenon Weak Interaction, An-Najah National University, Nablus, Palestine 21

Pairs of self-conjugate mesons that can be transformed to each other via flavour changing weak interaction transitions are: K = sd D = cu B = bd B = d s bs They are flavour eigenstates with definite quark content useful to understand particle production and decay B, B Apart from the flavour eigenstates there are mass eigenstates: eigenstates of the Hamiltonian B L, B H states of definite mass and lifetime They are propagating through space-time B L = p B + q B B H = p B q B Since flavour eigenstates are not mass eigenstates, the flavour eigenstates are mixed with one another as they propagate through space and time 22

Γ, i M HL HL, i t 2 HL, HL, B () t = e B ( t = ) + B B L H = p B + = p B q q B B Time evolution The probability to observe a B at time t if a B was produced at time t= is : ( ) 2 e Γt 2 B H B t = + Δmt (1 cos ) The probability to observe a B at time t if a B was produced at time t= is : ( ) 2 e Γt 2 B H B t = Δmt (1 cos ) This is the mixing phenomenon! N "#$%&'( N %&'( N "#$%&'( + N %&'( ~ cos Δmt Simplified 23 formulae assuming that the two mass eigenstates have the same lifetime and neglecting CP violation (q/p=1)

) Let s come back to the unitarity triangle Weak Interaction, An-Najah National University, Nablus, Palestine 24

Δm can be computed in the Standard Model Weak Interaction, An-Najah National University, Nablus, Palestine 25

The other side : B -B oscillations 2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd -1 1 γ β 2 (1 λ / 2) ρ 1 N "#$%&'( N %&'( N "#$%&'( + N %&'( ~ cos Δmt Δm d V td V tb 2 Weak Interaction, An-Najah National University, Nablus, Palestine

-1 1 Are the two types of measurements compatible? Weak Interaction, An-Najah National University, Nablus, Palestine

Is 2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd γ β 2 (1 λ / 2) ρ 1 in 2 (1 λ / 2) η agreement ub cb ud cd α VV tb cb td cd? with γ β 2 (1 λ / 2) ρ Weak Interaction, An-Najah National University, Nablus, Palestine 28 1

( CP violation Weak Interaction, An-Najah National University, Nablus, Palestine 29

V ub V ub à CP violation CP If you just have one amplitude : no sensitivity on phase ( V ij 2 = V ij 2 ) A 1 source A 1 A 2 B f A 2 3

) Let s come back to the unitarity triangle Weak Interaction, An-Najah National University, Nablus, Palestine 31

the unitarity triangle : + + = ub ud cb cd tb td 2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd γ β 2 (1 λ / 2) ρ 1 VudV ub γ = arg VcdVcb Weak Interaction, An-Najah National University, Nablus, Palestine 32

V us W - b c B - V cb D àkk u u u s K - VudV ub γ = arg VcdVcb B - (KK) D K - b u V ub W - D c àkk B - V cs s K - u u Weak Interaction, An-Najah National University, Nablus, Palestine 33

(KK) D K - CP B - D K - B + D K + B - D π - B + D π + significantly different from! Weak Interaction, An-Najah National University, Nablus, Palestine 34

A lot of decay modes Three different experiments (BaBar, BELLE & LHCb) γ = (7.5 ± 5.7) Weak Interaction, An-Najah National University, Nablus, Palestine 35

2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd γ β 2 (1 λ / 2) ρ 1 Weak Interaction, An-Najah National University, Nablus, Palestine 36

An example of CP induced by the interference between and decay : the β angle B Φ decay f Φ d = Φ mix-2 Φ decay Φ mix B -Φ decay Mixing Decay Weak Interaction, An-Najah National University, Nablus, Palestine 37

= sin(2β) sin(δmt) Pionnered by the B-factories Weak Interaction, An-Najah National University, Nablus, Palestine 38

Is 2 (1 λ / 2) η ub cb ud cd α VV tb cb td cd γ β 2 (1 λ / 2) ρ 1 in 2 (1 λ / 2) η agreement ub cb ud cd α VV tb cb td cd? with γ β 2 (1 λ / 2) ρ Weak Interaction, An-Najah National University, Nablus, Palestine 39 1

Sides and angles measurements in good agreement The CKM model of CP violation has been confirmed At the electroweak scale, the CKM mechanism dominates CP Violation Weak Interaction, An-Najah National University, Nablus, Palestine 4

Anti-matter in cosmic rays No sign of light emission (anti-galaxy ) No sign of anti-nuclei (anti-he 4... ) Searches on-going HCPSS 217 Heavy Flavours Marie-Hélène Schune 41

Anti-matter in the Universe and Big Bang Matter Anti-matter Matter Anti-matter Primordial Universe Today n baryon n antibaryon n : ~6 1?@A The 3 Sakharov conditions(1967) 1. Baryonic number violation: Xàp e - 2. C and CP symmetries violation: Γ(Xàp e - ) Γ(Xàp e + ) 3. To be out of equilibrium: Γ(Xàp e - ) Γ(p e - àx ) HCPSS 217 Heavy Flavours Marie- Hélène Schune 42

Anti-matter in the Universe and Big Bang Matter Anti-matter Matter Anti-matter Primordial Universe Today n baryon n antibaryon n : ~6 1?@A The 3 Sakharov conditions(1967) 1. Baryonic number violation: 2. C and CP symmetries violation: 3. To be out of equilibrium: Xàp e - But the CP violation phase of the SM is orders of magnitude Γ(Xàp e - ) Γ(Xàp too small e + ) Γ(Xàp e - ) Γ(p e - àx ) HCPSS 217 Heavy Flavours Marie- Hélène Schune 43

( Heavy Flavours Weak Interaction, An-Najah National University, Nablus, Palestine 44

u c t d s b Heavy flavours! m t >m W +m b Why not the top quark? The decay m 5 extremely short lifetime Hadronization time ~1-23 s no top hadrons t V tb ~1 Tevatron + LHC : V tb = 1.9±.31 W b [PDG] Phys. Lett. B 181 (157) Weak Interaction, An-Najah National University, Nablus, Palestine 45

Heavy Flavours why? β decay of the neutron Phenomena taking place at ~ 1 GeV reveals physics at the 1 GeV scale M ~ 1 GeV M ~ 1 GeV M ~ 8 GeV An Najah university, Nablus, Palestine, Nov 217 46

The top quark at an e+ e- collider with s=1 GeV in 1987! e + e - ϒ(4S) BB at s = 1.58 GeV Argus Collaboration Phys Lett B 192 p454 Production of coherent BB pairs B D - µ + ν B D - µ + ν! m Δm B.2 # t " GeV c 2.5ps 1 $ & % 2 ps m t >5 GeV First hint of a really large m top! An Najah university, Nablus, Palestine, Nov 217 47

Lepton Flavour Universality tests with B decays In the SM : l + l + l=e, μ or τ W + ν l Z l - R(K)= C EFF C E'' R=1 (at 1-3 ) in the SM Weak Interaction, An-Najah National University, Nablus, Palestine 48

R(K)= C EFF C E'' R(K)= C E FF C E ''. JHEP8 (217) 55 In particle physics there are some rules : 3 σ : evidence 5 σ : observation Weak Interaction, An-Najah National University, Nablus, Palestine 49

3 or 5 σ? 3 σ : probability, of.3 5 σ : probability, of 3x1-7 (1 in 3.5 million) this is the probability to draw the 4 aces in a game of 52 cards in this order : Weak Interaction, An-Najah National University, Nablus, Palestine 5

) Weak Interaction, An-Najah National University, Nablus, Palestine 51

Weak interaction in summary All quarks and leptons are sensitive to the weak interaction M W ~M Z ~1 GeV à short range Extremely weak : (~ 1-8 smaller intensity than the strong interaction at a distance of 1 fm) σ(νp) 1 43 cm 2 E The weak interaction ν ~ 3 MeV violates maximally C and P does not conserve the flavour Exhibits a tiny CP violation The weak and mass eigenstates of quarks are not the same, they are related via V CKM which is a natural source of CP violation Heavy flavours is a privileged way to search for New Physics and weak interaction means also neutrinos which we had very little time to discuss Weak Interaction, An-Najah National University, Nablus, Palestine 52