Lectures on B-physics 19-20 April 2011 Vrije Universiteit Brussel N. Tuning Niels Tuning (1)

Menu Time Topic Lecture 1 14:00-15:00 C, P, CP and the Standard Model 15:30-16:30 CKM matrix Lecture 2 10:00-10:45 Flavour mixing in B-decays 11:00-11:45 CP Violation in B-decays 12:00 -12:45 CP Violation in B/K-decays Lecture 3 14:00-14:45 Unitarity Triangle 15:00-15:45 New Physics? Niels Tuning (2)

Recap uI W dI u W d,s,b Diagonalize Yukawa matrix Yij Mass terms Quarks rotate Off diagonal terms in charged current couplings u d,s,b W Replace the derivative with the covariant derivative introducing the force carriers: gluons, weak vector bosons and photon. The constants g_s, g and g’ are the corresponding coupling constants of the gauge particles. Niels Tuning (3) 3

CKM-matrix: where are the phases? Possibility 1: simply 3 ‘rotations’, and put phase on smallest: Possibility 2: parameterize according to magnitude, in O(λ): u d,s,b W Niels Tuning (4)

This was theory, now comes experiment We already saw how the moduli |Vij| are determined Now we will work towards the measurement of the imaginary part Parameter: η Equivalent: angles α, β, γ . To measure this, we need the formalism of neutral meson oscillations… Niels Tuning (5)

Dynamics of Neutral B (or K) mesons… Time evolution of B0 andB0 can be described by an effective Hamiltonian: No mixing, no decay… No mixing, but with decays… (i.e.: H is not Hermitian!) With decays included, probability of observing either B0 or B0 must go down as time goes by: Niels Tuning (6)

Describing Mixing… Time evolution of B0 andB0 can be described by an effective Hamiltonian: Where to put the mixing term? Now with mixing – but what is the difference between M12 and G12? M12 describes B0  B0 via off-shell states, e.g. the weak box diagram G12 describes B0fB0 via on-shell states, eg. f=p+p- Niels Tuning (7)

Solving the Schrödinger Equation Eigenvalues: Mass and lifetime of physical states: mass eigenstates The physical particles are the eigenstates of the Hamiltonian. Solve the eigenvalues lambda by putting det (H11-lambda*I) = 0 This you can not see here. You just have to sit down and *do* it. Niels Tuning (8)

Solving the Schrödinger Equation Eigenvectors: mass eigenstates The physical particles are the eigenstates of the Hamiltonian. Solve the eigenvalues lambda by putting det (H11-lambda*I) = 0 This you can not see here. You just have to sit down and *do* it. Niels Tuning (9)

Time evolution With diagonal Hamiltonian, usual time evolution is obtained: Niels Tuning (10)

B Oscillation Amplitudes For an initially produced B0 or aB0 it then follows: (using: with For B0, expect: DG ~ 0, |q/p|=1 These formula’s just follow from substitution. No magic. Note that in the last step g_ gets a 90 degree phase ! Niels Tuning (11)

Measuring B Oscillations For B0, expect: DG ~ 0, |q/p|=1 Examples: B0B0 Decay probability Use cos^2 (dmt/2) = 0.5 * (1 + cos(dmt)) Proper Time  Niels Tuning (12)

Probability to measure P or P, when we start with 100% P Compare the mesons: Probability to measure P or P, when we start with 100% P P0P0 P0P0 <> Δm x=Δm/Γ y=ΔΓ/2Γ K0 2.6 10-8 s 5.29 ns-1 Δm/ΓS=0.49 ~1 D0 0.41 10-12 s 0.001 fs-1 ~0 0.01 B0 1.53 10-12 s 0.507 ps-1 0.78 Bs0 1.47 10-12 s 17.8 ps-1 12.1 ~0.05 Probability  By the way, ħ=6.58 10-22 MeVs x=Δm/Γ: avg nr of oscillations before decay Time  Niels Tuning (13)

Summary (1) Start with Schrodinger equation: Find eigenvalue: Solve eigenstates: Eigenstates have diagonal Hamiltonian: mass eigenstates! (2-component state in P0 and P0 subspace) Niels Tuning (14)

Summary (2) Two mass eigenstates Time evolution: Probability for |P0>  |P0> ! Express in M=mH+mL and Δm=mH-mL  Δm dependence

Time dependence (if ΔΓ~0, like for B0): Let’s summarize … p, q: Δm, ΔΓ: x,y: mixing often quoted in scaled parameters: q,p,Mij,Γij related through: Time dependence (if ΔΓ~0, like for B0): with Niels Tuning (16)

Box diagram and Δm Inami and Lim, Prog.Theor.Phys.65:297,1981 Niels Tuning (17)

Box diagram and Δm Niels Tuning (18)

Box diagram and Δm: Inami-Lim K-mixing C.Gay, B Mixing, hep-ex/0103016

Box diagram and Δm: Inami-Lim B0-mixing C.Gay, B Mixing, hep-ex/0103016

Box diagram and Δm: Inami-Lim Bs0-mixing C.Gay, B Mixing, hep-ex/0103016

Next: measurements of oscillations B0 mixing: 1987: Argus, first 2001: Babar/Belle, precise Bs0 mixing: 2006: CDF: first 2010: D0: anomalous ?? Niels Tuning (22)

B0 mixing Niels Tuning (23)

B0 mixing What is the probability to observe a B0/B0 at time t, when it was produced as a B0 at t=0? Calculate observable probility Y*Y(t) A simple B0 decay experiment. Given a source B0 mesons produced in a flavor eigenstate |B0> You measure the decay time of each meson that decays into a flavor eigenstate (either B0 orB0) you will find that Exercise idea: compare tau, dm of K0 and B0 Niels Tuning (24) 24

B0 mixing: 1987 Argus B0 oscillations: First evidence of heavy top  mtop>50 GeV Needed to break GIM cancellations NB: loops can reveal heavy particles! Phys.Lett.B192:245,1987 Niels Tuning (25)

B0 mixing: 2001 B-factories You can really see this because (amazingly) B0 mixing has same time scale as decay t=1.54 ps Dm=0.5 ps-1 50/50 point at pDm  t Maximal oscillation at 2pDm  2t Actual measurement of B0/B0 oscillation Also precision measurement of Dm! Exercise idea: compare tau, dm of K0 and B0 Niels Tuning (26) 26

Bs0 mixing Niels Tuning (27)

Bs0 mixing: 2006 Niels Tuning (28) 28

Bs0 mixing (Δms): SM Prediction CKM Matrix Wolfenstein parameterization Vts Ratio of frequencies for B0 and Bs Vts ~ 2 Vtd ~3  Δms ~ (1/λ2)Δmd ~ 25 Δmd  = 1.210 +0.047 from lattice QCD -0.035 Niels Tuning (29)

Bs0 mixing (Δms): Unitarity Triangle CKM Matrix Unitarity Condition Niels Tuning (30) 30

Bs0 mixing (Δms) cos(Δmst) Proper Time t (ps) Δms=17.77 ±0.10(stat)±0.07(sys) ps-1 hep-ex/0609040 Bs b b s s t t W Bs g̃ x b̃ s̃ cos(Δmst) Proper Time t (ps) Niels Tuning (31)

Bs0 mixing (Δms): New: LHCb LHCb-CONF-2011-005 Bs b b s s t t W Bs g̃ x b̃ s̃ Niels Tuning (32)

Mixing  CP violation? NB: Just mixing is not necessarily CP violation! However, by studying certain decays with and without mixing, CP violation is observed Next: Measuring CP violation… Finally Niels Tuning (33)

Meson Decays Formalism of meson oscillations: Subsequent: decay Niels Tuning (34)

Notation: Define Af and λf Niels Tuning (35)

Some algebra for the decay P0  f Interference P0 f P0P0 f Niels Tuning (36)

Some algebra for the decay P0  f Niels Tuning (37)

The ‘master equations’ (‘direct’) Decay Interference Niels Tuning (38)

The ‘master equations’ (‘direct’) Decay Interference Niels Tuning (39)

Classification of CP Violating effects CP violation in decay CP violation in mixing CP violation in interference Niels Tuning (40)

Classification of CP Violating effects - Nr. 3: Consider f=f : If one amplitude dominates the decay, then Af = Af CP violation in interference Niels Tuning (41)

Break? What’s the time? Niels Tuning (42)

Menu Time Topic Lecture 1 14:00-15:00 C, P, CP and the Standard Model 15:30-16:30 CKM matrix Lecture 2 10:00-10:45 Flavour mixing in B-decays 11:00-11:45 CP Violation in B-decays 12:00 -12:45 CP Violation in B/K-decays Lecture 3 14:00-14:45 Unitarity Triangle 15:00-15:45 New Physics? Niels Tuning (43)

Diagonalize Yukawa matrix Yij Recap Tuesday Diagonalize Yukawa matrix Yij Mass terms Quarks rotate Off diagonal terms in charged current couplings Replace the derivative with the covariant derivative introducing the force carriers: gluons, weak vector bosons and photon. The constants g_s, g and g’ are the corresponding coupling constants of the gauge particles. Niels Tuning (44) 44

The CKM matrix W- b gVub u Couplings of the charged current: Recap Tuesday The CKM matrix Couplings of the charged current: Wolfenstein parametrization: b W- u gVub Magnitude: Complex phases: Niels Tuning (45)

“The” Unitarity triangle Recap Tuesday “The” Unitarity triangle We can visualize the CKM-constraints in (r,h) plane Niels Tuning (46)

Neutral Meson Oscillations (1) Recap Morning Neutral Meson Oscillations (1) Start with Schrodinger equation: Find eigenvalue: Solve eigenstates: Eigenstates have diagonal Hamiltonian: mass eigenstates! (2-component state in P0 and P0 subspace) Niels Tuning (47)

Neutral Meson Oscillations (2) Recap Morning Neutral Meson Oscillations (2) Two mass eigenstates Time evolution: Probability for |P0>  |P0> ! Express in M=mH+mL and Δm=mH-mL  Δm dependence

Meson Decays Formalism of meson oscillations: Subsequent: decay P0 f Recap Morning Meson Decays Formalism of meson oscillations: Subsequent: decay Interference P0 f P0P0 f Interference (‘direct’) Decay

Classification of CP Violating effects Recap Morning Classification of CP Violating effects CP violation in decay CP violation in mixing CP violation in interference Niels Tuning (50)

Now: Im( λf) CP violation in decay CP violation in mixing CP violation in interference We will investigate λf for various final states f

CP violation: type 3 Niels Tuning (52)

|λf|=1 Final state f : J/ΨKs Interference between B0→fCP and B0→B0→fCP For example: B0→J/ΨKs and B0→B0→ J/ΨKs Lets’ s simplify … For B0 we have: Since fCP =fCP we have: The amplitudes |A( B0→J/ψKs)| and |A(B0→J/ψKs)| are equal: |λf|=1 B0 d B0 Niels Tuning (53)

Relax: B0J/ΨKs simplifies… Niels Tuning (54)

λf for B0 ® J/yK0S c J/y K0 B0 b s d b d s d |Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 s d Niels Tuning (55)

Time-dependent CP asymmetry λf for B0 ® J/yK0S Time-dependent CP asymmetry Theoretically clean way to measure b Clean experimental signature Branching fraction: O(10-4) “Large” compared to other CP modes! |Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 Niels Tuning (56)

Remember: C and P eigenvalue C and P are good symmetries (not involving the weak interaction) Can associate a conserved value with them (Noether Theorem) Each hadron has a conserved P and C quantum number What are the values of the quantum numbers Evaluate the eigenvalue of the P and C operators on each hadron P|y> = p|y> What values of C and P are possible for hadrons? Symmetry operation squared gives unity so eigenvalue squared must be 1 Possible C and P values are +1 and -1. Meaning of P quantum number If P=1 then P|y> = +1|y> (wave function symmetric in space) if P=-1 then P|y> = -1 |y> (wave function anti-symmetric in space) Niels Tuning (57)

Remember: P eigenvalues for hadrons The p+ meson Quark and anti-quark composite: intrinsic P = (1)*(-1) = -1 Orbital ground state  no extra term P(p+)=-1 The neutron Three quark composite: intrinsic P = (1)*(1)*(1) = 1 P(n) = +1 The K1(1270) Quark anti-quark composite: intrinsic P = (1)*(-1) = -1 Orbital excitation with L=1  extra term (-1)1 P(K1) = +1 Meaning: P|p+> = -1|p+> Niels Tuning (58)

Intermezzo: CP eigenvalue Remember: P2 = 1 (x  -x  x) C2 = 1 (ψ ψ  ψ )  CP2 =1 CP | f > =  | f > Knowing this we can evaluate the effect of CP on the K0 CP|K0> = -1| K0> CP| K0> = -1|K0 > CP eigenstates: |KS> = p| K0> +q|K0> |KL> = p| K0> - q|K0> |Ks> (CP=+1) → p p (CP= (-1)(-1)(-1)l=0 =+1) |KL> (CP=-1) → p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1) ( S(K)=0  L(ππ)=0 ) Niels Tuning (59)

CP eigenvalue of final state J/yK0S CP |J/y> = +1 |J/y> CP |K0S> = -1 |K0S> CP |J/yK0S> = -1 |J/yK0S> ( S(J/y)=1 ) ( S(B)=0  L(J/yK0S)=0 ) Relative minus-sign between state and CP-conjugated state: |Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 Niels Tuning (60)

Time dependent CP violation If final state is CP eigenstate then 2 amplitudes (w/o mixing): B0f and B0B0f B0 -B0 oscillation is periodic in time  CP violation time dependent Amplitude 1 Amplitude 2 + e-iφ (i=eiπ/2 δ=90o) (φ=2β) Niels Tuning (61)

Time dependent CP violation If final state is CP eigenstate then 2 amplitudes (w/o mixing): B0f and B0B0f B0 -B0 oscillation is periodic in time  CP violation time dependent 1 + e-iφ (i=eiπ/2 δ=90o) (φ=2β) Niels Tuning (62)

Sum of 2 amplitudes: sensitivity to phase What do we know about the relative phases of the diagrams? B0  f B0  B0  f f(strong)=f Decays are identical f(strong)=f K0 mixing exactly cancels Vcs f(weak)=0 f(weak)=2b f(mixing)=p/2 There is a phase difference of i between the B0 andB0 Niels Tuning (63)

Sum of 2 amplitudes: sensitivity to phase Now also look at CP-conjugate process Directly observable result (essentially just from counting) measure CKM phase b directly! N(B0  f)  |A|2  (1-cosf)2+sin2f = 1 -2cosf+cos2f+sin2f = 2-2cos(p/2-2b)  1-sin(2b) + = Γ(Bf)= sin(f) p/2+2b CP 1-cos(f) + = sin(f) Γ(Bf)= p/2-2b N(B0  f)  (1+cosf)2+sin2f = 2+2cos(p/2-2b)  1+sin(2b) 1+cos(f) Niels Tuning (64)

2 amplitudes 2 phases Remember! Necessary ingredients for CP violation: Two (interfering) amplitudes Phase difference between amplitudes one CP conserving phase (‘strong’ phase) one CP violating phase (‘weak’ phase) 2 amplitudes 2 phases Niels Tuning (65)

Remember! 2 amplitudes 2 phases Niels Tuning (66)

B0→J/ψKs B-system - Time-dependent CP asymmetry BaBar (2002) Niels Tuning (67) BaBar (2002)

Consistency with other measurements in (r,h) plane 4-fold ambiguity because we measure sin(2b), not b Prices measurement of sin(2β) agrees perfectly with other measurements and CKM model assumptions The CKM model of CP violation experimentally confirmed with high precision! 2 1 without sin(2b) h 3 4 r Method as in Höcker et al, Eur.Phys.J.C21:225-259,2001 Niels Tuning (68)

βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S Replace spectator quark d  s Niels Tuning (69)

βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S Niels Tuning (70)

Remember: The “Bs-triangle”: βs Replace d by s: Niels Tuning (71)

βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S Differences: B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1 Final state (spin) K0 : s=0 φ: s=1 Final state (K) K0 mixing - Niels Tuning (72)

βs: Bs0 ® J/yφ A║ A┴ A0 B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1 Vts large, oscilations fast, need good vertex detector A║ A0 A┴ l=2 l=1 l=0 3 amplitudes B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1 Final state (spin) K0 : s=0 φ: s=1 Final state (K) K0 mixing - Niels Tuning (73)

“Recent” excitement (5 March 2008) Niels Tuning (74)

Bs  J/ψФ : Bs equivalent of B J/ψKs ! The mixing phase (Vtd): φd=2β B0  f B0  B0  f Wolfenstein parametrization to O(λ5): Niels Tuning (75)

Bs  J/ψФ : Bs equivalent of B J/ψKs ! The mixing phase (Vts): φs=-2βs B0  f B0  B0  f Vts - s Ф Bs Bs Ф s s s Vts Wolfenstein parametrization to O(λ5): Niels Tuning (76)

Bs  J/ψФ : Bs equivalent of B J/ψKs ! The mixing phase (Vts): φs=-2βs B0  f B0  B0  f Vts - s Ф Bs Bs Ф s s s Vts Niels Tuning (77)

Break Niels Tuning (78)

Menu Time Topic Lecture 1 14:00-15:00 C, P, CP and the Standard Model 15:30-16:30 CKM matrix Lecture 2 10:00-10:45 Flavour mixing in B-decays 11:00-11:45 CP Violation in B-decays 12:00 -12:45 CP Violation in B/K-decays Lecture 3 14:00-14:45 Unitarity Triangle 15:00-15:45 New Physics? Niels Tuning (79)

Next: γ Niels Tuning (80)

CKM Angle measurements from Bd,u decays Sources of phases in Bd,u amplitudes* The standard techniques for the angles: bu Amplitude Rel. Magnitude Weak phase bc Dominant bu Suppressed γ td (x2, mixing) Time dependent 2β *In Wolfenstein phase convention. td B0 mixing + single bu decay B0 mixing + single bc decay Interfere bc and bu in B± decay. Niels Tuning (81)

Determining the angle g From unitarity we have: Must interfere b  u (cd) and b c(ud) Expect b  u (cs) and b c(us) to have the same phase, with more interference (but less events) g l3 l l2 1 l3 1 l2 l Niels Tuning (82)

Measure γ: B0s  DsK-/+ : both λf and λf 2 + Γ(Bf)= 2 + Γ(Bf )= NB: In addition B s  DsK-/+ : both λ f and λf Niels Tuning (83)

Measure γ: Bs  DsK-/+ --- first one f: Ds+K- This time | Af||Af|, so |λ|1 ! In fact, not only magnitude, but also phase difference: Niels Tuning (84)

Measure γ: Bs  DsK-/+ B0s  Ds-K+ has phase difference ( - ): Need B0s  Ds+K- to disentangle  and : Niels Tuning (85)

Kaons… Different notation: confusing! Smaller CP violating effects But historically important! Concepts same as in B-system, so you have a chance to understand… Niels Tuning (86)

Neutral kaons – 60 years of history 1947 : First K0 observation in cloud chamber (“V particle”) 1955 : Introduction of Strangeness (Gell-Mann & Nishijima) K0,K0 are two distinct particles (Gell-Mann & Pais) 1956 : Parity violation observation of long lived KL (BNL Cosmotron) 1960 : Dm = mL-mS measured from regeneration 1964 : Discovery of CP violation (Cronin & Fitch) 1970 : Suppression of FCNC, KLmm - GIM mechanism/charm hypothesis 1972 : 6-quark model; CP violation explained in SM (Kobayashi & Maskawa) 1992-2000 : K0,K0 time evolution, decays, asymmetries (CPLear) 1999-2003 : Direct CP violation measured: e’/e ≠ 0 (KTeV and NA48) … the θ0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ0's undergo the familiar decay into two pions. Niels Tuning (87) From G.Capon

Intermezzo: CP eigenvalue Remember: P2 = 1 (x  -x  x) C2 = 1 (ψ ψ  ψ )  CP2 =1 CP | f > =  | f > Knowing this we can evaluate the effect of CP on the K0 CP|K0> = -1| K0> CP| K0> = -1|K0 > CP eigenstates (almost): |KS> = p| K0> +q|K0> |KL> = p| K0> - q|K0> |Ks> (CP=+1) → p p (CP= (-1)(-1)(-1)l=0 =+1) |KL> (CP=-1) → p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1) ( S(K)=0  L(ππ)=0 ) Niels Tuning (88) 88

Decays of neutral kaons Neutral kaons is the lightest strange particle  it must decay through the weak interaction If weak force conserves CP then decay products of K1 can only be a CP=+1 state, i.e. |K1> (CP=+1) → p p (CP= (-1)(-1)(-1)l=0 =+1) decay products of K2 can only be a CP=-1 state, i.e. |K2> (CP=-1) → p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1) You can use neutral kaons to precisely test that the weak force preserves CP (or not) If you (somehow) have a pure CP=-1 K2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP… ( S(K)=0  L(ππ)=0 ) Niels Tuning (89) 89

Designing a CP violation experiment How do you obtain a pure ‘beam’ of K2 particles? It turns out that you can do that through clever use of kinematics Exploit that decay of K into two pions is much faster than decay of K into three pions Related to fact that energy of pions are large in 2-body decay t1 = 0.89 x 10-10 sec t2 = 5.2 x 10-8 sec (~600 times larger!) Beam of neutral Kaons automatically becomes beam of |K2> as all |K1> decay very early on… K1 decay early (into pp) Pure K2 beam after a while! (all decaying into πππ) ! Initial K0 beam Niels Tuning (90) 90

The Cronin & Fitch experiment Essential idea: Look for (CP violating) K2  pp decays 20 meters away from K0 production point Decay of K2 into 3 pions Incoming K2 beam If you detect two of the three pions of a K2  ppp decay they will generally not point along the beam line Niels Tuning (91) 91

The Cronin & Fitch experiment Essential idea: Look for K2  pp decays 20 meters away from K0 production point Decay pions Incoming K2 beam If K2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K2  pp decay) Niels Tuning (92) 92

The Cronin & Fitch experiment Essential idea: Look for K2  pp decays 20 meters away from K0 production point Decay pions K2  pp decays (CP Violation!) Incoming K2 beam K2  ppp decays Result: an excess of events at Q=0 degrees! CP violation, because K2 (CP=-1) changed into K1 (CP=+1) Note scale: 99.99% of K ppp decays are left of plot boundary Niels Tuning (93) 93

Nobel Prize 1980 "for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons" 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. James Watson Cronin   1/2 of the prize   University of Chicago Chicago, IL, USA b. 1931 Val Logsdon Fitch   1/2 of the prize   Princeton University Princeton, NJ, USA b. 1923 Niels Tuning (94)

Cronin & Fitch – Discovery of CP violation Conclusion: weak decay violates CP (as well as C and P) But effect is tiny! (~0.05%) Maximal (100%) violation of P symmetry easily follows from absence of right-handed neutrino, but how would you construct a physics law that violates a symmetry just a tiny little bit? Results also provides us with convention-free definition of matter vs anti-matter. If there is no CP violation, the K2 decays in equal amounts to p+ e- ne (a) p- e+ ne (b) Just like CPV introduces K2  ππ decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a) “Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K meson” Niels Tuning (95) 95

Intermezzo: Regeneration Different cross section for σ(p K0) than σ(pK0) Elastic scattering: same Charge exchange : same Hyperon production: more for K0 ! What happens when KL-beam hits a wall ?? Then admixture changes…: |KL> = p| K0> - q|K0> Regeneration of KS ! Could fake CP violation due to KS→π+π-… strong interactions: must conserve strangeness leave little free energy – unlikely! Niels Tuning (96)

KS and KL KL and KS are not orthogonal: Usual (historical) notation in kaon physics: Modern notation used in B physics: Regardless of notation: KL and KS are not orthogonal: Niels Tuning (97)

Three ways to break CP; e.g. in K0→ π+π- Niels Tuning (98)

Classification of CP Violating effects CP violation in decay CP violation in mixing CP violation in interference Niels Tuning (99)

Time evolution Niels Tuning (100)

B-system 2. CP violation in mixing K-system CPLEAR, Phys.Rep. 374(2003) 165-270 BaBar, (2002) CPLear (2003)

B-system 2. CP violation in mixing K-system BaBar, (2002) NA48, (2001) L(e) = (3.317  0.070  0.072)  10-3 Niels Tuning (102)

B0→J/ψKs B-system 3.Time-dependent CP asymmetry BaBar (2002) Niels Tuning (103) BaBar (2002)

B0→J/ψKs K0→π-π+ B-system 3.Time-dependent CP asymmetry K-system ~50/50 decay as Ks and KL + interference! K0 _ K0 p+p- rate asymmetry BaBar (2002) CPLear (PLB 1999)

The Quest for Direct CP Violation Indirect CP violation in the mixing:  Direct CP violation in the decay: ’ A fascinating 30-year long enterprise: “Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction?” Niels Tuning (105)

B system 1. Direct CP violation K system B0→K+π- B0→K-π+ K0→π-π+ K0→π-π+ K0→π0π0 K0→π0π0 Different CP violation for the two decays  Some CP violation in the decay! ε’≠ 0 Niels Tuning (106)

Menu Time Topic Lecture 1 14:00-15:00 C, P, CP and the Standard Model 15:30-16:30 CKM matrix Lecture 2 10:00-10:45 Flavour mixing in B-decays 11:00-11:45 CP Violation in B-decays 12:00 -12:45 CP Violation in B/K-decays Lecture 3 14:00-14:45 New Physics? 15:00-15:45 Unitarity Triangle Niels Tuning (107)