CP/ Andreas Meyer. Hamburg University. DESY Summer Student Lectures, 1+4 August 2003 (this file including slides not shown in the lecture) Part 1

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1 CP/ Part 1 Andreas Meyer Hamburg University DESY Summer Student Lectures, 1+4 August 2003 (this file including slides not shown in the lecture)

2 Friday: CP-Violation Violation of Particle Anti-particle Symmetry Symmetries Parity-Operation and Charge-Conjugation The neutral K-Meson-System Discovery of CP-violation (1964) CP-Violation in the Standard model Measurements at the CPLEAR Experiment (CP Violation in K 0 -Mixing) Slides only: Latest Results from NA48 (CP Violation in K 0 -Decays) Monday: Recap: Discovery of CP-Violation The neutral B-Meson-System CKM Matrix and Unitarity Triangle Prediction for the B-System from K-Results B-Factories BaBar and Belle (Test of Standard Model) Future Experiments, CP-Violation in the Lepton-Sector? Summary

3 The Universe Matter exceeds Antimatter, why? Big-Bang model: Creation of matter and antimatter in equal amounts Baryogenesis: Where did the antimatter go? Three necessary conditions for Baryogenesis: A. Sacharov, 1967 Baryon-number violation no problem for gauge theories but not seen yet Thermodynamical non-equilibrium C and CP-violation (!) What is CP-Violation?

4 CP: Symmetry between Particles and Antiparticles CP-Symmetry is known to be broken: The Universe Matter only, no significant amount of antimatter The neutral K-Meson (most of todays lecture) discovered 1964 (Fitch, Cronin, Nobel-Prize 1980) almost 40 years of K-physics with increasing precision The neutral B-Meson (on Monday) measured 2001 (expected in Standard Model)

5 Symmetry Image = Mirror-Image Image =/ Mirror-Image

6 World Mirror World 90% 10% 10% 90% World! Mirror World (parity violation)

7 Parity is fully violated.

8 Symmetry broken here?

9 Symmetries in Physics Rotational symmetry around z y Symmetry broken φ-angle y (x,y,z) or (r, θ,φ) x x z z Reduced number of variables Simplified description More variables needed Harder to calculate

10 Symmetries in Physics System is invariant w.r.t transformation symmetry Continuous transformations Conservation Law Translation in time Homogeneity of time Energy Translation in space Homogeneity of space Momentum Rotation in space Isotropy of space Angular momentum Gauge transformation charge Symmetry Conservation Law E.Noether, 1918 (for continuous symmetries only) Discrete transformations Parity Charge conjugation Time-reversal mirror matter antimatter playing the movie backwards

11 Translation Rotation Reflection (parity) R RRRRRRRRR R RRRR RRRRRR R R continuous continuous discrete

12 Discrete Symmetries Parity Transformation: P : r = (x, y, z) r = ( x, y, z) QM System is invariant under Parity transformation P if P is the same for initial and final state P is a good quantum number P [ commutates with Hamiltonian, P, Ĥ] = 0

13 Parity-Operation Parity Operation on a quantum mechanical state, ie. wavefunction: P ψ( r, t) = P a ψ( r, t) Possible Eigenvalues of the Parity-Operator are ±1. P P ψ( r, t) = ψ( r, t) P 2 a = 1 P a = ±1 A consequence of the Dirac-equation is that the parity of fermions and antifermions must be opposite: P f P f = 1 This has experimentally been confirmed in e + + e γγ

14

15 Û + Û p + Û p - Û Û 0 Û 0 p 0 Û p 0

16 CPT P : x x Parity mirror Ĉ : q q Charge-conjugation matter antimatter T : t t Time-reversal playing the movie backwards CPT-Theorem: In relativistic field theories CPT is a fundamental symmetry Particle and antiparticle must have same mass, lifetime, charge,... T : Play the movie backwards, P : look at it in a mirror, Ĉ : change everything (including yourself!?) into antimatter the laws of physics must be the same.

17 Interactions vs. Symmetries Interaction particles medium lifetime [s] C P CP T CPT strong quarks gluons el-mag. charged photon weak all W ±, Z X X X X In weak interactions: P and C are maximally violated CP is violated T is violated In all interactions: CPT is conserved

18 Historical Overview 1954: CPT Theorem: In 1954 C,P and T were believed to be conserved individually 1957: Parity and Charge-Conjugation are broken Wu et al., Lee, Yang, Nobel Prize : First theory of charged weak interactions (V-A theory) 1964: Discovery of CP-violation Fitch, Cronin et al, Nobel Prize : CKM Matrix, Kobayashi, Maskawa CP violation possible within Standard model, if 3 generations of quarks 1974: Discovery of the Charm Quark Ting, Richter, Nobel Prize : Discovery of the Beauty Quark 1988: Direct CP violation (NA31 Experiment, CERN) 1995: Discovery of the Top Quark 2001: Measurement of CP violation in the B-Meson System

19 Wu et al., 1957 Discovery of Parity-Violation β-decay: 60 Co(J = 5) 60 Ni (J = 4) + e (J = 1/2) + ν e (J = 1/2) Distribution of decay electrons opposite to direction of spin

20 P and C-Violation in the π-decay Left-handed neutrinos and right-handed antineutrinos only. In weak interactions P and C are violated maximally. CP can still be conserved.

21 Strangeness π p K 0 Λ S Associated production of strangeness in strong interactions S = 0, ie. s s quark pair strangeness conserved copious rates (strong i.a.) Decays : e.g. K 0 π + π and Λ π p strangeness violated very slow (strange!)

22 Weak Decays Strangeness is violated in charged weak interactions: Λ { d s u u d u } p W - u- d } π -

23 K 0 -K 0 -Mixing K 0 and K 0 can both decay into 2π (CP=+1) or 3π (CP= 1) They can also oscillate into each other (via their common final states) { } K 0 2π K 0 3π u s d K 0 W W K 0 d s u W s d K 0 u u K 0 d s W

24 Eigenstates of P,C and CP? P K 0 = K 0 P K 0 = K 0 Ĉ K 0 = K 0 Ĉ K 0 = K 0 ĈP K 0 = + K 0 ĈP K 0 = + K 0 Construct CP-Eigenstates by linear combination of flavour-eigenstates CP-Eigenstate ) Decay Symmetry Lifetime [s] K1 0 = 1 2 ( K 0 + K 0 2π CP=+1 τ 1 = ) K2 0 = 1 2 ( K 0 K 0 3π CP= 1 τ 2 = K 0 1, K 0 2 are the Eigenstates of CP of charged weak interaction. Note the large difference in lifetime.

25 Time-development: Oscillations K 0 1(t) = K 0 1(0) e (im 1+Γ 1 /2)t K 0 2(t) = K 0 2(0) e (im 2+Γ 2 /2)t t = 0: Assume pure K 0 beam (equal amounts of K 0 1(0) and K 0 2(0)). K 0 t=0 = 1 2 ( K 0 1 (0) + K 0 2 (0) ) Development of beam intensities with time (Schrödinger-Eq.) I(K 0 ) = K 0 (t) K 0 (t) 2 = I 0 ( e Γ 1 t + e Γ2t + 2e (Γ 1+Γ 2 )t/2 cos ((m 2 m 1 ) t) ) 4 I(K 0 ) = K 0 (t) K 0 (t) 2 = I 0 ( e Γ 1 t + e Γ2t 2e (Γ 1+Γ 2 )t/2 cos ((m 2 m 1 ) t) ) 4 Mass difference between K 1 and K 2 required for oscillations to occur!

26 Oscillations 1 m τ 1 = 0.5 K 0 Intensity K t/τ 1 Mass difference measured from rate of K 0 decays as fct of time: m = ( ± ) hs MeV/c 2

27 Discovery of CP-Violation Incoming K 2 beam, Helium filled decay volume Christenson, Cronin, Fitch, Turlay (Phys.Rev.Lett. 13, , 1964)

28 Signal: 56 events BR(K 2 π + π ) =

29 CP Violation in the Standard Model Following years: Confirmation and other manifestations of the same phenomenon, e.g. K L π 0 π 0 and charge asymmetries in K L π ± l ν. By : Two theoretical models had survived scrutiny Superweak CP-violating new force Wolfenstein this implied no direct CP violation falsified experimentally only recently CP violation encorporated in 3x3 CKM matrix of quark mixings Kobayashi-Maskawa, 1973

30 Three Quark-Doublets: CKM Matrix Mixing of down-type quarks in charged weak interactions: CKM-Matrix V CKM : d V ud V us V ub d s = V cd V cs V cb s b V td V ts V tb b

31 CP-Violation in CKM Matrix 3x3 Matrix with four free parameters Wolfenstein parametrisation: 1 λ2 2 λ Aλ 3 (ρ iη) V CKM = λ 1 λ2 2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aη 2 1 Complex elements V td and V ub allow for CP violation E.g.: CP-violating weak amplitudes from box-diagrams: s K 0 W W K 0 d V td u, c, t V td u,c,t d s s K 0 u,c,t u, c, t K 0 d V td W W V td d s CP-Violation is a built-in feature of the Standard Model

32 0 K K 0 Kaon decays in the CP-mirror CP-Violation: Different Rates for K 0 and K 0 π + π 1) 2) 0 K K 0 CP Mirror K 0 4) 0 K 3) 3) π + π π + π Possible sources: 1) CP/ in mixing from CPT / K 0 K 0 K 0 K 0 2) CP/ in mixing from T/ K 0 K 0 K 0 K 0 3) Direct CP/ in decay K 0 π + π K 0 π + π 4) CP/ in interference between mixing and decay K 0 π + π K 0 π + π (Interference between CP-violating phases of different mixing and decay channels)

33 CP Violation Three types of CP Violation (from T Violation) CP violation in mixing Γ(K 0 K 0 ) Γ(K 0 K 0 ) Seen in K-System: ɛ CP violation in decay ( direct CP violation) Γ(A B) Γ(A B) Seen in K-System: ɛ CP violation in interference between decays with and without mixing: Seen in B-system: sin(2β) ( on Monday)

34 CP Violation in Mixing The CP-Eigenstates K 0 1 (CP=+1) and K 0 2 (CP= 1) are modifed by ɛ-admixtures to form the physical short-lived and long-lived states K 0 S and K0 L K 0 S = p K 0 + q K 0 = K 0 L = p K0 q K 0 = ɛ 2 ( K0 1 ɛ K 0 2 ) ɛ 2 (ɛ K0 1 + K0 2 ) Γ(K 0 K 0 ) Γ(K 0 K 0 ) q/p 1 CP is violated CP violation via mixing: ɛ = p q p + q q/p = 1 2Re(ɛ)

35 Data Taking Period: p p - Associated production of K-pairs (via strong i.a.)

36 Tag whether K 0 or K 0 by charge of other Kaon

37 G 0 p + p -! G 0 p + p - Difference from Interference between K 0 and K 0

38 h +- p + p - p + p - (2.284±0.018) 10-3 (43.3±0.5)" h 00 p 0 p 0 p 0 p 0 (2.23±0.11) 10-3 (43.2±1.0)" h +-» h 00

39 Direct CP Violation K 0 π + π K 0 π + π s K d 0 u,c,t W g,z, γ d u u d + π π Interference of amplitudes with different isospins ɛ Im( A 2 A 0 exp(i(δ 2 δ 0 )) modifies measured ɛ from CP/ in mixing by small amount ɛ : η + = K L π + π K S π + π = ɛ + ɛ η 00 = K L π 0 π 0 K S π 0 π 0 = ɛ 2ɛ R = Γ(K L π 0 π 0 )/Γ(K S π 0 π 0 ) Γ(K L π + π )/Γ(K S π + π ) 1 6Re(ɛ ɛ )

40 NA48 simultaneous and collinear K S and K L beams 12 ~ protons per spill Bent cristal SPS spill length : 2.38 s Cycle time : 14.4 s Proton momentum : 450 GeV/c K L Target Ks tagging station 7 Muon sweeping ( ~3. 10 protons per spill) Ks Target Last collimator K anticounter S (AKS) K S 6.8 cm K L Decay Region (~ 40 m long) not to scale! 0.6 mrad NA48 Detector ~ 126 m ~ 114 m K S and K L beams are distinguished by proton tagging upstream of the K S target.

41 NA48 detector Muon veto sytem Hadron calorimeter Liquid krypton calorimeter Hodoscope Drift chamber 4 Anti counter 7 Helium tank Drift chamber 3 Magnet Drift chamber 2 Anti counter 6 Drift chamber 1 Kevlar window Magnetic spectrometer to detect π + π events + scintillator hodoscope for event time measurement Quasi homogeneous Liquid Krypton calorimeter to detect π 0 π 0 events

42 Measurement at NA48 R = Γ(K L π 0 π 0 )/Γ(K S π 0 π 0 ) Γ(K L π + π )/Γ(K S π + π ) 1 6Re(ɛ ɛ ) K 0 L target: 126 m upstream Average K 0 -momentum: 110 GeV Decay lengths: K 0 S : 5.9 m, K0 L : 3400 m Relative angle of KS 0 -beam: 0.6 mrad Select KS 0 and K0 L by timing of tagged protons ( t < 2 ns) Correct for contamination in charged decays, using horizontally separated decay vertices.

43 Tagging K π + π - (vertex selected) Events Tagging Window K L K S Kaon time - nearest proton time (ns) IF at least one proton is in coincidence (within ±2 ns) with the event time identified as K S ELSE identified as K L Tagging inefficiency P(K S K L ) : α + SL = (1.12 ± 0.03) 10 4 Accidental tagging P(K L K S ) : α + LS = (8.115 ± 0.010)% (it was ( ± 0.008)% in 98-99) In the Double Ratio we account for the accidental tagging

44 Precise results from Na48 and KTeV Re(ε, /ε) E ± 5.9 NA ± 6.5 NA48 01 (prel) 15.3 ± 2.6 KTEV 01 (prel) 20.7 ± (x10-4 ) New World Ave ± 1.8

45 History of ɛ /ɛ measurements

46 Kaons According to PDG 2002 K 0 S K 0 L 69% π + π 21% 3π 0 31% π 0 π 0 13% π + π π 0 27% πµν 39% πeν 0.2% π + π 0.1% π 0 π 0 1 m K 0 L m K 0 S = ( ± ) hs ɛ = (2.282 ± 0.017) 10 3 δ L = (3.27 ± 0.12) 10 3 ɛ /ɛ = (1.8 ± 0.4) 10 3 Note: absolute value of ɛ is O(10 6 )

47 Summary CP violation: Necessary ingredient for baryogenesis. Observed for the first time 1964 in the Kaon system (ɛ = ) In contrast: P and C are maximally violated Kaon physics over last 40 years, impressive precision reached Direct CP Violation established recently (ɛ = ) Incorporated in Standard model (Complex phase in CKM matrix) Predictions for CP violation in the B-System! Since 1999: B-Factories: Test of Standard Model on Monday