CP/ Part 1 Andreas Meyer Hamburg University DESY Summer Student Lectures, 1+4 August 2003 (this file including slides not shown in the lecture) CP-Violation Violation of Particle Anti-particle Symmetry Friday: 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 • 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? 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) Symmetry Image = Mirror-Image Image =/ Mirror-Image World Mirror World 90% 10% 10% 90% World _ Mirror World (parity violation) ¢ ¦¨§ ¡ ¡£ ¤ Parity is fully violated. ¥ Symmetry broken here? Symmetries in Physics Rotational symmetry around z Symmetry broken φ-angle y y ! (x,y,z) or (r, θ,φ ) x x z z Reduced number of variables More variables needed • • Simplified description Harder to calculate • • 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 mirror Charge conjugation matter antimatter $ Time-reversal playing the movie backwards Translation Rotation Reflection RR (parity) RRR R R R RR R R R RR R R R RR R R continuous continuous discrete Discrete Symmetries Parity Transformation: P : ~r = (x; y; z) ~r = ( x; y; z) ! − − − − QMb System is invariant under Parity transformation P if P is the same for initial and final state • b P is a "good" quantum number • P commutates with Hamiltonian, P ; H = 0 • h i b b b Parity-Operation Parity Operation on a quantum mechanical state, ie. wavefunction: P (~r; t) = P ( ~r; t) a − Possible Eigenvalues of the Parity-Operator are 1. b P P (~r; t) = (~r; t) P 2 = 1 P = 1 ) a ) a A consequence of the Dirac-equation is that the parity of fermions b b and antifermions must be opposite: P P ¯ = 1 f f − + This has experimentally been confirmed in e + e− γγ ! - - - - ' - - + - Û + Û p+ Û p- Û Û 0 Û 0 p0 Û p0 CPT P : x x Parity mirror ! − C : q q Charge-conjugation matter antimatter b ! − $ T : t t Time-reversal playing the movie backwards b ! − CPT-Theob rem: 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, Cb : change everything (including yourself !?) into antimatter b the laws of physics must be the same. ) b Interactions vs. Symmetries Interaction particles medium lifetime [s] C P CP T CPT 22 24 strong quarks gluons 10− 10− p p p p p − 16 21 el-mag. charged photon 10− 10− p p p p p − 0 3 13 weak all W ; Z 10 10− X X X X p − In weak interactions: { P and C are maximally violated { CP is violated T is violated $ In all interactions: { CPT is conserved 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 1957 • 1958: First theory of charged weak interactions (V-A theory) • 1964: Discovery of CP-violation Fitch, Cronin et al, Nobel Prize 1980 • 1973: 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 1976 • 1977: 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 • Discovery of Parity-Violation Wu et al., 1957 ∗ β-decay: 60Co(J = 5) 60 Ni (J = 4) + e−(J = 1=2) + ν (J = 1=2) ! e Distribution of decay electrons opposite to direction of spin 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. Strangeness − π p K0Λ ! S 0 0 +1 1 − Associated production of strangeness in strong interactions ∆S = 0, ie. ss¯ quark pair • strangeness conserved • copious rates (strong i.a.) • Decays : e:g: K0 π+π− and Λ π−p ! ! strangeness violated • very slow (strange!) • Weak Decays Strangeness is violated in charged weak interactions: u u Λ d d p { s u } - W u- π - d } K0-K0-Mixing 0 K0 and K can both decay into 2π (CP=+1) or 3π (CP= 1) − They can also oscillate into each other (via their common final states) 2π 0 K0 K $ ( 3π ) $ u W s d s d 0 0 K0 W W K K0 u u K j i j i j i j i d s d s u W Eigenstates of P,C and CP ? 0 0 P K0 = K0 P K = K j i −| i j i −| i 0 0 C K0 = K C K = K0 b b j i −| 0i j i0 −| i CP K0 = + K CP K = + K0 bj i j i b j j i Construct CP-Eigenstatesd by linear combinationd of flavour-eigenstates CP-Eigenstate Decay Symmetry Lifetime [s] 0 1 0 0 10 K = K + K 2π CP=+1 τ = 0:9 10− j 1 i p2 j i j i ! 1 × 0 1 0 0 7 K = K K 3π CP= 1 τ = 0:5 10− j 2 i p2 j i − j i ! − 2 × K0, K0 are the Eigenstatesof CP of charged weak interaction. 1 2 ! Note the large difference in lifetime. Oscillations Time-development: 0 0 (im1+Γ1=2)t K (t) = K (0) e− j 1 i j 1 i 0 0 (im2+Γ2=2)t K (t) = K (0) e− j 2 i j 2 i 0 0 0 t = 0: Assume pure K beam (equal amounts of K1 (0) and K2 (0)). 1 K0 = K0(0) + K0(0) j i t=0 p2 j 1 i j 2 i Development of beam intensities with time (Schr¨odinger-Eq.) 2 I I(K0) = K0(t) K0(t) = 0 e−Γ1t + e−Γ2t + 2e−(Γ1+Γ2)t=2 cos ((m m ) t) h j i 4 2 − 1 2 0 0 0 I0 −Γ1t −Γ2t −(Γ1+Γ2)t=2 I(K ) = K (t) K (t) = e + e 2e cos ((m2 m1) t) h j i 4 − − Mass difference between K1 and K2 required for oscillations to occur! Oscillations 1 ∆m τ1 = 0:5 · K0 y Intensit K0 0 0 10 t/τ1 Mass difference measured from rate of K0 decays as fct of time: 10 1 12 2 ∆m = (0:5303 0:0009) 10 hs¯ − 3:5 10− MeV=c × ' × Discovery of CP-Violation Incoming K2 beam, Helium filled decay volume Christenson, Cronin, Fitch, Turlay (Phys.Rev.Lett. 13, 138-140, 1964) el.se/physics/laureates/1980/fitch-lecture.html Signal: 56 events http://www.nob + 3 BR(K π π−) = 2 10− 2 ! × CP Violation in the Standard Model Following years: • Confirmation and other manifestations of the same phenomenon, 0 0 e.g. K π π and charge asymmetries in K πl∓ν. L ! L ! By 1973-74: • 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 CKM Matrix Three Quark-Doublets: Mixing of down-type quarks in charged weak interactions: CKM-Matrix VCKM : d0 Vud Vus Vub d s = V V V s 0 0 1 0 cd cs cb 1 · 0 1 b V V V b B 0 C B td ts tb C B C @ A @ A @ A CP-Violation in CKM Matrix 3x3 Matrix with four free parameters Wolfenstein parametrisation: ! λ2 3 1 2 λ Aλ (ρ iη) − 2 − λ 2 4 VCKM = λ 1 Aλ + (λ ) 0 − − 2 1 O Aλ3(1 ρ iη) Aη2 1 B − − − C @ A Complex elements Vtd and Vub allow for CP violation E.g.: CP-violating weak amplitudes from box-diagrams: ∗ ∗ u; c; t Vtd W Vtd s d s d 0 0 K0 W W K K0 u,c,t u; c; t K j i j i j i j i d s d s Vtd u,c,t Vtd W CP-Violation is a "built-in feature" of the Standard Model Kaon decays in the CP-mirror 0 0 + CP-Violation: Different Rates for K and K π π− ! K0 + Possible sources: 0 π π 1) CP/ in mixing from CPT/ K 0 0 K0 K0 = K K , ! 6 ! 0 2) CP/ in mixing from T/ K 0 0 K0 K = K K0 , ! 6 ! CP Mirror 3) Direct CP/ in decay 0 + 0 + K π π− = K π π− , ! 6 ! 1) 0 3) 4) CP/ in interference K between mixing and decay + 0 + 0 + 0 π π K π π− = K π π− K 4) (Interference, !between CP-violating6 !phases 2) 3) of different mixing and decay channels) K0 CP Violation Three types of CP Violation (from T Violation) CP violation in mixing • Γ(K0 K0) = Γ(K0 K0) ! 6 ! 3 Seen in K-System: 2 10− ∼ × CP violation in decay ('direct' CP violation) • Γ(A B) = Γ(A B) ! 6 ! 6 Seen in K-System: 0 5 10− ∼ × CP violation in interference between decays with and without • mixing: Seen in B-system: sin(2β) ( on Monday) ! CP Violation in Mixing The CP-Eigenstates K0 (CP=+1) and K0 (CP= 1) 1 2 − are modifed by -admixtures to form the physical short-lived and 0 0 long-lived states KS and KL 0 0 0 1 0 0 KS = p K + q K = ( K1 K2 ) j i j i j i 1 + 2 j i − j i j j 0 0 0 1 0 0 KL = p K q K = p ( K1 + K2 ) j i j i − j i 1 + 2 j i j i j j p 0 0 Γ(K0 K ) = Γ(K K0) q=p = 1 CP is violated ! 6 ! ) j j 6 ) CP violation via mixing: p q = − q=p = 1 2Re() p + q ) j j − Data Taking Period: 1990-1996 ® - 0p+ + 0p- Associated production