Andreas Meyer Hamburg University

CP/ Part 1

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 ψ(~r, t) = P ψ( ~r, t) a − Possible Eigenvalues of the Parity-Operator are 1. b

P P ψ(~r, t) = ψ(~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 → Y Y

Y ' Y Y '

Y Û ' Û L' Û LY Û

Û + Û + L+ Û L+ 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− √ √ √ √ √ − 16 21 el-mag. charged photon 10− 10− √ √ √ √ √ − 0 3 13 weak all W , Z 10 10− 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 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 | i | i | i | i d s d s u W Eigenstates of P,C and CP ?

0 0 P K0 = K0 P K = K | i −| i | i −| i 0 0 C K0 = K C K = K0 b b | i −| 0i | i0 −| i CP K0 = + K CP K = + K0 b| i | i b | | 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− | 1 i √2 | i | i → 1 × 0 1 0 0 7 K = K K 3π CP= 1 τ = 0.5 10− | 2 i √2 | i − | 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− | 1 i | 1 i 0 0 (im2+Γ2/2)t K (t) = K (0) e− | 2 i | 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) | i t=0 √2 | 1 i | 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 | 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 | i 4 − −

Mass diﬀerence between K1 and K2 required for oscillations to occur! Oscillations

∆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   cd cs cb  ·   b V V V b  0   td ts tb          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 )  − − 2  O Aλ3(1 ρ iη) Aη2 1  − − −    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 | i | i | i | 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 ) | i | i | i 1 + 2 | i − | i | | 0 0 0 1 0 0 KL = p K q K = p ( K1 + K2 ) | i | i − | i 1 + 2 | i | i | | p 0 0 Γ(K0 K ) = Γ(K K0) q/p = 1 CP is violated → 6 → ⇒ | | 6 ⇒ CP violation via mixing: p q = − q/p = 1 2Re() p + q ⇒ | | − Data Taking Period: 1990-1996

^ Y +L' ' +LY

Associated production of K-pairs (via strong i.a.) 0 Tag whether K0 or K by charge of other Kaon

¤ ¡£¢ Y L '

^ + h _ Y L ' L ^ + h 0 K Interference and 0 from K een w et Diﬀerence b Õ & 0 ) Õ + & E + ) . ) , ++ . E / - %

) Ç . / % R Z . Y Y Z ' + . Ç , Y + Z & , 3 Z Y Y + + , & L L L L + , ) ' + ' + , ) + L L L L + E E / ^ ^ ^ ^ . 3 - - ) ) - - % % Y + ' +

Ç Ç Direct CP Violation

0 + 0 + K π π− = K π π− → 6 →

W s d + u π u,c,t 0 K g,Z, γ u π− d d Interference of amplitudes with diﬀerent isospins

A2 0 Im( exp(i(δ2 δ0)) ∼ A0 − modiﬁes measured from CP/ in mixing by small amount 0: + KL π π− η+ = → + = + 0 − KS π π− → 0 0 KL π π η = → = 20 00 K π0π0 − S → 0 0 0 0 Γ(K π π )/Γ(K π π ) 0 R = L → S → 1 6Re( ) Γ(K π+π )/Γ(K π+π ) ' − L → − S → − NA48 simultaneous and collinear KS and KL beams not to scale ! SPS spill length : 2.38 s K S anticounter Cycle time : 14.4 s Ks (AKS) Proton momentum : 450 GeV/c Target

K Target NA48 L 12

6.8 cm ~1.5 10 protons per spill ~1.5 10 protons per 0.6 mrad ¢£ ¢£ ¢£ ¢£ ¢£ ¢£ ¢£ ¢£ ¢£

¢£ K ¢£ Detector ¡ Muon sweeping L ¡ ¡ ¡ ¡

Bent ¡ ¡ ¡ ¡ ¡ ¡

cristal ¡ Last collimator Ks tagging station Decay Region ( ~3. 10 7 protons per spill) (~ 40 m long)

~ 126 m ~ 114 m

KS and KL beams are distinguished by proton tagging upstream of the KS target.

CERN Seminar 8 Guillaume Unal 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 π0π0 events

CERN Seminar 13 Guillaume Unal Measurement at NA48

0 0 0 0 Γ(K π π )/Γ(K π π ) 0 R = L → S → 1 6Re( ) Γ(K π+π )/Γ(K π+π ) ' − L → − S → −

K0 target: 126 m upstream • L Average K0-momentum: 110 GeV • Decay lengths: K0: 5.9 m, K0: 3400 m • S L Relative angle of K0-beam: 0.6 mrad • S Select K0 and K0 by timing of tagged protons (∆t < 2 ns) ⇒ S L Correct for contamination in charged decays, using horizontally ⇒ separated decay vertices. Tagging

K→π+π- (vertex selected)

Tagging Window Events

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 + 4 P(K K ) : α − = (1.12 0.03) 10− S → L SL × Accidental tagging + P(KL KS ) : αLS− = (8.115 0.010)% (it was→(10.649 0.008)% in 98-99) In the Double Ratio we account for the accidental tagging

M. Lenti CERN Seminar Precise results from Na48 and KTeV Re(ε,/ε)

E731 93 7.4 ± 5.9 NA31 93 23.0 ± 6.5 NA48 01 (prel) 15.3 ± 2.6

KTEV 01 (prel) 20.7 ± 2.8

0 10 20 30 (x10-4)

New World Ave. 17.2 ± 1.8 History of 0/ measurements Kaons According to PDG 2002

0 0 KS KL + 0 69% π π− 21% 3π 0 0 + 0 31% π π 13% π π−π 27% πµν 39% πeν + 0.2% π π− 0.1% π0π0

10 1 m 0 m 0 = (0.5303 0.0009) 10 hs¯ − KL − KS × 3 = (2.282 0.017) 10− × 3 δL = (3.27 0.12) 10− × 3 0/ = (1.8 0.4) 10− × Note: absolute value of 0 is (10−6) O Summary

CP violation: Necessary ingredient for baryogenesis. 3 Observed for the ﬁrst time 1964 in the Kaon system ( = 2 10− ) × In contrast: P and C are maximally violated

Kaon physics over last 40 years, impressive precision reached ∼ 6 Direct CP Violation established recently (0 = 5 10− ) ×

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 →