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Lectures 1 & 2 The Violation of Symmetry between Matter and Antimatter Andreas Höcker CERN CERN Summer Student Lectures, August 7-10, 2007 CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) M.C. Escher 1 A definition, which we will understand later in this lecture: The matter-antimatter symmetry violation in physics reactions corresponds to the breaking of the so-called CP symmetry C∙P CERN Summer Student Lectures 2007 violation A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 2 Matter-Antimatter Asymmetry q q 1 Early universe ? Current universe CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 3 Sakharov Conditions Is baryon asymmetry initial condition ? Possible ? Dynamically generated ? Sakharov conditions (1967) for Baryogenesis 1. 2. Baryon number violation new physics ! C and CP violation (probably) new physics ! 3. Departure from thermodynamic equilibrium (non-stationary system) CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 4 Note: ring is not necessarily due to dark matter ! Something Else is Strange Out There … CERN Summer Student Lectures 2007 Hubble space telescope picture of Cluster ZwCl0024+1652 Image: NASA, ESA, M.J. JEE AND H. FORD (Johns Hopkins University) A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 5 Something Else is Strange Dark Matter Out There … Dark matter does not emit or reflect sufficient electromagnetic radiation to be detected Evidence for dark matter stems from: gravitational lensing kinetics of galaxies Bullet cluster: Collision of galaxy clusters: baryonic matter, stars – weakly affected by collisions – and strongly Dark energy affected gas (pink in picture),Image and collisionless dark matter Dark matter (blue) Free H and He Stars Neutrinos 65% Heavy elements strongest gravitational lensing Foreground cluster anisotropy of cosmic microwave background (blackbody) radiation 30% 0.03% 0.03% 0.5% 4% gravitational lensing Mass density contours superimposed over photograph taken with Hubble Space Telescope CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 6 And: There is Much More Strangeness … Empirical and Theoretical Limitations of the Standard Model Dark matter (and, perhaps, dark energy) Baryogenesis (CKM CPV too small) Grand Unification of the gauge couplings The gauge hierarchy Problem (Higgs sector, NP scale ~ 1 TeV) The strong CP Problem (why is ~ 0 ?) Neutrino masses CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 7 The understanding of matter-antimatter symmetry violation is crucial if we want to move closer into the heart of the Big CERN Summer Student Lectures 2007 Bang A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 8 Lecture Themes I. Introduction Antimatter Discrete Symmetries II. The Phenomena of CP Violation Electric and weak dipole moments The strong CP problem The discovery of CP violation in the kaon system III. CP Violation in the Standard Model The CKM matrix and the Unitarity Triangle B Factories CP violation in the B-meson system and a global CKM fit Penguins IV. CP Violation and the Genesis of a Matter World Baryogenesis and CP violation Models for Baryogenesis CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 9 digression: CP Violation, a Family History of Flavour Discovery of strange particles Neutral kaons can mix (Rochester, Butler) (Gell-Mann, Pais) (1946-47) (1952) KL discovery (Lederman et al.) (1956) Parity (P) violation: possible explanation (Lee, Yang) (1956) P Violation found in decay (Wu et al.) later: maximum P and C violation, but CP invariance (1957) Cabibbo-Theory (1963) CP violation (CPV) discovered GIM-Mechanism (Glashow, Illiopolous, Maiani) J/ Resonance: c quarks CERN Summer Student Lectures 2007 (Cronin, Fitch et al.) (Ting, Richter) (1964) (1970) (1974) A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 10 digression: CP Violation, a Family History of Flavour CPV Phase requires 3 families Discovery of lepton: 3rd family (Kobayashi-Maskawa) (Perl et al.) (1973) (1975) resonance: b quarks (Lederman et al.) (1977) Neutral Bd mesons mix (ARGUS) (1987) t-Quark discovery (CDF) (1995) -Oscillation discovery (Super-K) Direct CP violation in K system (1998) (NA31, NA48, KTeV) (1999) Start of Bd Factories: BABAR (PEP II), Belle (KEKB) (1999) CPV in Bd system : sin(2) 0 (2001) Direct CPV in Bd system (BABAR, Belle) (BABAR, Belle) (2004) Bs mesons oscillate (CDF) (2006) D0 mesons oscillate (BABAR & Belle) (2007) CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 11 Through the Looking Glass What’s the Matter with Antimatter ? David Kirkby, APS, 2003 CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 12 Paul Dirac (1902 – 1984) Combining quantum mechanics with special relativity, and the wish to linearize /t, leads Dirac to the equation i x,t m x,t 0 (1928) for which solutions with negative energy appear Dirac, imagining holes and seas in 1928 Energy E me s 1/ 2 Dirac identified holes in this sea as “antiparticles” with opposite charge to particles … (however, he conjectured that these holes were protons, despite their large difference in mass, because he thought “positrons” would have been discovered already) 0 me Vacuum represents a “sea” of such negative-energy particles (fully filled according to Pauli’s principle) E s 1/ 2 This picture fails for bosons ! CERN Summer Student Lectures 2007 An electron with energy E can fill this hole, emitting an energy 2E and leaving the vacuum (hence, the hole has effectively the charge +e and positive energy). A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 13 Positron – Antiparticle incoming of the Electron Antineutron Antiproton incoming antiproton discovery 1955 antiproton 6 GeV Fixed target threshold 1956 Discovered in cosmic rays by Carl Anderson in 1932 (Caltech) energy required to produce p + p p + p + anti-p + p Reproduction Antiproton chargeof an Has the same mass as the electron but positive charge antiproton exchangeannihilation reaction into star asneutron-antineutron seen in nuclear emulsion pair in 63 MeV (source: O. Chamberlain, Lecture) propane bubble Nobel chamber Anderson saw a track in a cloud positron chamber left by “something (source: E.G. Segrè, Nobel Lecture) track positively charged, and with the same mass as an electron” 6mm Pb plate p + anti-p n + anti-n History of antiparticle discoveries: 23 MeV “annihilation star”positron (large energy release track from antiproton destruction) 1955: antiproton (Chamberlain-Segrè, Berkeley) “annihilation star” antineutron (Cork et al., LBNL) (large energy release 1965: antideuteron (Zichichi, CERN and Lederman,from BNL)antineutron destruction) 1995: antihydrogen atom (CERN, by now millions produced !) Every particle has an antiparticle Some particles (e.g., the photon) are their own antiparticles ! outgoing 1956: charged particles CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 14 Particles and Antiparticles Annihilate Fermilab What happens if we bring particles and antiparticles together ? A modern A particle can annihilate with its example: antiparticle to form gamma rays An example whereby matter is converted into pure energy by Einstein’s formula E = mc2 Conversely, gamma rays with sufficiently high energy can turn ALEPH into a particle-antiparticle pair Higgs candidate ee ZH (Z ) qqbb CERN Summer Student Lectures 2007 Particle-antiparticle tracks in a bubble chamber A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 15 Symmetries A symmetry is a change of something that leaves the physical description of the system unchanged. 1. Physical symmetries: People are approximately bilaterally symmetric Spheres have rotational symmetries 2. Laws of nature are symmetric with respect to mathematical operations, that is: an observer cannot tell whether or not this operation has occurred Pollen of the hollyhock exhibits spherical symmetry (magnification x 100,000) CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 16 Continuous Symmetries and Conservation Laws In classical mechanics we have learned that to each continuous symmetry transformation, which leaves the scalar Lagrange density invariant, can be attributed a conservation law and a constant of movement (E. Noether, 1915) Continuous symmetry transformations lead to additive conservation laws Symmetry Invariance under movement in time Homogeneity of space Isotropy of space Transformation Translation in time Translation in space Rotation in space Conserved quantity Energy Linear momentum Angular momentum No evidence for violation of these symmetries seen so far CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 17 digression: Symmetry of Reference Systems Another type of symmetry has to do with reference frames moving with respect to one in which the laws of physics are valid (inertial reference frames): Physical laws are unchanged when viewed in any reference frame moving at constant velocity with respect to one in which the laws are valid Note that while laws are unchanged between reference frames, quantities are not The fact that the laws of motion are unchanged between frames, plus the fact that the speed of light is always the same lead to the theory of special relativity with two consequences Two events that are simultaneous in one reference frame are not necessarily simultaneous in a reference frame moving with respect to it There are some quantities (called Lorentz scalars) that have values independent of the reference frame in which their value is calculated CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 18 Continuous Symmetries and Conservation Laws In general, if U is a symmetry of the Hamiltonian H, one has: H,U 0 H U †HU f H i Uf H Ui f U †HU i f H i Accordingly, the Standard Model Lagrangian satisfies local gauge symmetries (the physics must not depend on local (and global) phases that cannot be observed): U(1) gauge transformation Electromagnetic interaction SU(2) gauge transformation Weak interaction SU(3)C gauge transformation Strong interaction (QCD) Conserved additive quantum numbers: Electric charge (processes can move charge between quantum fields, but the sum of all charges is constant) Similar: color charge of quarks and gluons, and the weak charge Quark (baryon) and lepton numbers (however, no theory for these, therefore believed to be only approximate asymmetries) evidence for lepton flavor violation in “neutrino oscillation” CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 19 Discrete Symmetries Discrete symmetry transformations lead to multiplicative conservation laws The following discrete transformations are fundamental in particle physics: Parity P (“handedness”): Reflection of space around an arbitrary center; In particle physics: P eL eR These are interesting because it is not obvious whether the laws of nature should look the same for anyP of these Particle-antiparticle transformation C : P n n transformations, and the answer was surprising when Change of all additive quantum numbers (for example the Ce e these symmetries were firstconjugation”) tested ! electrical charge) in its opposite (“charge P invariance cannot know whether we live in this world, or in its mirror world 0 L 0 L Cu u Time reversal T : Cd d The time arrow is reversed in the equations; T invariance if a movement is allowed by a the physics law, the movement in the opposite direction is also allowed C 0 0 Time reversal symmetry (invariance under change of time direction) does certainly not correspond to our daily experience. The macroscopic violation of T symmetry follows from maximising thermodynamic entropy (leaving a parking spot has a larger solution space than entering it). In the microscopic world of single particle reactions thermodynamic effects can be neglected, and T invariance is realised. CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 20 C, P, T Transformations and the CPT Theorem Quantity P C T –x x x t t –t –p p –p s s –s Electrical field –E –E E Magnetic field B –B –B Space vector Time Momentum Spin The CPT theorem (1954): “Any Lorentz-invariant local quantum field theory is invariant under the successive application of C, P and T ” proofs: G. Lüders, W. Pauli; J. Schwinger Fundamental consequences: Relation between spin and statistics: fields with integer spin (“bosons”) commute and fields with half-numbered spin (“fermions”) anticommute Pauli exclusion principle Particles and antiparticles have equal mass and lifetime, equal magnetic moments with opposite sign, and opposite quantum numbers Best experimental test: CERN Summer Student Lectures 2007 m K 0 mK 0 / mK 0 1018 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 21 If CPT is Conserved, how about P, C and T ? Parity is often violated in the macroscopic world: Strongly Left-sided Strongly Right-sided Mixed Sided Handedness 5% 72% 22% Footedness 4% 46% 50% (?) Eyedness 5% 54% 41% Earedness 15% 35% 60% Porac C & Coren S. Lateral preferences and human behavior. New York: Springer-Verlag, 1981 About 25% of the population drives on the left side: why ? In ancient societies people walked (rode) on the left to have their sword closer to the middle of the street (for a right-handed man) !? The DNA is an oriented double helix Two right-handed polynucleotide chains that are coiled about the same axis: CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 22 Not so in the microscopic World ? Electromagnetic and strong interactions are (so far) C, P and T invariant Example: neutral pion decays via electromagnetic (EM) interaction : 0 but not 0 0 1 uu dd L 0,S 0 2 C B, E B, E , C 0 0 , C the initial (0) and final states () are C even: hence, C is conserved ! Generalization: P qq 1 L1 qq , C qq 1 LS qq , G uu (d ) 1 L S I uu (d ) Experimental tests of P and C invariance of the EM interaction: P invariance: BR 4 6.9 10 C invariance: BR 0 3 3.1 10 8 0 7 Experimental tests of C invariance of strong interaction: compare rates of positive and negative particles in reactions like: pp X , K K X CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 23 And … the Surprise in Weak Interaction ! T.D. Lee and C.N. Yang pointed out in 1956 (to explain the observation Lee & Yang: of the decays K 2 and 3 - the cosmic-ray / puzzle) that P invariance “Past experiments on theinteraction weak interactions hadperformed actually noinbearing on had not been tested in weak C.S. Wu of parity conservation.” 1957the thequestion experiment they suggested and observed parity violation “In strong interactions, ... there were indeed many experiments that Angular distribution of electron intensity: established parity conservation to a high degree of accuracy...” Pe v unequivocally whether parity is conserved in weak interactions, I (“To ) 1decide 1 cos E c e one must perform an experiment to determine whether weak interactions differentiate the right from where: - spin vector of electron helicity the left.” Pe - electron momentum Ee - electron energy Yang, C. N., The law of parity conservation and other symmetry laws of physics, Nobel Lectures Physics: 1942-1962, 1964. Lee, T. D., and C. N. Yang, Question of Parity Conservation in Weak Interactions, The Physical Review, 104, Oct 1, 1956. 1 for electron 1 for positron It was found that parity is even maximally violated in weak interactions ! CERN Summer Student Lectures 2007 TCO ~ 0.01 K polarized in magnetic field A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 24 P and C Violation in Weak Interaction Goldhaber et al. demonstrated in 1958 that in the decay of the nucleus, the neutrino (e–) is left-handed, while the antineutrino (e+) is right-handed: Particle : e Helicity : v / c e +v / c 1 1 ( C violation ! ) In the Dirac theory, fermions are described as 4-component spinor wave functions upon which 44 Operators i apply, which are classified according to their space reflection properties : † 0 , scalar (S ) 5 , pseudoscalar (P ) 4 4 current Lorentz-covariant bilinear , vector (V ) 5 , axial vector (A) , tensor (T ) P -even P -odd P -even P -odd antisymmetric tensor 2i CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 25 P and C Violation in Weak Interaction Let’s consider the reaction: n e p General ansatz for the current-current some constants matrix element : G M F p i n e i Ci 5Ci v 2 i S,... One transparency a bit of math Use the helicity projection with operators for Dirac spinors: u u uL uR uL… uRsorry uL u… L uR uR so that one has for a V interaction: while for a scalar interaction: uL / R 1 1 5 u 2 at high energies, the EM interaction conserves the helicity of the scattered fermions won’t happen again (almost) … 1 uL uR u L uR 4 u (1 52 )u 0 and similar for A 1 1 u (1 5 )u 0 2 and similar for P, T Now, consider the weak neutrino-electron current in the relativistic limit: ue V A u ue 1 1 5 u ue,L ue,R u ,L ue,L u ,L 2 It projects upon the left handed helicities, and hence violates P maximally, as required ! CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 26 P and C Violation in Weak Interaction Weak interaction violates both C and P symmetries e e Consider the collinear decay of a polarized muon: polarized P The preferred emission direction of the light left-handed electron is opposite to the muon polarization. handedness of the electron: C suppressed P transformation (i.e. reversing all three directions in space) yields constellation that is suppressed in nature. Similar situation for C transformation (i.e. replace all particles with their antiparticles). suppressed handedness of the positron: CERN Summer Student Lectures 2007 B. Cahn, LBL Applying CP, the resulting reaction—in which an antimuon preferentially emits a positron in the same direction as the polarization—is observed. A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 27 … and tomorrow, we will CERN Summer Student Lectures 2007 see A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 28 CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 29 Lecture Themes I. Introduction Antimatter Discrete Symmetries II. The Phenomena of CP Violation Electric and weak dipole moments The strong CP problem The discovery of CP violation in the kaon system III. CP Violation in the Standard Model The CKM matrix and the Unitarity Triangle B Factories CP violation in the B-meson system and a global CKM fit Penguins IV. CP Violation and the Genesis of a Matter World Baryogenesis and CP violation Models for Baryogenesis CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 30 CP Violation CP Symmetry requires that processes and their anti-processes have the same rates 1. Due to the CPT theorem, CP symmetry also requires T symmetry 2. CP violation would enable us to distinguish between particles and antiparticles, and between past and future in an absolute way(*) ! two worlds that are far away want to gather together: if one were made of matter, and the other one of antimatter, the spaceship of the one that landed on the planet of the other would lead to a disastrous annihilation. This could be prevented by measuring a CP violation parameter (if exists) by both worlds and comparing the results. CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) © CPEP (*)Imagine 31 Dipole moments Can there be CP violation in the electromagnetic or neutral weak current ? Let’s modify the Standard Model Lagrangian to allow for CP violation through electromagnetic and weak dipole moments: LCP i 5 2 d EM F d weak Z where F and Z are electric and weak field strength tensors. In the nonrelativistic limit one obtains the Pauli equation with the additional terms: LCP d EM E d weak Z But…. why do these dipole moments violate CP symmetry ? CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 32 Dipole Moments and CP Violation Spin is the only explicit “direction” of an elementary particle. Hence the dipole moment must be proportional to it d s The electric dipole moment is the average of a charge density distribution polar vector d d 3 x (x) x spin The spin has the form of angular momentum axial vector s r p Parity transformation gives: Pd d , Ps s d 0 + – P dipole moment – + P invariance Time reversal transformation gives Td d , Ts s d 0 T invariance T + – + – Non-vanishing electric or weak dipole moments require the presence of a P- and T-violating (=CP-violating) interaction CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 33 Experimental Limit on dEM (e.cm) d(muon) 7×10–19 neutron: electron: 10-20 10-20 10-22 10-22 10-24 10-24 10-26 Multi Higgs Electromagnetic d(proton) 6×10–23 d(neutron) 6×10– SUSY 26 d(electron) 1.6×10– 27 10-28 Left-Right present experimental limits 10-30 10-30 none of this seen yet, why ? 1960 1970 1980 1990 2000 10-32 The Measurement of EDMs: History of the experimental progress 10-34 Standard Model 10-36 10-38 CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 34 digression: CP Violation in the QCD Lagrangian It was found in 1976 that the perturbative QCD Lagrangian was missing a term L LQCD LpQCD perturbative QCD L , where: L P ,T -violating s 8 a G G ,a , and G ,a Gluon field tensors 1 G ,a 2 dual field tensor that breaks through an axial triangle anomaly diagram the U(1)A symmetry of LpQCD , which is not observed in nature when classical symmetries are broken on the quantum level, it is denoted an anomaly a ,a a The term G is P-and T-odd, since: G ,a contained in LpQCD is CP-even, while G G GG Ea Ba a 2 GG Ea Ba a 2 E P,T 2 a a P,T Ea Ba a Ba 2 color electric and magnetic fields Relativistic invariants, similar to electric field tensors: F F , F F F j , F 0 Maxwell equations This CP-violating term contributes to the EDM of the neutron: dn 5 1016 ecm, so that tiny or zero "Strong CP (finetuning) Problem" CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 35 The Strong CP Problem Remarks: If at least one quark were massless, L could be made to vanish; if all quarks are massive, one has uncorrelated contributions, which have no reason to disappear Peccei-Quinn suggested a new global, chiral UPQ(1) symmetry that is broken, with the “axion” as pseudoscalar Goldstone boson; the axion field, a ,compensates the contribution from L : a ,a axion coupling to SM particles is L a s G G suppressed by symmetry-breaking fa 8 scale (= decay constant) QCD nonperturbative effects (“instantons”) induce a potential for a with minimum at a = fa The axion mass depends on the UPQ(1) symmetry-breaking scale fa 107 GeV ma 0.62 eV , f (GeV) a and axion coupling strength: ga ma If fa of the order of the EW scale (v), ma~250 keV excluded by collider experiments CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 36 The Search for Axions (the axion is a dark matter candidate) The axion can be made “invisible” by leaving scale and coupling free, so that one has: ma ~ 10–12 eV up to 1 MeV 18 orders of magnitude ! Axion scale and mass, together with the exclusion ranges from experimental non-observation Axion decays to 2, just as for the 0, or in a static magnetic field: a f Schematic view of CAST experiment at CERN: Axion source CERN Summer Student Lectures 2007 Axion detection (LHC magnet) A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 37 The Discovery of CP Violation CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 38 Ingredients … Strange Particles Strange mesons have an “s” valence quark Non-strange particles: ( , , )I 1 : ud , (uu dd ) / 2 (,, )I 0 : (uu dd ) / 2 neutral particles are eigenstates of C operator (K ,K , )I 1/ 2 : K us , K us, K 0 ds , K 0 ds Strange particles: neutral strange particles are not eigenstate of C operator Production of strange particles via strong or electromagnetic interaction has to respect conservation of the S (“strangeness”) quantum number (they are “eigenstates” of these interactions) S 0 S 0 S 0 p S 0 S 0 S 0 p S 1KS01 S 0 pS 0KS1KS01 S 0 pS 0 pS 0 S 0 S0KS1KS01 S 0 , S0KS1KS01 S 0 e S 0 S 0 S 0 CERN Summer Student Lectures 2007 e S 0 KS01KS01 S 0 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 39 The Discovery of CP Violation Empirically (in the experiment) one does however not observe the neutral “flavor eigenstates” K 0 and K 0 but rather long- and short-lived neutral states: KL and KS Their observed pionic decays are: KS and it was believed that: CP KS KS 0 and K L and CP KL KL 0 Larger phase space of 2 decay: KL / KS 580 However, Cronin, Fitch et al. discovered in 1964 the CP-violating decay: K L Measurement of opening angle of pion tracks and their invariant mass: + – Jim Cronin KL events Today’s most precise measurement of amplitude ratio: A K L A KS 2.282 0.017 10 3 Val Fitch CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 40 Observing CP Violation at the Factory The KLOE experiment at the Factory DANE (Frascati, Italy) can detect single CPviolating decays: K 0K 0 and equivalently: KS K L KS K L Note that the quantum coherence is broken after the decay of one of the two K0’s CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 41 The Discovery of CP Violation in the Charged Weak Current To understand the observed CP violation from the flavor perspective, let us construct CP eigenstates with CP eigenvalues ±1: K1 , CP 1 K2 , CP 1 1 K0 K0 2 1 K0 K0 2 While the flavor eigenstates are distinguished by their production mechanism, the CP eigenstates are distinguished by their decay into an even and odd number of pions. Since there is CP violation, the physical states (“mass eigenstates”) are not exactly the same as the CP eigenstates: KS 1 K 1 L where: q / p 1 / 1 CERN Summer Student Lectures 2007 2 K1 K 2 K K 1 2 0 1 p q K 0 2 p q K 0.995 1 (!) A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 42 CP Violation and Neutral Kaon Mixing CPLEAR (CERN) measured the rates of K 0 ,K 0 (t ) (using initial state strangeness tagging) as a function of the decay time, t, and finds quite a surprise: after acceptance correction and background subtraction K 0 rates are at different for the s-tagging production: two flavor states 0 K K pp 0 charge of K K K K 0 there is a non-exponential component (?) CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 43 Neutral Kaon Mixing Neutral kaons can “mix” through the charged weak current, which does not conserve strangeness, and neither P nor C. Weak interaction cannot distinguish K 0 from K 0 Simple picture: they mix through common virtual states: 0 K0 K0 0 Neutral kaons with fixed strangeness quantum number do not exist in nature ! Note: A priori, mixing has nothing to do with Because Δm(K) = m(KL) – m(KS) = 3.5 10–12 MeV > 0, a K 0 will change with time into CP violation ! a and K 0 vice versa These oscillations are described in QCD by ΔS = 2 Feynman “box” diagrams: [S=2] s K CERN Summer Student Lectures 2007 0 t,c d W d W t ,c s K0 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 44 Neutral Kaon Mixing An initially pure K0 state, will evolve into a superposition of states: K (t ) g(t ) K 0 h(t ) K 0 The time dependence is obtained by solving the time-dependent Schrödinger equation: K 0 (t ) d i 0 dt K (t ) K 0 (t ) M i 0 2 K (t ) with 22 matrices M, , of which the offdiagonals Δm, Δ govern the mixing The respective time-dependent intensities are found to be (neglecting CP violation): I (T ) / I (0) K0 IK 0 t e Lt 2e Lt / 2 cos m t IK 0 t e Lt 2e Lt / 2 K L0 cos m t K0 After several KS lifetimes, only KL are left T t /S CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 45 Neutral Kaon Mixing and CP Violation Since KS and KL are not CP eigenstates, the time dependence has to be slightly modified by the size of , giving rise to an additional sine term. K 0+ K 0 – Let’s get back rates: Asymmetry: Ato the 0 decay cos m t K K 0 Neglecting other sources of CP violation & assuming arg() = /4. CPLEAR 1999 dominated by KS+– K 0 A N(KS+–) ~ N(KL+–amplitude ) || Large interference with opposite sign K 0 CERN Summer Student Lectures 2007 dominated by KL+– A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 46 There are in Fact Four Meson Systems with Mixing Pairs of self-conjugate mesons that can be transformed to each other via flavor changing weak interaction transitions are: K 0 sd Bd0 bd D0 cu Bs0 bs They have very different oscillation properties that can be understood from the “CKM couplings” (see later in this lecture) occurring in the box diagrams N(T ) / N0 for the plot xsD == 15 0.02 ysD == 0.10 0 sD == 00 Bs0 Bs0 00 0 0 B 00 B 0 K s s0 D KD B d Bd mixing probability: ~~ =210 18%–6 50% K L0 Bd0 Bd0 0 K K0 T CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 47 Three Types of CP Violation The CP violation discovered by Cronin, Fitch et al. involves two types of CPV: CP Violation in mixing: Prob(K 0 K 0 ) Prob(K 0 K 0 ) CP Violation in interference between decays with and without mixing : also called: “indirect CPV” Prob(K 0 (t ) ) Prob(K 0 (t ) ) However, there is yet another, conceptually “simpler” type of CP violation yet to discover: CP Violation in the decay: Prob(K f ) Prob(K f ) CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) also called: “direct CPV” 48 “Direct” CP Violation = CP Violation in Decay General signature: rate differences between CP-conjugated processes: i f i f It necessarily involves interference of amplitudes contributing to the processes. To obtain interference, we need phases that change sign under CP Example: if the decay amplitudes are given by: a1,2 ,1,2 A i f A i f a1e i1e i1 a2e i2 e i2 a e 1 i1 e i1 a2e i2 e i2 e 2i (i f ) j alters sign under CP (“weak phase”) j CP invariant (“strong phase”) unphysical phase where: i f A i f 2 and i f A i f 2 We can define the following CP asymmetry ACP: ACP i i f CERN Summer Student Lectures 2007 f i i f f a 2a1a2 sin 1 2 sin 1 2 2 2 1 a2 2a1a2 cos 1 2 cos 1 2 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 49 CP Violation in the Kaon Decay We have seen that at least two amplitudes with different CP-violating (weak) and conserving (strong) phases have to contribute to the decay for direct CPV. This suppresses this type of CPV, so that the observable effect should be small compared to . To allow for (small) direct CPV, we need to slightly modify our previous definitions: 2 K L KS and use also: 2 2 KL 0 0 KS 0 0 “Clebsch-Gordon isospin” factor when passing from charged to neutral pions If the observed CP violation is different in the two decay modes, we have a prove for a contribution from direct CP violation. From the measurement of the ratio of these decayrate ratios we can determine ’ The observable KL 0 0 KS 0 0 KL KS 2 2 1 6 Re First order Taylor expansion CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 50 The Discovery of CP Violation in the Decay Due to the smallness of the effect, it took several experiments and over 30 years of effort to establish the existence of direct CPV Feynman graphs: K 0 “Tree” (born-level) amplitudes K 0 s d s d u d u d W W u u d d Experimental average Indeed, a very small CPV effect ! 0 0 (16.7 ± 2.3)10–4 Interference W “Penguin” (loop-level) amplitude s K 0 d CERN Summer Student Lectures 2007 t, c,u g d u u d A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 51 And the Theory ? Direct CP violation is in general very hard to calculate due to its sensitivity to the relative size and phase of different amplitudes of similar size… Many theoretical groups have put serious efforts into this. All agree that the effect is much smaller than the indirect CPV (which is a success for the Standard Model !), but the theory uncertainties are much larger than the measurement errors: Theoretical pre(post)dictions plot not updated ! ...the ball is on the theory side courtesy: G. Hamel de Monchenault e n d CERN Summer Student Lectures 2007 o f L e c t u r e 1&2 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 52 Conclusions of the first two Lectures No CP violation without antimatter ! P, C, T are good symmetries of electromagnetic and strong interactions P, C are maximally violated in weak interaction CP, T are not good symmetries of weak interaction no other source of CP violation has been found so far (EDM’s) CP violation has been first discovered in the kaon system, and both, Cartoon shownCP by N.violation Cabibbo in 1966… then, there was tremendous direct and indirect havesince been observed progress in the understanding (better: description) of CP violation next lecture ! CERN Summer Student Lectures 2007 A. Höcker: The Violation of Symmetry between Matter and Antimatter (1 & 2) 53