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The Violation of Symmetry between Matter and Antimatter

Lecture 3. The Violation of Symmetry between Matter and Antimatter. Andreas Höcker CERN. CERN Summer Student Lectures, August 5 – 8, 2008. M.C. Escher. Lecture Themes. Introduction Antimatter Discrete Symmetries The Phenomena of CP Violation Electric and weak dipole moments

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The Violation of Symmetry between Matter and Antimatter

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  1. Lecture 3 The Violation of Symmetry between Matter and Antimatter Andreas Höcker CERN CERN Summer Student Lectures, August 5 – 8, 2008 M.C. Escher

  2. Lecture Themes • Introduction • Antimatter • Discrete Symmetries • The Phenomena of CP Violation • Electric and weak dipole moments • The strong CP problem • The discovery of CP violation in the kaon system • 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 • The Future at the LHC • CP Violation and the Genesis of a Matter World • Baryogenesis and CP violation • Models for Baryogenesis

  3. CP Violation in the Standard Model We have learned that different types of CP violation have been observed … we will later see that there is also CP violation in meson systems other than kaons. All these phenomena can be described by a unique parameter in the Standard Model !

  4. Left-handed quarks are fermions organized in doublets: up-type quarks (Ui): down-type quarks (Di): …and similar for the leptons. The Standard Model • The Standard Model forces and their gauge bosons: • The charged weak current is of V–A type: The operator projects upon left-handed particles (and right-handed antiparticles) – which means that the W± boson is blind to the right-handed particles (and left-handed antiparticles)

  5. flavor representation There are 33 of these • Again: since mass and flavor eigenstates are not the same  quark mixing: Cabibbo-Kobayashi-Maskawa (CKM) matrix– 1973 (KM) Three-Generation Quark Mixing • The charged weak current generates transitions between generations, i.e., the flavoured quarks are not the same as the physical quarks: Quark mixing would simplify (= reduced parameter space) if some of the quarks had equal masses and would hence not be distinguishable !

  6. Recall: Since H = H(Vij), complex Vij would generate [T,H]  0  CP violation only, if: CP Violation in the Standard Model • What does CP or T conjugation with the Hamiltonian H ? • Simple exercise: The T (and CP) operations are anti-unitary, which is complex conjugation ! • CP conservation is: (up to unphysical phase) =

  7. The Quark-Mixing Matrix • The |Vij |2 are transition probabilities and hence the matrix must be unitary • For example, a t quark can decay into a d, s, or b quark and nothing else; thus, the sum of the decay probabilities into these quarks must be one: • Unitarity condition: • The unitarity condition sets strong constraints on the Vij , which initially has 2N2 unknowns (N is number of generations)

  8. Example for N = 2 generations: • 8 Unknowns – 4 moduli and 4 phases • Unitarity gives 4 constraints : • For 4 quarks, we can adjust 3 relative phases Only 1 parameter, a rotation (= Cabibbo) angle left: no phase  no CPV Quark-Mixing Matrices for Different Generations • Example for N = 1 generation: • 2 Unknowns – module and phase: • Unitarity determines |V| = 1 • The phase is arbitrary (non-physical): …with same physics No phase, no CPV

  9. Number of rotation angles : • For N generations: Number of phases : Quark-Mixing Matrices for Different Generations • Example for N = 3: • 18 Unknowns – 9 moduli and 9 phases • Unitarity gives 9 constraints • For 6 quarks, we can adjust 5 relative phases 4 Unknown parameters left, 3 rotation (Euler) angles and 1 phase  CPV ! • Example for N = 4: • 32 Unknowns, 16 unitarity constraints, 7 arbitrary phases 9 Unknown parameters left, 6 rotation angles and 3 phases  lots of CPV !

  10. Flavour-changing transition by charged weak current (boldness indicates transition probability  |Vij|) 3 Quark generations Smallest couplings are complex  CP violation Quark Flavours in the Standard Model • Quarks (as leptons) in the SM are organized in 3 generations: Charge: 1/3 Charge: +2/3 log10( mass [MeV/c2] ) top bottom charm strange down up

  11. The CKM Matrix in the Wolfenstein Parameterization • The 3-generation CKM matrix has 4 unknowns, one of which is a phase • Flavor-changing transitions between families are allowed, but are small • We can develop the CKM matrix elements around the small flavor-changing transition between the 1st and the 2nd family (the Cabibbo mixing), denoted   0.2 : • Decay-rate measurements give: Strong-interaction form factor (taken from theory) • How can we determine the CP-violating phase ?

  12. multiply multiply multiply CKM-type CP violation is always a rare phenomenon: • Either the CP asymmetry is small • Or/and the decay rate is suppressed Im relative size of CP-violating effect The CKM Matrix and the “Unitarity Triangle(s)” • The 9 unitarity conditions of the 33 generations CKM matrix:   multiplying a line with its complex conjugate • The 6 complex “Unitarity Triangles” involve different physics processes

  13. Im Im Im Q q W– Q CP Violation (Im[...]  0) VqQ q Re Re Re phase invariant : The CKM Matrix and the Unitarity Triangle Kobayashi-Maskawa, 1973 d s b u c t    Culminating Point SM or new phases (fields)?

  14. KEK E391a  KAMI  ATLAS BTEV  III  KEK / J-PARC Super-BABAR  ??? ??? ??? Super-KEKB ??? Planned experiments that were not ratified FNAL P940 Approved experiments (mostly in construction) New proposals ??? E787/949 NA48 NA48/3 upgrade ??? CLEO-c LOI-04/05 Currently running or recently ended programs CKM Physics and CP Violation Worldwide Experimental Facilities

  15. The B-Meson System The study of CP violation, mixing and rare decays of B mesons allows to over-determine the Unitarity Triangle (UT) • Relative CP-violating effects are expected to be large • Requires dedicated experiments • Goal: measure all three angles, , , , and the sides of the UT concentrate lecture on this measurement

  16. The BdSystem(e+e–(4S) factories) the Bd is also produced by the hadron machines

  17. Like for the K0, the B0 can first mix and then decay into the “CP eigenstate (?)” J/K0 not bad  • Also the K0 in the decay must mix for interference good  The Measurement of (… or more precisely: sin2) We need to identify the processes that involve the CKM matrix elements that occur in the definition of  : • The decay b  c : is that what we want ? 

  18. Why do you call these Penguin diagrams?They don’t look like penguins! A controversy… I’ve never seen a Feynman diagramthat looks like you c b mix mix c W+ B0 mixing K0 mixing s d d s d d b s d d b c b g c u c t s Mirror image of Richard Feynman d d B0 decay Penguin : 1. Clean CP phase 2. Nodirect CPV Single weak phase: Courtesy: G. Hamel de Monchenault The Golden Channel: Relative phase: B0 decay

  19. What are the Experimental Requirements ? • The Observable : • We need to measure: • Identify a final state that is CP eigenstate (e.g., J/KS) • Determine the flavour of the decaying B0 (assume here it is a B0) • How can we do this if J/KScan be reached by both B flavors ? • If we could produce the B0B0 pairs in a coherent quantum state, we could “tag” the flavor of the decaying B0 from the flavor of the other B, not decaying into a CP eigenstate  see later • Since the coherence is destroyed once one of the two B’s decays, we need the decay time difference between the two B’s to calculate the flavor of the tagged B at the time when the B0 decayed: t Δt _ We must determine the decay time difference of the B’s by measuring their decay vertices

  20. digression: Quantum Mechanics for (4S)  BB Decay proper times: J PC = 1– – Two pseudoscalar bosons in a P-wave antisymmetric wave function flavor and mass eigenstates: • initial state: • double proper-time wave function: where:

  21. Quantum Coherence at (4S)  BB Decay one and one Quantum coherence (due to synchronous evolution) for t = 0, the system is the superposition of: one and one one and one An Einstein-Podolsky-Rosen phenomenon: The measurement of the flavor (or CP) of one meson (e.g. from its decay products)determines the flavor (or CP) of the other meson at the same proper time (it is opposite) For the study of time evolution, one needs to measure t. However, at the (4S): flight distance d* ~ 30 m (beyond experimental reach) Cannot perform decay-time-dependent measurements ?

  22. Pier Oddone’s Clever Idea (1987) Why not produce the (4S) with a strong boost?One could deduce the t from the distance between the two B vertices along the boost axis. What we need is an asymmetric-energy B Factory with peak luminosity of order 5X1033 cm–2s–1 PEP-II: 9 GeV e– on 3.1 GeV e+ : • Coherent neutral B pair production and decay (P-wave) • Boost of (4S) in lab frame : = 0.56 Pier Oddone,LBL (now: FNAL) Oddone & Dorfan in PEP-II Tunnel, 2003 10 years later exist two asymmetric B Factories :PEP-II at SLAC and KEKB at KEK

  23. The B Factories: PEP-2 (SLAC, USA) and KEK-B (KEK, Japan) Linac Fixed Target Experiments BABAR SLD (& MARK II) PEP-II delivered L = 557 fb–1 Peak record: 1.2 1034 cm–2s–1 KEKB delivered L = 850 fb–1 Peak record: 1.7 1034 cm–2s–1

  24. The Asymmetric B Factory KEK-B EMC 6580 CsI(Tl) crystals 1.5 Tsolenoid e+ (3.1GeV) DIRC (PID) 144 quartz bars 11000 PMTs Drift Chamber 40 stereo layers e– (9 GeV) Silicon Vertex Tracker 5 layers, double-sided strips Instrumented Flux Return iron / RPCs (muon / neutral hadrons) The BABAR Detector

  25. PEP-2 (SLAC) Analysis Technique at the B Factories B-Flavor Tagging ~ 68% of events can be tagged. Quality Q ~ 30.5%  ~ 1/Q Exclusive B Meson Reconstruction Vertexing &Time DifferenceDetermination

  26. Flavor tag : Recoil B + vertex separation = time difference

  27. BABAR CP mixing CP = –1 (J/ KS …) decay Wonderful measurements … … what do they tell us ? . • Direct CP Violation is due to interference of decay amplitudes with different weak and hadronic phases BABAR First observed by NA48 and KTeV in kaon system . Discovery of CP Violation in the B System • CP Violation due to the interference of decays with and without mixing = sin(2) = 0 with : and for B  J/ K0, K0 Already seven charmless modes with evidence or hints for direct CPV !

  28. A Standard Model Prediction for sin(2)? How ?  Since the CKM matrix describes all CP-violating effects by a single phase, and the complete quark-mixing matrix depends only on 4 parameters, we can constrain it (for example, using the CP measurements in the kaon sector) and hence obtain a prediction for sin(2). We can even overconstrain the CKM matrix by a global fit using all the available information, and thus search for inconsistencies that would reveal the presence of new physics !

  29. Some processes need larger data samples, now approached by the B factories: • CP-violation measurements in B0  +–, +– +– determine • Direct-CP-violation measurements in B  DK determine • The rates of b dloop transitions determine |Vtd| • The leptonic decay B+ + (“tree annihilation”) determines |Vub| The Global CKM Fit • To determine (and then predict) the phase of the CKM matrix we need to measure processes that involve the matrix elements Vuband Vtd, i.e.:  and  • Some processes are already well established: • The rate of b u transitions determine |Vub| • Indirect CP Violation in the kaon system () is sensitive to Vtd • Neutral Bd mixing determines |Vtd| (reduce theory uncertainty by also using neutral Bs mixing) • Mixing-induced CP violation in B system determines sin(2)[arg(Vtd)]

  30. FIT RESULTS FIT INPUT Results for Summer 2007 http://CKMfitter.in2p3.fr

  31. & The Unitarity Triangle f r o m t h e g l o b a l C K M f i t Inputs: lower limit

  32. The global fit shows that the Kobayashi-Maskawa mechanism is the dominant source of CP violation at the energy scale of the electroweak interaction No need so far for physics beyond the Standard Model The Unitarity Triangle f r o m t h e g l o b a l C K M f i t SUMMER2008 The big picture

  33. New Physics?  digression: Are All Measurements Consistent ? • Almost, but not quite all yet …  more sensitivity to unknown heavy fields from loop diagrams Diagram: Tree“Penguin”-loop diagram CP observable: sin(2)[J/ K0] sin(2)[K0] • The penguin diagram prefers heavy virtual fields in the loop; penguin-to-tree ratio: • GUT-inspired example for SUSY penguin diagram:

  34. Naïve average: neglecting theory uncertainties !!! digression:CP Violation in Penguin Modes 3.7 discrepancy 2.7 discrepancy 2.8 discrepancy Summer ‘07 Winter ‘05 Summer ‘05 Summer ‘06 Naïve average has bad CL, which may indicate that it is indeed problematic

  35. ATLAS CMS ALTAS and CMS concentrate on “high-pT” discovery physics. Their B-physics potential relies on the low-pT performance of the Trigger systems. LHCb LHCb is not a fixed-target exp-eriment (looks like one). It con-centrates on low-pTB physics. Virtues over ATLAS & CMS: Low-pTtrack trigger, particle ID & better mass resolution The Future of B Physics and CP Violation at the LHC

  36. B Physics at Tevatron and LHC ATLAS B physics at hadron colliders is complementary to the e+e–B factories. Strengths: High statistics; accesses the Bs; sensitive to very rare modes, if clean signature; production of b baryons and Bc mesons Weaknesses: Worse tagging (no quantum coherence) and background; no rare modes with neutrinos can be reconstructed; less efficient for 0;

  37. mixing frequency: mixing phase: Frequency: just measured by CDF! CKM fit prediction not very precise yet (needs ) Phase: not measured yet, but precisely known in SM: excellent probe for new physics digression: B Physics at Tevatron and LHC digression: B Physics at Tevatron and LHC Prime Measurements:(many, many more interesting measurements to be done!) • Bs mixing frequency and phase: • Bs +– : FCNC (box & EW-penguin-mediated) rare decay (BR ~ 3 ∙10–9; current limit (CDF) < 5.8 ∙10–8 at 95% CL)

  38. CP Violation and the Genesis of a Matter World … and tomorrow ? … we’ll talk about US !

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