1. November 19, 1999CP Violation in B Meson Decays1 Math/Physics Undergraduate Colloquium Daniel Marlow Princeton University November 19, 1999

2. CP Violation in B Meson Decays2 Outline Introduction to Particle Physics P, C, CP, T and CPT CP Violation in the B System Kobayashi Maskawa Quark Mixing Direct CP Violation B mixing (matter-antimatter oscillations) The EPR effect The Tools (mainly photographs) The Accelerator The Detector

3. November 19, 1999CP Violation in B Meson Decays3 Princeton People PhDs: Kazu Hanagaki, Ted Liu*, DRM, Eric Prebys Graduate Students: Kirill Korotushenko, Jack Laiho, Christos Leonidopoulos, Chris Mindas*, Sven Vahsen Undergraduates: Matt Ahart*, Tom Fertig*, Hulya Guler*, Rachel Mandelbaum, Emma Torbert Technical Staff: Carl Bopp, Stan Chidzik, Bill Groom, Bob Klemmer, Ted Lewis, Allan Nelson, Dick Rabberman, Bill Sands, Bob Wixted*

4. November 19, 1999CP Violation in B Meson Decays4 The Standard Model Quarks Leptons Forces Carriers Hadrons photon vector bosons gluon EM Weak Strong

5. November 19, 1999CP Violation in B Meson Decays5 Feynman Diagrams Electron radiates a photon Electron absorbs a photon

6. November 19, 1999CP Violation in B Meson Decays6 Feynman Diagrams Electron -electron scattering Photon is never seen

7. November 19, 1999CP Violation in B Meson Decays7 Feynman Diagrams Muon radiates a W boson The W rematerializes as an electron and an anti- electron neutrino.

8. November 19, 1999CP Violation in B Meson Decays8 Feynman Diagrams Muon decay

9. November 19, 1999CP Violation in B Meson Decays9 Feynman Diagrams Quark transitions

10. November 19, 1999CP Violation in B Meson Decays10 Parity & Charge Conjugation What is CP? What is P? Answer: parity ( ) What is C? Answer: charge conjugation. Note that C also flips lepton and baryon number. Note further that neutral particles can be eigenstates of C.

11. November 19, 1999CP Violation in B Meson Decays11 Parity Falls Until the mid-50’s, people believed that both P and C would be conserved. However, in 1957, Wu et al., who were pursuing ideas of Lee & Yang (inspired by experimental data on K decays) observed parity violation in nuclear decay. Although parity is conserved in strong and electro-magnetic interactions it is in a sense “maximally violated” in weak interactions.

12. November 19, 1999CP Violation in B Meson Decays12 Parity Falls In particular, neutrinos, which are massless (or nearly so), have a definite ``handedness’’. are left handed are right handed. In a “symmetric” interaction, one would expect both helicities to exist, as is the case, for example, in electromagnetism, where photons have both left- and right-circular polarizations.

13. November 19, 1999CP Violation in B Meson Decays13 Parity & Charge Conjugation Fall The last hope was that the product of the two operators (i.e. CP) would be conserved. C C P P left-handed CP right-handed OK!

14. November 19, 1999CP Violation in B Meson Decays14 CP Falls Hopes for CP conservation were dashed in 1964 by a Princeton group led by Val Fitch and Jim Cronin, who detected a tiny CP violating effect in neutral K decays. This is a wonderful story, but one that we won’t go into here. Reasons for further study: CP violation is “surprising” CP violation represents a matter-antimatter asymmetry (we’ll see how later on) and is an essential element in understanding the baryon-antibaryon asymmetry in Universe. CP effects involving b quarks are expected to be large.

15. November 19, 1999CP Violation in B Meson Decays15 The CPT Theorem All that is left is an operator called CPT, where “T” stands for time-reversal. Although the experimental tests of CPT are somewhat limited, the CPT theorem is part of the “theoretical bedrock” of field theory. If we assume that CPT is a good symmetry, then

16. November 19, 1999CP Violation in B Meson Decays16 Time Reversal In non-relativistic QM, the time-reversal operator is such that: thus left-mover right-mover As one would expect, the T operator reverses momenta (but not positions).

17. November 19, 1999CP Violation in B Meson Decays17 Time Reversal The expectation value of an operator transformed by T is Operators with complex phases (e.g., p and L), are not T invariant (and therefore are not CP invariant).

18. November 19, 1999CP Violation in B Meson Decays18 Quark Mixing Experimentally we know that the eigenstates of the weak Hamiltonian and the mass eigenstates are different. For simplicity we start with a two-quark-doublet version of nature, i.e., If the quarks acted like leptons, then only vertical transitions would be allowed and the s quark would be stable. However, the kaon decays in 12 ns. It appears that there are generation- crossing transitions.

19. November 19, 1999CP Violation in B Meson Decays19 Quark Mixing Rather than saying that the strange quark is decaying directly to an up quark, we write the following And say that the s-quark in the kaon has a component that can decay into a u-quark. Weak eigenstate Mass eigenstate Q: What does this have to do with CP violation? Cabibbo mixing

20. November 19, 1999CP Violation in B Meson Decays20 Quark Mixing Ans: Nothing! (yet) However, even before the discovery of the c-quark (and two decades before the observation of the t-quark) Kobayashi and Maskawa proposed a three-generation scheme Weak eigenstates Mass eigenstates

21. November 19, 1999CP Violation in B Meson Decays21 Quark Mixing KM Mixing Both Cabibbo (2x2) and KM (3x3) mixing are described by unitary transformations. In general where

22. November 19, 1999CP Violation in B Meson Decays22 Quark Mixing Case Parameter(s) The essential contribution of Kobayashi and Maskawa was the observation that only a 3x3 scheme would provide the phase needed for T violation (and hence CP violation). Cabibbo KM

23. November 19, 1999CP Violation in B Meson Decays23 Quark Mixing Original Kobayashi-Maskawa parameterization. where & This parameterization is valid, but it is not especially intuitive.

24. November 19, 1999CP Violation in B Meson Decays24 Quark Mixing This approximation ( ) reflects the theoretical prejudice (and experimental reality) that the elements get smaller as one moves off the diagonal. A more popular choice is the Wolfenstein parameterization: Allowed suppressed doubly suppressed

25. November 19, 1999CP Violation in B Meson Decays25 Quark Mixing The appearance of the KM phase offers a natural explanation for standard-model CP violation. Moreover, there is a wealth of other (non-CP) experimental data that supports the KM picture. However, to date there have been no quantitative tests of its predictions regarding CP violation.

26. November 19, 1999CP Violation in B Meson Decays26 The Unitarity Triangle In particular, the “d b” unitarity relation yields Unitarity implies

27. November 19, 1999CP Violation in B Meson Decays27 The Unitarity Triangle Like any sum of complex numbers can be plotted as a triangle in the complex plane. The Bjorken Triangle

28. November 19, 1999CP Violation in B Meson Decays28 Direct CP Violation Consider the CP mirror processes: The CP asymmetry is defined as The decay amplitudes are Note that the KM phase changes sign.

29. November 19, 1999CP Violation in B Meson Decays29 Direct CP Violation However, We see no effect! This is so even though the weak interaction is in a sense maximally CP violating. We need some sort of interference, two amplitudes (i.e., two Feynman diagrams). Consider add amplitudes

30. November 19, 1999CP Violation in B Meson Decays30 Direct CP Violation The resulting amplitudes are: Note that there is one more slight complication: the addition of a strong phase (but this is a good thing).

31. November 19, 1999CP Violation in B Meson Decays31 Direct CP Violation Despite its conceptual and experimental “simplicity”, there are two problems with direct CP violation: Cases where there are two comparable amplitudes that are large are (probably) rare. The strong phases are poorly understood, making it difficult to extract the weak (KM) phases that are of greatest interest. We need a better way. Such a way, which goes by the name of “Indirect CP Violation,” has been found and will be the topic of all that follows.

32. November 19, 1999CP Violation in B Meson Decays32 Matter-Antimatter Oscillations First observed in the neutral kaon (strange quark) system, neutral meson mixing represents an oscillation between matter and anti-matter. In the neutral B system, the reaction proceeds by the following Feynman diagram:

33. November 19, 1999CP Violation in B Meson Decays33 Matter-Antimatter Oscillations As a consequence, an initially pure develops in time according to the expression given below. where the KM matrix element determines. mixing

34. November 19, 1999CP Violation in B Meson Decays34 Indirect CP Violation Thus for a decay where is a CP eigenstate, we have two “indistinguishable” decay paths Working through the algebra, yields a time- dependent CP asymmetry Where and are the weak phases for the mixing and decay diagrams, respectively and

35. November 19, 1999CP Violation in B Meson Decays35 Indirect CP Violation One complication is that since CP eigenstates are neutral, they give no information as to whether the decaying meson was a Fortunately there is a solution in the form of...

36. November 19, 1999CP Violation in B Meson Decays36 Quantum Weirdness One way to make is to produce pairs at an collider. In practice this means making using of resonant production, i.e., Where the is a radial excitation of a “quarkonium” bound state. The important point is that the pair is produced in a coherent state.

37. November 19, 1999CP Violation in B Meson Decays37 Quantum Weirdness Tags this particle as a This particle must have decayed as a Tagging side CP eigenstate side If then the particle on the CP eigenstate must be a. Note that the tagging information is communicated across space instantaneously despite the fact that the B’s could be separated by a finite distance (a few hundred microns). This is an instance of the EPR paradox.

38. November 19, 1999CP Violation in B Meson Decays38 The Measurement tag CP The times involved are too short (~1 ps) to measure directly, instead we measure the decay positions and convert these positions to times.

39. November 19, 1999CP Violation in B Meson Decays39 The Measurement The time-dependent asymmetry appears mainly as a mean shift in the distribution between events tagged as decays and events tagged as decays.

40. November 19, 1999CP Violation in B Meson Decays40 The KEK-B Asymmetric Collider KEK-B is a recently completed accelerator situated in Tsukuba City, Japan. It is designed to produce an order of magnitude more luminosity (collisions per unit cross section) than any existing machine.

41. November 19, 1999CP Violation in B Meson Decays41 Ring Parameters

42. November 19, 1999CP Violation in B Meson Decays42 Electron Source

43. November 19, 1999CP Violation in B Meson Decays43 The Linac

44. November 19, 1999CP Violation in B Meson Decays44 The Storage Rings RF Cavity Stations

45. November 19, 1999CP Violation in B Meson Decays45 The Storage Rings Arc Section

46. November 19, 1999CP Violation in B Meson Decays46 The “IR” Where matter and anti-matter collide!

47. November 19, 1999CP Violation in B Meson Decays47 The Magnet

48. November 19, 1999CP Violation in B Meson Decays48 The BELLE Collaboration About 200 physicists About 50 institutions Countries: Australia, China (both!), India, Japan, Korea, Poland, Russia, Ukraine, United States

49. November 19, 1999CP Violation in B Meson Decays49 Cosmic Ray How I spent my sabbatical year!

50. November 19, 1999CP Violation in B Meson Decays50 Meters to Microns

51. November 19, 1999CP Violation in B Meson Decays51 The Magnet

52. November 19, 1999CP Violation in B Meson Decays52 The Silicon Vertex Detector

53. November 19, 1999CP Violation in B Meson Decays53 The Central Drift Chamber

54. November 19, 1999CP Violation in B Meson Decays54 The Aerogel Silica aerogel is a very low-density glass that provides just the right index of refraction to produce Cerenkov light. In the momentum range of interest pions emit Cerenkov light while the somewhat heavier kaons don’t.

55. November 19, 1999CP Violation in B Meson Decays55 The Cesium Iodide Detector Upper management looks on anxiously while $35M worth of salt is craned into place. Each scintillator crystal is read by two photodiodes.

56. November 19, 1999CP Violation in B Meson Decays56 K_L Muon Detector The muon detectors, which are the largest, are made from standard soda-lime float glass (window glass). An endcap module is installed.

57. November 19, 1999CP Violation in B Meson Decays57 Data Acquisition The tip of the electronic iceberg.

58. November 19, 1999CP Violation in B Meson Decays58 Key Belle Milestones Early 1990’s - Japanese groups begin working. January 1994 - Collaboration forms. April 1995 - TDR Submitted. …lots of work by lots of people in lots of places... Dec 18, 1998 - Belle detector completed (including SVD) Jan 26, 1999 - First cosmic ray with full detector. May 1, 1999 - Belle rolled into place. June 1, 1999 - First hadronic event!!!!! June 1999 About 1200 hadron events obtained before vacuum pipe mishap. July 1999 More data (30K events) and lots learned.

59. November 19, 1999CP Violation in B Meson Decays59 June 1, 1999: Our First Hadronic Event

60. November 19, 1999CP Violation in B Meson Decays60 More Fun: SVD Included

61. November 19, 1999CP Violation in B Meson Decays61 First J/  Candidate J/  ee – M(ee) = 3.1 GeV

62. November 19, 1999CP Violation in B Meson Decays62 SVD Performance

63. November 19, 1999CP Violation in B Meson Decays63 SVD Performance

64. November 19, 1999CP Violation in B Meson Decays64 CsI EM Calorimeter Performance

65. November 19, 1999CP Violation in B Meson Decays65 Physics from the First Runs: Energy Scan

66. November 19, 1999CP Violation in B Meson Decays66 Lepton-pair Spectrum

67. November 19, 1999CP Violation in B Meson Decays67 B Mixing

68. November 19, 1999CP Violation in B Meson Decays68 Conclusions & Outlook We will soon have new measurements of CP violation. The experiments are highly complex and large in scale and can only be carried out by large scientific and technical teams. The fun of data analysis is now beginning.