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T. D. Lee

1. Symmetry and Asymmetry in Electroweak Interaction. T. D. Lee A lecture given at the Workshop on Possible Parity Restoration at High Energy, on June 11, 2007, Beijing (50 years since the discovery of parity nonconservation ). 2. • Symmetry Violation : the discovery

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T. D. Lee

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  1. 1 Symmetry and Asymmetry in Electroweak Interaction T. D. Lee A lecture given at the Workshop on Possible Parity Restoration at High Energy, on June 11, 2007, Beijing (50 years since the discovery of parity nonconservation )

  2. 2 •Symmetry Violation : the discovery Present Status : the complexity Restoration of P, C, T Symmetries New Symmetry: A Unified View of and

  3. 3 (May 31, 1912 - Feb. 17, 1997)

  4. 4 The initial setups of these two experiments on Co60 decay are exact mirror images, but the final electron distributions are not, as indicated by different readings on the counters.

  5. Discovery of Parity Nonconservation 5

  6. 6 … …

  7. 7

  8. 8 • TCP invariance√ • established by W. Pauli in 1955 • Parity Violation P X • right-left asymmetry • Charge Conjugation Violation C X • particle-antiparticle asymmetry • both discovered by Wu et. al. in 1957 • Time Reversal Violation T X • CP Violation CP X • proposed in 1957 • discovered by Christenson, Cronin, Fitch andTurlayin 1964

  9. 9 Symmetry Violation : the discovery • Present Status : the complexity Restoration of P, C, T Symmetries New Symmetry: A Unified View of and

  10. All known matter ( our kind of matter; i.e., , nuclei, atoms, molecules, DNA, genes, earth, sun, stars, galaxies, … ) are made of twelve elementary particles: 10

  11. All known matter ( our kind of matter; i.e., , nuclei, atoms, molecules, DNA, genes, earth, sun, stars, galaxies, … ) are made of twelve elementary particles: 11 of these, only were known 50 years ago.

  12. 12 : neutrino mapping matrix : Cabibbo, Kobayashi, Maskawa Both and are 3 x 3 unitary matrices. They are two corner stones of particle physics. Yet, they are very different!

  13. 13 CKM

  14. 14 Neutrino Mapping Very different from ! How can we understand it ?

  15. 15 Symmetry Violation : the discovery Present Status : the complexity • Restoration of P, C, T Symmetries New Symmetry: A Unified View of and

  16. 15a Symmetry Violation : the discovery Present Status : the complexity • Restoration of P, C, T Symmetries New Symmetry: A Unified View of and •Equation of motion is symmetric, but solutions are not

  17. 16

  18. 17 We assume • P, C, T asymmetries are all due to spontaneous Symmetry Breaking Mechanism of spin 0 Higgs Fields . • Without , all spin fields are Symmetry Conserving and of Zero Mass; these include graviton, photon, , quarks and leptons.

  19. 18 Consequences • Besides and , there should exist and of heavier masses . • Can ILC be an effective means to detect and ?

  20. 19 Why are Higgs not yet seen? Because of complex structure, like Cooper pairs in superconductivity.

  21. 20 Symmetry Violation : the discovery Present Status : the complexity Restoration of P, C, T Symmetries • New Symmetry: A Unified View of and

  22. A Simple ExampleFriedberg, Lee (HEP & NP 30(2006)591) 21 New Symmetry: Neutrino Mass Operator is invariant under: In the approximation of T invariance. Consequence: There exists a zero mass neutrino state.

  23. 22 Neutrino Mass Matrix (in terms of )

  24. 23 pf Harrison and Scott, Phys. Lett. B535, 163(2002) Z. Z. Xing, Phys. Lett. B533, 85(2002) X. G. He and Z. Zee, Phys. Lett. B560, 87(2003)

  25. 24 Thus, this example of new symmetry in is (approx.) correct , • This new symmetry assumes T invariance.

  26. Questions and How to Improve 1. In why (not ) approx. zero mass? 2. How about approx. sym. for 3. Can approx. T invariance be related to masses of 25

  27. 26 R. Friedbergand T.D. Lee arXiv: 0705.4156[hep-ph] • 0th Approx. • First Approx. A Unified View of and

  28. 27 • The quarks of charge and of charge in are not mass eigenstates u, c, t and d, s, b Hidden Symmetry • Likewise for leptons

  29. 28 both and are unitary. Likewise,

  30. 29 Leptons both and are unitary.

  31. 30 assuming T inv.

  32. 31 Mass Operator in sector (likewise for ) : 0th approximation: T inv. all real New Symmetry: is invariant under with and

  33. Proof 32 gives

  34. 33 neglecting T violation and With

  35. 34 With T violation (1) Set from particle data group (1) gives consistent with particle data book value

  36. Thank you

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