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Lecture　2

Italian Physical Society International School of Physics “Enrico Fermi”. Lecture　2. Lecture 　２. Edm Krammer’s degeneracy Particle physics How do you measure pion spin? How do you show that pion is a pseudoscalar? G-parity C,P,T in particle physics. To test T invarience look for edm.

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Lecture　2

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  1. Italian Physical Society International School of Physics “Enrico Fermi” Lecture　2

  2. Lecture　２ • Edm • Krammer’s degeneracy • Particle physics • How do you measure pion spin? • How do you show that pion is a pseudoscalar? • G-parity • C,P,T in particle physics

  3. To test T invarience look for edm For an elementary particle For an elementary particle, only vector you have is spin! Different transformation property under T

  4. + ＋ ＋ - ーー Edm of an electron is T violating. This is easy to understand. Edm of an electron can be measured in a system with Large number of electrons, like an atom. Why? Don’t many electron system have edm without T violation?

  5. Definition Electric dipole moment Energy shift in an electric field

  6. ＋ ＋ ーー What about water molecule? If oxygen atom had an edm, can it be seen? Does water molecule have an edm? If so, it will be a background. How do we know that it does not produce an energy shift which is linear in E-leading to water molecule edm?

  7. Parity even state

  8. Parity odd state Which is more energetic?

  9. Lets turn on an electric field Consider a pair of opposite parity states Water molecule does not have an edm! Ground state is non-degenerate!

  10. + + + - - - What about the dumbell? These states are degenate If a non-degenerate system possesses an edm, it implies T violation

  11. If you find an edm of a non-degenerate system, then it implies T violation.

  12. ed ed ed ed Shiff’s theorem • Atoms consist of non-relativistic particles, which interact only electro-statically. • The edm distribution of each atomic constituent is identical to its charge distribution. Then even if the constituents possessed edm, they are totally shielded. Relativistic effects of large Z atoms and various atomic effects enhance atomic edm

  13. Krammer’s Degeneracy Allows for half integer spin |a> and T|a> are degenerate

  14. U is real Half integer Spin!

  15. Particle physics

  16. Detect a free particle Experimentalists shoot a free particle

  17. Scattering Scattered wave Incident wave Definition of asymptotic states

  18. Time reversal in particle scattering S-matrix

  19. Meson octet s u d

  20. ＋ Ｋ ０ Ｋ ー ０ Ｋ ー Ｋ SU(3) symmetry invariant under rotation among Mesons made out of quarks π＋ π― η π０

  21. How did our forefathers measured them?

  22. T invariance Detail balance

  23. Hermiticity of H also implies detail balance π meson spin =0

  24. scalar Pseudo-scalar angular distribution shows that π meson is peudoscalar

  25. Compute the angular distribution for both cases

  26. C, P, T of elementary particles

  27. Photons

  28. Spin 0 particles

  29. Fermions

  30. After the second quantization, Phase degree of freedom Charge conjugation and internal symmetry

  31. It is convenient to define invariance under SU(2) rotation Consider isodoublet

  32. G-parity We want to find an operator for which the triplet of pions is an eignstate

  33. 3 1 2 π

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