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Lecture 9

Lecture 9. Bound states. Already done a lot to understand the basic particles of nature. Strong, weak,em ?. Lepton universality. Isospin singlets. 175000. Isospin multiplets. small. small. C-parity. small. Parity. CP. G-parity. Neutrino oscillations/mass. Quark composition.

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Lecture 9

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  1. FK7003 Lecture 9 Bound states

  2. FK7003 Already done a lot to understand the basic particles of nature Strong, weak,em ? Lepton universality Isospin singlets 175000 Isospin multiplets small small C-parity small Parity CP G-parity Neutrino oscillations/mass Quark composition OZI rule OZI rule Understand most of the properties and decays of the low lying particles with symmetry invariance/violation arguments. What about the excited states ?

  3. FK7003 Hadrons Not possible meson Similarly, we can’t use Feynman diagrams to show that 3 quarks form a bound baryon state. baryons

  4. FK7003 Strategy for understanding hadron masses • Study the contributions to a hadron mass • Quark masses • Definition of quark masses • Binding energy of the quark system from the strong force • Analogy with atomic physics • Spin-spin couplings • Energy levels • Extract a form for the strong potential.

  5. Start with quark masses N/A 171000 FK7003

  6. FK7003 How does the proton get its mass and the quarks get their effective masses, a

  7. FK7003 Contribution of the strong force to hadron mass

  8. FK7003 Story so far • Two types of quark mass • Bare mass • Effective mass • Quarks get their effective mass from their motion and the confining force • Effective mass  bare mass for hadrons with c,b quarks • What else contributes to mass ?

  9. FK7003 Angular momentum

  10. ud system • Ground states of most particle configurations are stable (eg weak, electromagnetic decays). • Ground state of ud – p+ • Higher masses become indeterminate/uncertain • Decay after 10-23s (resonances – lecture 4) a1 a1 p-1300 p-1300 a2 a2  width a0 a0 b1 b1 r+ r+ p p p p p+ p+ JP JP FK7003

  11. FK7003 Bound state behaviour – eg electromagnetism Electron in a potential well exists in energy states with increasing energy indeterminacy for higher energy states.

  12. FK7003 Angular momentum of a bound state Le e- r p

  13. FK7003 The first reason – two body motion Le e- r p Lp r m

  14. FK7003 L Using reduced mass m r O

  15. FK7003 Three bodies with orbital angular momentum

  16. FK7003 The second reason – fine and hyperfine structure Fine Hyperfine Hydrogen

  17. Positronium positronium H FK7003

  18. FK7003 Positronium energy levels

  19. More on positronium FK7003

  20. Positronium states FK7003

  21. FK7003 Question • Decide whether parapositronium or othopositronium can decay into 3 photons. • Which of the two states would you expect to have the longer lifetime ? With knowledge that orthopositronium has a lifetime of 1.42x10-7 s estimate the lifetime of parapositronium.

  22. Spin-spin coupling FK7003

  23. FK7003 Spin-spin corrections

  24. FK7003 Baryons

  25. FK7003 Another way of thinking about the mass 2R

  26. FK7003 It seems to work j

  27. FK7003 Quarkonium • Time to extract rigorous results on mass states and the strong force potential • qq bound state • Easiest to deal with charmonium, bottomium (rest mass > quark kinetic energy) • Non-relativistic treatment possible – Schrödinger’s equation • Compare with positronium

  28. Production of onium states resonances Narrow – OZI FK7003

  29. FK7003 Heavy onium states

  30. FK7003 Can we work backwards ? • We have the mass splittings. • What does it tell us about the strong force? • Is the form of the strong force the same for bottomium and charmonium ?

  31. FK7003 Positronium, charmonium and bottomium mass/energy levels Strong force Electromagnetic force

  32. FK7003 Expected differences when changing the potential 3s 3p 3s 2p 3p 2s 2s 2p 1s 1s

  33. FK7003 Quark-antiquark potential from charmonium and bottomium

  34. FK7003 Summary • Understanding hadron masses is messy • Two definitions of quark masses • Strong force responsible for observed mass of hadrons containing light quarks • Hadron masses partially understood • Energy levels in analogy to atomic physics • Positronium • Hyperfine splitting • Quantitative study made with heavy onia states • Confining force consistent with a string like behaviour

  35. FK7003 (Almost) finished studying the properties of the basic particles of nature Strong, weak,em ? Quark masses Lepton universality Isospin singlets 175000 Isospin multiplets small small C-parity small Parity CP G-parity Neutrino oscillations/mass Mass differences: spin-spin Quark composition OZI rule Understand most of the properties and decays of the low lying particles with symmetry invariance/violation arguments and quantum mechanics

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