Heraeus School Flavour Physics and CP Violation

1. Heraeus School Flavour Physics and CP Violation 29./30. August 2005

2. Contents • Historical Intro: Discovery of the tau • Basic Properties • Branching Ratios • Kinematics • Mass • Lifetime • Hot Topics • QCD / Isospin • Lepton Flavour Violation

3. Discovery

4. The World Around Us 1937: Consistent Picture

5. Who ordered that ? Isidor Rabi The Muon e Discovery 1937 µ Cloud chamber

6. for ex.: K0L µ+µ- s µ- K0L µ+ d GIM mechanism needs the c-Quark The World before the Tau The missing c-Quark: predicted from symmetry predicted from GIM mechanism W  u d W  u s Z  d s Z  d d Z  u u Z  s s

7. Discovery of the c-Quark Sam Ting BNL Burt Richter SLAC November 1974 Autumn 1974

8. charmonium: cc-atom Discovery of the c-Quark D0D0 / D+D- production open charm threshold mass / energy

9. Ψ J J Ψ Discovery of the c-Quark Sam Ting BNL Burt Richter SLAC

10. SPEAR Stanford Positron Electron Accelerator Ring e+e- 3 … 7 GeV center-of-mass energy November 1974

11. Martin Perl SPEAR Stanford Positron Electron Accelerator Ring e+e- 3 … 7 GeV center-of-mass energy November 1974

12. lepton number p+ m+nm m- e-nenm Z0m+m- Z0  e+m- Who ordered that ? LEP Hypothesis: e+ e-t+ t- t- m-nmnt t+ e+nent But ! Discovery of the tau Lepton e+ e-e+m- missing energy

13. The Name greek triton the third

14. The Neutrino Hypothesis tm kinematically forbidden tm n 2-body-decay mono-energetic µ tm n n 3-body-decay continious spectrum Discovery or the tau-neutrino ?

15. Ve 2 Vµ 1 17,84 % 17,36 % = The Neutrino Hypothesis 2 ortho-lepton t+e+nene t+m+nµne t+≡ e+ t+e+ e+ e- para-lepton t+e+nene t+m+nµne t+≡ e- sequential lepton t+e+nent t+m+nµnt tits own generation okay

16. Direct Neutrino Detection DONUT July 2000

17. υτ - Strahl

21. Tau Decays

22. Tau Decays: Basics υτ τ f W f’ τ→υτeυe 20 % 20 % 60 % τ→υτµυµ τ→υτud us ub x 3 colours

23. Branching Ratios approx. 100 known decays

24. Tau Decays: Selection Rules 1 hadronic tau decay 2. Cabibbo suppression 1. phase space suppression ud ~ |Vud|2 ≈ 0.9483 us ~ |Vus|2 ≈ 0.0484 dΓ~ (1 - Q2/mτ2)2 (1 + 2 Q2/mτ2)J

25. Not all JPG can be created from qq Tau Decays: Selection Rules 2 5. helicity suppression 4. isospin suppression 5. exotic states separate JP = 0- and 0+ 0-~ (mu + md) / mτ 0+~ (mu - md) / mτ ~ (mu + md) / mτ

26. Tau Decays: Summary

28. υτ τ e µ W υe υµ Lepton Universality bre = 17.824 ± 0.052 % brµ = 17.331 ± 0.048 % 0.9999 ± 0.0020 τ decay - µdecay 0.9982 ± 0.0021 Corrections:

29. Tau Production τ e • e+e- storage rings e τ back-back kinematics • hadron decays: i.e. Ds→ τυτ • boson decays: W→ τυτ • Exotics: z.B. H → ττ, τ̃→χ0τ

30. Decay Kinematics boost t+had+nt had nt 2-body-decay Ehad* = (mτ2 + mhad2) / 2 mτ Ehad, mhad mt and mn decay angle or tau direction tau energy nt had beam spot

31. Tau Mass

32. Threshold Scan • Corrections: • final state radiation • vacuum polarization • initial state radiation • Coulomb correction • beam energy spread 2 mτ σ = 4 πα2/ 3E2β ( (3-β2)/2 )

33. Beijing Electron Positron Collider

34. Beijing Electron Positron Collider

35. Beijing Electron Spectrometer

36. 1776.96+0.31 MeV -0.27 The Threshold Scan

37. Threshold Scan: Spin e+e- t+t- Spin determines thershold behavious DELCO

38. Pseudo Tau Mass ARGUS:e+e- t+t-at 10.58 GeV τ-→p-p+p-υτ Ehad, mhad  measured mt and mn  mn = 0, mt ? decay angle or tau direction  not measured tau energy  known from Ebeam

39. Pseudo Tau Mass mt = 1776.3 ± 2.8 MeV

40. Tau Mass

41. CPT Test CPT symmetry: Static properties of particle and anti-particle must be identical  m(t+) = m(t-) measure t+ and t- separately: ( m(t+) - m(t-) ) / m(t) = 0.0 ± 1.8 10-3

42. Lifetime

43. decay length l = g b c t sin qt Secondary Vertex a typical event at OPAL / LEP e+e-Z0t+ t- t+m+nmnt t-p-p-p+nt

44. Secondary Vertex SLC / SLD Ecm = 91 GeV e+e-→ τ+τ-

45. Primary Vertex τ-→p-p+p-υτ to scale at SLC / LEP / CESR

46. Decay Length: OPAL 3-prong Eτ = Ecm / 2 βγ cτ= 2.3 mm τ = 290.6 fsec

47. Decay Length: BaBar 289.40 ± 0.91 ± 0.90 fsec CPT:

48. Impact Parameter for 1 – prong decays Yxy track d0 secondary vertex primary vertex l = g b ct sin qt sin Yxy

49. Impact Parameter Sum Yxy track + d0 secondary vertex primary vertex Yxy track - d0 secondary vertex Impact Parameter Sum: d0+ + d0- independent of the primary vertex

50. Impact Parameter Sum track + Yxy d0 secondary vertex primary vertex Yxy track - d0 secondary vertex Impact Parameter Sum: d0+ + d0- independent of the primary vertex