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. QCD in Tau Decays

4. Gluon Γhad Γe Rτ = = NC Sew ( 1 + δpert(αs) +δnon-pert+δew) 0.1910 -0.023 0.0010 Tau Decays υτ τ 20% 20% 60% e µ u u u W υe υµ d’ d’ d’

5. B (τ→υτhad) B(τ→υτe υe) = 1 - B (τ→υτeυe) -B (τ→υτµυµ) B(τ→υτe υe) = 1 B(τ→υτe υe) - 1.9726 = B(τ→υτe υe) = 0.1784 ± 0.0006  αs (mZ)= 0.121 ± 0.003 Determination of the strong coupling Γ (τ→υτhad) Γ(τ→υτe υe) Rτ=

6. PDG PDG 2004

7. One of the most precise measurements of as • Many tests of QCD predictions

8. Outline of Theoretical Calculation 1. Definition of Rt mt Rt = = ∫ ds Ghad Ge 1 Ge dGhad ds 0 2. Optical Theorem GF 2 1 2 mt LmnS 0 |Jm| had   had |Jn†| 0  dfhad dFn dGhad = (2p)4 d4(...) GF 2 1 2 mt dGhad = Lmn 2 Im0 | Jm Jn† | 0 dFn

9. Outline of Theoretical Calculation 3. Lorentz decomposition 0 | Jm Jn† | 0 = (qmqn – gmn q2) P(1)(q2) + qmqnP(0)(q2) 4. Extension to the Complex Plain ds mt2 s mt2 2 s mt2 ∫ Rt = 6 pi(1 – )2(1 + ) P(1)(q2)

10. Γhad Γe Rτ = = NC Sew ( 1 + δpert(αs) +δnon-pert+δew) 0.1910 -0.023 0.0010 Result perturbative, strong correction calculated to 3rd order theorists working on 4th order corrections

11. Spectral Functions mτ2 12 πSew |Vud|2 mτ2 s mτ2 2s mτ2 ImΠ(s) Rτ = ds (1 - )2 (1 + ) 0 v(s) = 2π Im Π(s) a(s) = 2π Im Π(s)

12. s0 mτ2 mτ2 s0 s0 Running Coupling 12 πSew |Vud|2 mτ2 s mτ2 2s mτ2 ImΠ(s) Rτ = ds (1 - )2 (1 + ) 0  αs()

13. Running Coupling Okay down to ≈ 1 GeV

14. Running Coupling PDG 2004

15. Vector and Axial Vector consistent

16. Brookhaven: g-2 Deviations from standard model ?

17. e+e-→ had Spectral Functions optical theoreme Π(s) universal function τ→ ντhad (g-2)μ

18. gm - 2 2 am = Contributions to g-2 exp QED hadr. contribution weak contribution new physics? 10-11 10-9 10-7 10-5 10-3

19. Comparison (2003: 204 ± 7)

21. Conserved Vector Current Isospin Violation ?

22. Isospin Violation υτ • quark charge •  QED radiation •  theor. estimate τ q W 2. quark mass  phase space correction  negligible q’ 3. pion mass (po≠ p+)  phase space correction  taken into account e q 4. meson masses (ro≠ r+ ?)  phase space correction  should be small but ....... g q e

23. but .......

24. but .......

25. PDG

26. Outlook • Discrapency unresolved • Better theoretical estimates of isospin violation • More precise and more careful measurements e+e-: radiative return DaΦne, CLEO-c, b-factories, Nowosibirsk e+e-: direct measurement Nowosibirsk τ: new measurements τcf, CLEO-c, b-factories

27. Lepton Flavour Violation

28. t-  m- nm nt t+  m+ nm nt t-  p- p+ p- nt D- t- nt t-  K- nt Lepton Number Conservation S (leptons – anti-leptons)initial = S (leptons – anti-leptons)final each generation separately B0 D-t+ nt e+e-t+ t- t bt+ nt no violation observed

29. Neutrino Oscillations p -> m nm violate lepton numbers nm nt

31. t-  m- Lepton Number Affects the Tau ? nt t- nm W- m-

32. neutrino oscillation ntnm t-  m- Lepton Number Affects the Tau ? nt t- nm W- m- okay But: energy/momentum conservation violated

33. t-  m- g Lepton Number Affects the Tau ? nt t- nm g W- m- branching ratio standard model: 10-40 other Models: 10-40… 10-6

34. Lepton Number Affects the Tau ? nt m+ t- nm m- W- m- t-  m- m+m- branching ratio standard model: 10-40… 10-14 other models: 10-40… 10-7

35. υ1 υ2 υ3 υe υµ υτ mixing matrix = GIM Mechanism n m ~ SUti Uim t W W m Z m

36. New Physics breaks the GIM mechanism

37. Experimental Searches t-  m- g • inv. mass (m,g) = tau mass • energy (m,g) = tau energy Background: • tm n n g • tm n n + random g • other background tm m m is experimentally easier, but lower branching ratio (?)

38. Experimental Searches

39. t-  e- g Search

40. t-  m- g Search

41. Other Channels DE = Ereco - s/2 Dm = mreco - mt

42. Current Status

43. t-  m- m+m- Search: at the LHC tau sources: Advantage: more taus Disadvantage: more background 1 year @ low luminosity

44. t-  m- m+m- bei CMS Simulation with underlying event (low luminosity)

45. t-  m- m+m- at CMS W  t nt 10.000 events trigger track reconstruction

46. Kinematics @ LHC h = -ln tan q/2

47. Kinematics @ LHC Level-1 Trigger: Single Muon pT > 14 GeV Di-Muon pT > 3 GeV

48. Outlook b-factories: can approach 10-8 in most channels LHC: only t m m m > 1012 taus (low lumi) efficiency 1% possible ??? limits of 10-10 LHC: can we use high-lumi running ??? work has just begun !

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