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

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

4. τ υeυe υµυµ υτυτ W eµu d’ uu R τ == N C S ew ( 1 + δ pert (α s ) + δ non-pert + δ ew ) Γ had Γ e 0.1910 -0.023 0.0010 Gluon 20% 20% 60%

5. Γ (τ → υ τ had) Γ (τ → υ τ e υ e ) Rτ =Rτ = B (τ → υ τ had) B (τ → υ τ e υ e ) = = 1 - B (τ → υ τ e υ e ) - B (τ → υ τ µ υ µ ) B (τ → υ τ e υ e ) 1 B (τ → υ τ e υ e ) = - 1.9726 B (τ → υ τ e υ e ) = 0.1784 ± 0.0006  α s (m Z ) = 0.121 ± 0.003

6. PDG 2004

7. One of the most precise measurements of  s Many tests of QCD predictions

8. 1. Definition of R  R  = = ∫ ds  had  e ee d  had ds 0 mm 2. Optical Theorem d  had = (2  ) 4  4 (...) 1 2 m  GF2GF2 L    0 |J  | had   had |J † | 0  d  had d  d  had = 1 2 m  GF2GF2 L  2 Im   0 | J  J † | 0  d 

9. s m  2 3. Lorentz decomposition 4. Extension to the Complex Plain  0 | J  J † | 0  = (q  q – g  q 2 )  (1) (q 2 ) + q  q  (0) (q 2 ) R  = 6  i (1 – ) 2 (1 + )  (1) (q 2 ) ds m  2 ∫ 2 s m  2

10. R τ == N C S ew ( 1 + δ pert (α s ) + δ non-pert + δ ew ) Γ had Γ e 0.1910 -0.023 0.0010 perturbative, strong correction calculated to 3rd order theorists working on 4th order corrections

11. R τ = 12 π S ew |V ud | 2 m τ 2 ds (1 - ) 2 (1 + ) smτ2smτ2 2s m τ 2 Im Π (s) 0 mτ2mτ2 v(s) = 2 π Im Π(s) a(s) = 2 π Im Π(s)

12. R τ = 12 π S ew |V ud | 2 m τ 2 ds (1 - ) 2 (1 + ) smτ2smτ2 2s m τ 2 Im Π (s) 0  α s ( ) s0s0 s0s0 mτ2mτ2 mτ2mτ2 s0s0

13. Okay down to ≈ 1 GeV

14. PDG 2004

15. consistent

16. Deviations from standard model ?

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

18. 10 -11 10 -9 10 -7 10 -5 10 -3 QED hadr. contribution weak contribution new physics? exp a  = g  - 2 2

19. (2003: 204 ± 7)

21. Isospin Violation ?

22. τ υτυτ W q q’ e  q q e 2. quark mass  phase space correction  negligible 1.quark charge  QED radiation  theor. estimate 3. pion mass (  o ≠  + )  phase space correction  taken into account 4. meson masses (  o ≠  + ?)  phase space correction  should be small but.......

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

28.  (leptons – anti-leptons) initial =  (leptons – anti-leptons) final each generation separately -  --  -  -   -  +  -   +  ++  + -  K--  K- B 0  D -  +  t  b  +  e + e -   +  - D -   -  no violation observed

29.  ->   violate lepton numbers     

31. Affects the Tau ? -- --   W-W-  -   -

32. Affects the Tau ? -- --   W-W-  -   - neutrino oscillation      okay But: energy/momentum conservation violated

33. Affects the Tau ? -- --   W-W-  -   -   branching ratio standard model: 10 -40 other Models: 10 -40 … 10 -6

34. Affects the Tau ? -- --   W-W-  -   -  +  - branching ratio standard model: 10 -40 … 10 -14 other models: 10 -40 … 10 -7 -- ++

35.     W W Z = υeυµυτυeυµυτ mixing matrix υ1υ2υ3υ1υ2υ3 ~  U  i U i 

36. breaks the GIM mechanism

37.  -   -   inv. mass ( ,  ) = tau mass  energy ( ,  ) = tau energy Background:         random    other background    is experimentally easier, but lower branching ratio (?)

39.  -  e - 

40.  -   - 

41.  E = E reco -  s/2  m = m reco - m 

43.  -   -  +  - at the LHC Advantage: more taus Disadvantage: more background tau sources: W   1.7 10 8  /Z   8.0 10 8 D s   X 1.5 10 12 B 0   X 4.0 10 11 B ±   X 3.8 10 11 B s   X 7.9 10 10 1 year @ low luminosity

44.  -   -  +  -  bei CMS Simulation with underlying event (low luminosity)

45.  -   -  +  -  at CMS W    10.000 events trigger track reconstruction

46.  = -ln tan  /2

47. Level-1 Trigger: Single Muonp T > 14 GeV Di-Muonp T > 3 GeV

48. b-factories:can approach 10 -8 in most channels LHC:only     10 12 taus (low lumi) efficiency 1% possible ??? limits of 10 -10 LHC:can we use high-lumi running ??? work has just begun !

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