1. Niels Tuning (1) Topical lectures December 2010 CP violation Hour 3 N. Tuning

2. Menu TimeTopicSpeaker Monday 13/12 9.45 – 10.30C, P, CP and the Standard ModelNiels 10.45 – 11.30CKM matrixNiels 11.45 – 12.30Flavour mixing in B-decaysNiels 14.00 – 14.45CP Violation in B-decaysNiels 15.00 – 15.45CP Violation in B-decaysNiels Niels Tuning (2)

3. This was theory, now comes experiment We already saw how the moduli |V ij | are determined Now we will work towards the measurement of the imaginary part –Parameter: η –Equivalent: angles α, β, γ. To measure this, we need the formalism of neutral meson oscillations… Niels Tuning (3)

4. Niels Tuning (4) Dynamics of Neutral B (or K) mesons… No mixing, no decay… No mixing, but with decays… (i.e.: H is not Hermitian!)  With decays included, probability of observing either B 0 or B 0 must go down as time goes by: Time evolution of B 0 and  B 0 can be described by an effective Hamiltonian:

5. Niels Tuning (5) Describing Mixing… Where to put the mixing term? Now with mixing – but what is the difference between M 12 and  12 ? M 12 describes B 0  B 0 via off-shell states, e.g. the weak box diagram  12 describes B 0  f  B 0 via on- shell states, eg. f=     Time evolution of B 0 and  B 0 can be described by an effective Hamiltonian:

6. Niels Tuning (6) Solving the Schrödinger Equation Eigenvalues: – Mass and lifetime of physical states: mass eigenstates

7. Niels Tuning (7) Solving the Schrödinger Equation Eigenvectors: – mass eigenstates

8. Time evolution Niels Tuning (8) With diagonal Hamiltonian, usual time evolution is obtained:

9. Niels Tuning (9) B Oscillation Amplitudes For B 0, expect:  ~ 0, |q/p|=1 For an initially produced B 0 or a  B 0 it then follows: (using: with

10. Niels Tuning (10) Measuring B Oscillations Decay probability B0B0B0B0 B0B0B0B0 Proper Time  For B 0, expect:  ~ 0, |q/p|=1 Examples:

11. Niels Tuning (11) Compare the mesons: P0P0P0P0 P0P0P0P0 Probability to measure P or P, when we start with 100% P Time  Probability  <><> ΔmΔmx=Δm/Γy=ΔΓ/2Γ K0K0 2.6 10 -8 s5.29 ns -1 Δm/ Γ S =0.49 ~1 D0D0 0.41 10 -12 s0.001 fs -1 ~00.01 B0B0 1.53 10 -12 s0.507 ps -1 0.78~0 Bs0Bs0 1.47 10 -12 s17.8 ps -1 12.1~0.05 By the way, ħ=6.58 10 -22 MeVs x=Δm/ Γ : avg nr of oscillations before decay

12. Summary (1) Start with Schrodinger equation: Find eigenvalue: Solve eigenstates: Eigenstates have diagonal Hamiltonian: mass eigenstates! (2-component state in P 0 and P 0 subspace)

13. Summary (2) Two mass eigenstates Time evolution: Probability for |P 0 >  |P 0 > ! Express in M=m H +m L and Δm=m H -m L  Δm dependence

14. Niels Tuning (14) Let’s summarize … p, q: Δm, Δ Γ: x,y: mixing often quoted in scaled parameters: q,p,M ij, Γ ij related through: with Time dependence (if ΔΓ~0, like for B 0 ) :

15. Box diagram and Δm

17. Box diagram and Δm: Inami-Lim C.Gay, B Mixing, hep-ex/0103016 K-mixing

18. Box diagram and Δm: Inami-Lim C.Gay, B Mixing, hep-ex/0103016 B 0 -mixing

19. Box diagram and Δm: Inami-Lim C.Gay, B Mixing, hep-ex/0103016 B s 0 -mixing

20. Next: measurements of oscillations 1.B 0 mixing:  1987: Argus, first  2001: Babar/Belle,precise 2.B s 0 mixing:  2006: CDF: first  2010: D0: anomalous ??

21. B 0 mixing

22. Niels Tuning (22) B 0 mixing What is the probability to observe a B 0 /B 0 at time t, when it was produced as a B 0 at t=0? –Calculate observable probility *(t) A simple B 0 decay experiment. –Given a source B 0 mesons produced in a flavor eigenstate |B 0 > –You measure the decay time of each meson that decays into a flavor eigenstate (either B 0 orB 0 ) you will find that

23. B 0 oscillations: –First evidence of heavy top –  m top >50 GeV –Needed to break GIM cancellations B 0 mixing: 1987 Argus Phys.Lett.B192:245,1987

24. Niels Tuning (24) B 0 mixing: 2001 B-factories You can really see this because (amazingly) B 0 mixing has same time scale as decay – =1.54 ps – m=0.5 ps -1 –50/50 point at m   –Maximal oscillation at 2m  2 Actual measurement of B 0 /B 0 oscillation –Also precision measurement of m!

25. B s 0 mixing

26. Niels Tuning (26) B s 0 mixing: 2006

27. Niels Tuning (27) B s 0 mixing (Δm s ): SM Prediction V ts CKM Matrix Wolfenstein parameterization Ratio of frequencies for B 0 and B s  = 1.210 +0.047 from lattice QCD -0.035 V ts ~ 2 V td ~ 3   Δm s ~ (1/ λ 2 ) Δm d ~ 25 Δm d

28. Niels Tuning (28) B s 0 mixing (Δm s ): Unitarity Triangle CKM Matrix Unitarity Condition

29. Niels Tuning (29) B s 0 mixing (Δm s ) Δm s =17.77 ±0.10(stat)±0.07(sys) ps -1 cos(Δm s t) Proper Time t (ps) hep-ex/0609040 BsBs bb b ss st tt W W BsBs g̃BsBs BsBs bb s ss b x x b̃ s̃ g̃

30. Niels Tuning (30) Mixing  CP violation? NB: Just mixing is not necessarily CP violation! However, by studying certain decays with and without mixing, CP violation is observed Next: Measuring CP violation… Finally

31. Meson Decays Formalism of meson oscillations: Subsequent: decay

32. Notation: Define A f and λ f

33. Some algebra for the decay P 0  f Interference P0 fP0 fP 0  P 0  f

34. Some algebra for the decay P 0  f

35. The ‘master equations’ Interference(‘direct’) Decay

36. The ‘master equations’ Interference(‘direct’) Decay

37. Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference

38. Consider f=f : If one amplitude dominates the decay, then A f = A f 3.CP violation in interference Classification of CP Violating effects - Nr. 3: