1. Niels Tuning (1) Particle Physics II – CP violation (also known as “Physics of Anti-matter”) Lecture 3 N. Tuning

2. Plan 1)Mon 2 Feb: Anti-matter + SM 2)Wed 4 Feb: CKM matrix + Unitarity Triangle 3)Mon 9 Feb: Mixing + Master eqs. + B 0  J/ψK s 4)Wed 11 Feb:CP violation in B (s) decays (I) 5)Mon 16 Feb:CP violation in B (s) decays (II) 6)Wed 18 Feb:CP violation in K decays + Overview 7)Mon 23 Feb:Exam on part 1 (CP violation) Niels Tuning (2)  Final Mark:  if (mark > 5.5) mark = max(exam, 0.8*exam + 0.2*homework)  else mark = exam  In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer  Tuesday + Thrusday

3. Plan 2 x 45 min 1)Keep track of room! 1)Monday + Wednesday:  Start:9:00  9:15  End: 11:00  Werkcollege: 11:00 - ? Niels Tuning (3)

5. Diagonalize Yukawa matrix Y ij –Mass terms –Quarks rotate –Off diagonal terms in charged current couplings Niels Tuning (5) Recap uIuI dIdI W u d,s,b W

6. Niels Tuning (6) Charged Currents A comparison shows that CP is conserved only if V ij = V ij * (Together with (x,t) -> (-x,t)) The charged current term reads: Under the CP operator this gives: In general the charged current term is CP violating

7. Niels Tuning (7) CKM-matrix: where are the phases? u d,s,b W Possibility 1: simply 3 ‘rotations’, and put phase on smallest: Possibility 2: parameterize according to magnitude, in O( λ):

8. 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 (8)

9. Neutral Meson Oscillations Why? Loop diagram: sensitive to new particles Provides a second amplitude  interference effects in B-decays Niels Tuning (9) b s s b

10. Niels Tuning (10) 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:

11. Niels Tuning (11) 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:

12. Niels Tuning (12) Solving the Schrödinger Equation Eigenvalues: – Mass and lifetime of physical states: mass eigenstates

13. Niels Tuning (13) Solving the Schrödinger Equation Eigenvectors: – mass eigenstates

14. Time evolution Niels Tuning (14) With diagonal Hamiltonian, usual time evolution is obtained:

15. Niels Tuning (15) 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 ~

16. Niels Tuning (16) Measuring B Oscillations Decay probability B0B0B0B0 B0B0B0B0 Proper Time  For B 0, expect:  ~ 0, |q/p|=1 Examples: ~ ~

17. Niels Tuning (17) 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

18. 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) Niels Tuning (18)

19. 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

20. Niels Tuning (20) Summary 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 ) :

21. Personal impression: People think it is a complicated part of the Standard Model (me too:-). Why? 1)Non-intuitive concepts?  Imaginary phase in transition amplitude, T ~ e iφ  Different bases to express quark states, d’=0.97 d + 0.22 s + 0.003 b  Oscillations (mixing) of mesons: |K 0 > ↔ |  K 0 > 2)Complicated calculations? 3)Many decay modes? “Beetopaipaigamma…” –PDG reports 347 decay modes of the B 0 -meson: Γ 1 l + ν l anything ( 10.33 ± 0.28 ) × 10 −2 Γ 347 ν ν γ<4.7 × 10 −5 CL=90% –And for one decay there are often more than one decay amplitudes… Niels Tuning (21)

22. Niels Tuning (22) Describing Mixing 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:

23. Box diagram and Δm Niels Tuning (23) Inami and Lim, Prog.Theor.Phys.65:297,1981

24. Box diagram and Δm Niels Tuning (24)

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

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

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

28. 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 ?? Niels Tuning (28)

29. B 0 mixing Niels Tuning (29)

30. Niels Tuning (30) 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

31. B 0 oscillations: –First evidence of heavy top –  m top >50 GeV –Needed to break GIM cancellations NB: loops can reveal heavy particles! B 0 mixing: 1987 Argus Phys.Lett.B192:245,1987 Niels Tuning (31)

32. B 0 mixing pointed to the top quark: B 0 mixing: t quark GIM: c quark ARGUS Coll, Phys.Lett.B192:245,1987 b d d b d s μ μ K 0 →μμ pointed to the charm quark: GIM, Phys.Rev.D2,1285,1970 … … …

33. Niels Tuning (33) 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!

34. B s 0 mixing Niels Tuning (34)

35. Niels Tuning (35) B s 0 mixing: 2006

36. Niels Tuning (36) 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

37. Niels Tuning (37) B s 0 mixing (Δm s ): Unitarity Triangle CKM Matrix Unitarity Condition

38. Niels Tuning (38) 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

39. Niels Tuning (39) B s 0 mixing (Δm s ): New: LHCb 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 LHCb, arXiv:1304.4741

40. Niels Tuning (40) B s 0 mixing (Δm s ): New: LHCb LHCb, arXiv:1304.4741 Ideal Tagging, resolution Acceptance

41. Niels Tuning (41) 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

42. Meson Decays Formalism of meson oscillations: Subsequent: decay Niels Tuning (42)

43. Notation: Define A f and λ f Niels Tuning (43)

44. Some algebra for the decay P 0  f Interference P0 fP0 fP 0  P 0  f Niels Tuning (44)

45. Some algebra for the decay P 0  f Niels Tuning (45)

46. The ‘master equations’ Interference(‘direct’) Decay Niels Tuning (46)

47. The ‘master equations’ Interference(‘direct’) Decay Niels Tuning (47)

48. Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference Niels Tuning (48)

49. What’s the time? Niels Tuning (49)