Particle Physics II – CP violation (also known as “ Physics of Anti-matter ” ) Lecture 3

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

2. Plan • Mon 2 Feb: Anti-matter + SM • Wed 4 Feb: CKM matrix + Unitarity Triangle • Mon 9 Feb: Mixing + Master eqs. + B0J/ψKs • Wed 11 Feb: CP violation in B(s) decays (I) • Mon 16 Feb: CP violation in B(s) decays (II) • Wed 18 Feb: CP violation in K decays + Overview • Mon 23 Feb: Exam on part 1 (CP violation) • 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 Niels Tuning (2)

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

5. Recap uI u W W d,s,b dI Diagonalize Yukawa matrix Yij • Mass terms • Quarks rotate • Off diagonal terms in charged current couplings Niels Tuning (5)

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

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

8. This was theory, now comes experiment • We already saw how the moduli |Vij| 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. s b b s Neutral Meson Oscillations Why? • Loop diagram: sensitiveto new particles • Provides a second amplitude • interferenceeffects in B-decays Niels Tuning (9)

10. Dynamics of Neutral B (or K) mesons… Time evolution of B0 andB0can be described by an effective Hamiltonian: No mixing, no decay… No mixing, but with decays… (i.e.: H is not Hermitian!) • With decays included, probability of observing either B0orB0 must go down as time goes by: Niels Tuning (10)

11. M12 describes B0B0 via off-shell states, e.g. the weak box diagram G12 describes B0fB0 via on-shell states, eg. f=p+p- Describing Mixing… Time evolution of B0 andB0can be described by an effective Hamiltonian: Where to put the mixing term? Now with mixing – but what is the difference between M12 and G12? Niels Tuning (11)

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

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

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

15. B Oscillation Amplitudes For an initially produced B0 or aB0it then follows: (using: with For B0, expect: DG ~ 0, |q/p|=1 ~ Niels Tuning (15)

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

17. Compare the mesons: Probability to measure P or P, when we start with 100% P P0P0 P0P0 Probability  By the way, ħ=6.58 10-22 MeVs x=Δm/Γ: avg nr of oscillations before decay Time  Niels Tuning (17)

18. (2-component state in P0 and P0 subspace) Summary (1) • Start with Schrodinger equation: • Find eigenvalue: • Solve eigenstates: • Eigenstates have diagonal Hamiltonian: mass eigenstates! Niels Tuning (18)

19. Summary (2) • Two mass eigenstates • Time evolution: • Probability for |P0>  |P0> ! • Express in M=mH+mL and Δm=mH-mL Δm dependence

20. q,p,Mij,Γijrelated through: Summary • p, q: • Δm, ΔΓ: • x,y: mixing often quoted in scaled parameters: Time dependence (if ΔΓ~0, like for B0): with Niels Tuning (20)

21. Personal impression: • People think it is a complicated part of the Standard Model (me too:-). Why? • Non-intuitive concepts? • Imaginary phase in transition amplitude, T ~ eiφ • Different bases to express quark states, d’=0.97 d + 0.22 s + 0.003 b • Oscillations (mixing) of mesons: |K0> ↔ |K0> • Complicated calculations? • Many decay modes? “Beetopaipaigamma…” • PDG reports 347 decay modes of the B0-meson: • Γ1 l+ νl anything ( 10.33 ± 0.28 ) × 10−2 • Γ347ν ν γ <4.7 × 10−5 CL=90% • And for one decay there are often more than one decay amplitudes… Niels Tuning (21)

22. M12 describes B0B0 via off-shell states, e.g. the weak box diagram G12 describes B0fB0 via on-shell states, eg. f=p+p- Describing Mixing Time evolution of B0 andB0can be described by an effective Hamiltonian: Niels Tuning (22)

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

24. Box diagram and Δm Niels Tuning (24)

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

26. Box diagram and Δm: Inami-Lim • B0-mixing C.Gay, B Mixing, hep-ex/0103016

27. Box diagram and Δm: Inami-Lim • Bs0-mixing C.Gay, B Mixing, hep-ex/0103016

28. Next: measurements of oscillations • B0 mixing: • 1987: Argus, first • 2001: Babar/Belle, precise • Bs0 mixing: • 2006: CDF: first • 2010: D0: anomalous ?? Niels Tuning (28)

29. B0 mixing Niels Tuning (29)

30. B0 mixing What is the probability to observe a B0/B0 at time t, when it was produced as a B0 at t=0? Calculate observable probility Y*Y(t) A simple B0 decay experiment. Given a source B0 mesons produced in a flavor eigenstate |B0> You measure the decay time of each meson that decays into a flavor eigenstate (either B0 orB0) you will find that Niels Tuning (30)

31. B0 mixing: 1987 Argus • B0 oscillations: • First evidence of heavy top •  mtop>50 GeV • Needed to break GIM cancellations • NB: loops can reveal heavy particles! Phys.Lett.B192:245,1987 Niels Tuning (31)

32. s d d b b μ d μ B0 mixing: t quark GIM: c quark B0 mixing pointed to the top quark: K0→μμpointed to the charm quark: GIM, Phys.Rev.D2,1285,1970 ARGUS Coll, Phys.Lett.B192:245,1987 … … …

33. B0 mixing: 2001 B-factories You can really see this because (amazingly) B0 mixing has same time scale as decay t=1.54 ps Dm=0.5 ps-1 50/50 point at pDm  t Maximal oscillation at 2pDm  2t Actual measurementof B0/B0 oscillation Also precision measurementof Dm! Niels Tuning (33)

34. Bs0 mixing Niels Tuning (34)

35. Bs0 mixing: 2006 Niels Tuning (35)

36. Bs0 mixing (Δms): SM Prediction Vts Vts Vts  = 1.210 +0.047 from lattice QCD -0.035 Vts Wolfenstein parameterization CKM Matrix Ratio of frequencies for B0 and Bs Vts ~ 2 Vtd ~3 Δms ~ (1/λ2)Δmd ~ 25 Δmd Niels Tuning (36)

37. Bs0 mixing (Δms): Unitarity Triangle CKM Matrix Unitarity Condition Niels Tuning (37)

38. Bs0 mixing(Δms) b t s Bs W W Bs s t b x b̃ s̃ s b g̃ Bs g̃ Bs s̃ s b b̃ x Δms=17.77 ±0.10(stat)±0.07(sys) ps-1 hep-ex/0609040 cos(Δmst) Proper Time t (ps) Niels Tuning (38)

39. Bs0 mixing(Δms): New: LHCb b t s Bs W W Bs s t b x b̃ s̃ s b g̃ Bs g̃ Bs s̃ s b b̃ x LHCb, arXiv:1304.4741 Niels Tuning (39)

40. Bs0 mixing(Δms): New: LHCb Ideal Tagging, resolution Acceptance LHCb, arXiv:1304.4741 Niels Tuning (40)

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 Niels Tuning (41)

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

43. Notation: Define Af and λf Niels Tuning (43)

44. Some algebra for the decay P0 f Interference P0 f P0P0 f Niels Tuning (44)

45. Some algebra for the decay P0 f Niels Tuning (45)

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

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

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

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