1. Niels Tuning (1) Physics of Anti-matter Lecture 6 N. Tuning

2. Plan 1)Mon 3 Feb: Anti-matter + SM 2)Wed 5 Feb: CKM matrix + Unitarity Triangle 3)Mon 10 Feb: Mixing + Master eqs. + B 0  J/ψK s 4)Wed 12 Feb:CP violation in B (s) decays (I) 5)Mon 17 Feb:CP violation in B (s) decays (II) 6)Wed 19 Feb:CP violation in K decays + Overview 7)Mon 24 Feb:Mini-project (MSc. V. Syropoulos)  Wed 26 Feb:Exam Niels Tuning (2)  Final Mark: 2/3*Exam + 1/6*Homework + 1/6*Mini project  In March: 7 Lectures on Flavour Physics by prof.dr. R. Fleischer

4. Diagonalize Yukawa matrix Y ij –Mass terms –Quarks rotate –Off diagonal terms in charged current couplings Niels Tuning (4) Recap uIuI dIdI W u d,s,b W

5. Niels Tuning (5) Why bother with all this? CKM matrix has origin in L Yukawa  Intricately related to quark massed… Both quark masses and CKM elements show intriguing hierarchy There is a whole industry of theorist trying to postdict the CKM matrix based on arguments on the mass matrix in L Yukawa …

6. Niels Tuning (6) 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):

7. 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 (7)

8. Meson Decays Formalism of meson oscillations: Subsequent: decay Interference P0 fP0 fP 0  P 0  f Interference(‘direct’) Decay

9. Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference Niels Tuning (9)

10. Classification of CP Violating effects 1.CP violation in decay Example: 2.CP violation in mixing Example: 3.CP violation in interference Example: Niels Tuning (10) B 0 →J/ψK s

11. Remember! Necessary ingredients for CP violation: 1)Two (interfering) amplitudes 2)Phase difference between amplitudes –one CP conserving phase (‘strong’ phase) –one CP violating phase (‘weak’ phase) Niels Tuning (11)

12. Remember! Niels Tuning (12)

13. Niels Tuning (13) CKM Angle measurements from B d,u decays Sources of phases in B d,u amplitudes* The standard techniques for the angles: *In Wolfenstein phase convention. AmplitudeRel. MagnitudeWeak phase bcbcDominant0 bubuSuppressed γ t  d ( x2, mixing)Time dependent 2β2β B 0 mixing + single b  c decay B 0 mixing + single b  u decay Interfere b  c and b  u in B ± decay. bubu tdtd

14. Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference Niels Tuning (14)

15. Niels Tuning (15) Other ways of measuring sin2β Need interference of b  c transition and B 0 –B 0 mixing Let’s look at other b  c decays to CP eigenstates: All these decay amplitudes have the same phase (in the Wolfenstein parameterization) so they (should) measure the same CP violation

16. CP in interference with B  φK s Same as B 0  J/ψK s : Interference between B 0 → f CP and B 0 → B 0 → f CP –For example: B 0 → J/ΨK s and B 0 → B 0 → J/ΨK s –For example: B 0 → φ K s and B 0 → B 0 → φ K s Niels Tuning (16) + e -iφ Amplitude 2 Amplitude 1

17. CP in interference with B  φK s : what is different?? Same as B 0  J/ψK s : Interference between B 0 → f CP and B 0 → B 0 → f CP –For example: B 0 → J/ΨK s and B 0 → B 0 → J/ΨK s –For example: B 0 → φ K s and B 0 → B 0 → φ K s Niels Tuning (17) + e -iφ Amplitude 2 Amplitude 1

18. Niels Tuning (18) Penguin diagrams Nucl. Phys. B131:285 1977

19. Penguins?? Niels Tuning (19) The original penguin:A real penguin:Our penguin:

20. Funny Niels Tuning (20) Super Penguin: Penguin T-shirt: Flying Penguin Dead Penguin

21. Niels Tuning (21) The “b-s penguin” B 0  J/ψK S B0φKSB0φKS  … unless there is new physics! New particles (also heavy) can show up in loops: –Can affect the branching ratio –And can introduce additional phase and affect the asymmetry Asymmetry in SM b s μ μ “Penguin” diagram: ΔB=1

22. Niels Tuning (22) Hint for new physics?? sin2β sin2 β b  ccs = 0.68 ± 0.03 sin2β peng B J/ψ KsKs b d c c s d φ KsKs B s b d d s t s ? sin2 β peng = 0.52 ± 0.05 g,b,…? ~~ S.T’Jampens, CKM fitter, Beauty2006

23. Next… Something completely different? No, just K 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference

24. Kaons… Niels Tuning (24) Different notation: confusing! K 1, K 2, K L, K S, K +, K -, K 0 Smaller CP violating effects  But historically important!  Concepts same as in B-system, so you have a chance to understand…

25. Neutral kaons – 60 years of history … the θ 0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ 0 's undergo the familiar decay into two pions. 1947 : First K 0 observation in cloud chamber (“V particle”) 1955 : Introduction of Strangeness ( Gell-Mann & Nishijima ) K 0,K 0 are two distinct particles ( Gell-Mann & Pais ) 1956 : Parity violation observation of long lived K L ( BNL Cosmotron ) 1960 : m = m L -m S measured from regeneration 1964 : Discovery of CP violation ( Cronin & Fitch ) 1970 : Suppression of FCNC, K L   - GIM mechanism/charm hypothesis 1972 : 6-quark model; CP violation explained in SM ( Kobayashi & Maskawa ) 1992-2000 : K 0,K 0 time evolution, decays, asymmetries ( CPLear ) 1999-2003 : Direct CP violation measured: ’ ≠ 0 ( KTeV and NA48 ) From G.Capon Niels Tuning (25)

26. Intermezzo: CP eigenvalue Niels Tuning (26) Remember: –P 2 = 1 (x  -x  x) –C 2 = 1 ( ψ   ψ  ψ ) –  CP 2 =1 CP | f > =  | f > Knowing this we can evaluate the effect of CP on the K 0 CP|K 0 > = -1| K 0 > CP| K 0 > = -1|K 0 > CP eigenstates: |K S > = p| K 0 > +q|K 0 > |K L > = p| K 0 > - q|K 0 > |K s > (CP=+1) →   (CP= (-1)(-1)(-1) l=0 =+1) |K L > (CP=-1) →  (CP = (-1)(-1)(-1)(-1) l=0 = -1) ( S( K )=0  L( ππ )=0 )

27. Niels Tuning (27) Decays of neutral kaons Neutral kaons is the lightest strange particle  it must decay through the weak interaction If weak force conserves CP then –decay products of K 1 can only be a CP=+1 state, i.e. |K 1 > (CP=+1) →   (CP= (-1)(-1)(-1) l=0 =+1) –decay products of K 2 can only be a CP=-1 state, i.e. |K 2 > (CP=-1) →  (CP = (-1)(-1)(-1)(-1) l=0 = -1) You can use neutral kaons to precisely test that the weak force preserves CP (or not) –If you (somehow) have a pure CP=-1 K 2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP… ( S( K )=0  L( ππ )=0 )

28. Niels Tuning (28) Designing a CP violation experiment How do you obtain a pure ‘beam’ of K 2 particles? –It turns out that you can do that through clever use of kinematics Exploit that decay of K into two pions is much faster than decay of K into three pions –Related to fact that energy of pions are large in 2-body decay –  1 = 0.89 x 10 -10 sec –  2 = 5.2 x 10 -8 sec (~600 times larger!) Beam of neutral Kaons automatically becomes beam of |K 2 > as all |K 1 > decay very early on… Initial K 0 beam K 1 decay early (into ) Pure K 2 beam after a while! (all decaying into πππ ) !

29. Niels Tuning (29) The Cronin & Fitch experiment Incoming K 2 beam Decay of K 2 into 3 pions If you detect two of the three pions of a K 2   decay they will generally not point along the beam line Essential idea: Look for (CP violating) K 2   decays 20 meters away from K 0 production point

30. Niels Tuning (30) The Cronin & Fitch experiment Incoming K2 beam Decay pions If K 2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K 2   decay) Essential idea: Look for K 2   decays 20 meters away from K 0 production point

31. Niels Tuning (31) The Cronin & Fitch experiment Incoming K 2 beam Decay pions Result: an excess of events at =0 degrees! K 2   decays (CP Violation!) Essential idea: Look for K 2   decays 20 meters away from K 0 production point K 2   decays Note scale: 99.99% of K   decays are left of plot boundary CP violation, because K 2 (CP=-1) changed into K 1 (CP=+1 )

32. "for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons" Val Logsdon Fitch 1/2 of the prize Princeton University Princeton, NJ, USA b. 1923 James Watson Cronin 1/2 of the prize University of Chicago Chicago, IL, USA b. 1931 The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments. Nobel Prize 1980 Niels Tuning (32)

33. Cronin & Fitch – Discovery of CP violation Conclusion: weak decay violates CP (as well as C and P) –But effect is tiny! (~0.05%) –Maximal (100%) violation of P symmetry easily follows from absence of right-handed neutrino, but how would you construct a physics law that violates a symmetry just a tiny little bit? Results also provides us with convention-free definition of matter vs anti-matter. –If there is no CP violation, the K 2 decays in equal amounts to  + e - e (a)  - e + e (b) –Just like CPV introduces K 2  ππ decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a) –“Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K meson” Niels Tuning (33)

34. Intermezzo: Regeneration Different cross section for σ(p K 0 ) than σ(p  K 0 ) o Elastic scattering: same o Charge exchange : same o Hyperon production: more for  K 0 ! What happens when K L -beam hits a wall ?? Then admixture changes…: |K L > = p| K 0 > - q|  K 0 >  Regeneration of K S ! Could fake CP violation due to K S →π + π - … strong interactions: must conserve strangeness leave little free energy – unlikely! Niels Tuning (34)

35. K S and K L K L and K S are not orthogonal: Usual (historical) notation in kaon physics: Modern notation used in B physics: Regardless of notation: Niels Tuning (35)

36. Three ways to break CP; e.g. in K 0 → π + π - Niels Tuning (36)

37. Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference Niels Tuning (37)

38. Time evolution Niels Tuning (38)

39. B-system 2. CP violation in mixing K-system CPLear (2003) BaBar, (2002) CPLEAR, Phys.Rep. 374(2003) 165-270

40. B-system 2. CP violation in mixing K-system NA48, (2001)  L (e) = (3.317  0.070  0.072)  10 -3 BaBar, (2002) Niels Tuning (40)

41. B-system 3.Time-dependent CP asymmetry B 0 →J/ψK s BaBar (2002) Niels Tuning (41)

42. B-system 3.Time-dependent CP asymmetry K-system     rate asymmetry CPLear (PLB 1999) K0→π-π+K0→π-π+ B 0 →J/ψK s ~50/50 decay as K s and K L + interference! BaBar (2002) K0K0 K0K0 _

43. The Quest for Direct CP Violation Indirect CP violation in the mixing :  Direct CP violation in the decay:  ’ A fascinating 30-year long enterprise: “Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction?” Niels Tuning (43)

44. B system 1. Direct CP violation K system Different CP violation for the two decays  Some CP violation in the decay! B 0 →K + π - ε’≠ 0  B 0 →K - π + K 0 →π - π + K 0 →π 0 π 0 K0→π-π+K0→π-π+ K0→π0π0K0→π0π0 Niels Tuning (44)

45. Niels Tuning (45)

46. Niels Tuning (46) Hints for new physics? φ KsKs B s b d d s t s g,b,…? ~~ 1) sin2β≠sin2β ? 4 th generation, t’ ? 3) β s ≠0.04 ? 2) A CP (B 0  K + π - )≠A CP (B +  K + π 0 ) ? 4) P(B 0 s →  B 0 s ) ≠ P(B 0 s ←  B 0 s )

47. Present knowledge of unitarity triangle Niels Tuning (47)

48. “The” Unitarity triangle We can visualize the CKM-constraints in () plane

49. Present knowledge of unitarity triangle

50. I) sin 2 β

52. II) ε and the unitarity triangle: box diagram CP violation in mixing

53. II) ε and the unitarity triangle: box diagram

54. Im(z 2 )=Im( (Rez+iImz) 2 )=2RezImz

55. II) ε and the unitarity triangle ρ Niels Tuning (55)

56. III.) |V ub | / |V cb | Measurement of V ub –Compare decay rates of B 0  D *- l + and B 0   - l + –Ratio proportional to (V ub /V cb) 2 –|V ub /V cb | = 0.090 ± 0.025 –V ub is of order sin( c ) 3 [= 0.01]

57. IV.) Δm d and Δm s Δm depends on V td V ts constraints hadronic uncertainties

58. Present knowledge of unitarity triangle Niels Tuning (58)

59. Niels Tuning (59) Hints for new physics? φ KsKs B s b d d s t s g,b,…? ~~ 1) sin2β≠sin2β ? 4 th generation, t’ ? 3) β s ≠0.04 ? 2) A CP (B 0  K + π - )≠A CP (B +  K + π 0 ) ? 4) P(B 0 s →  B 0 s ) ≠ P(B 0 s ←  B 0 s )

60. Niels Tuning (60) More hints for new physics? 5) ε K ?  Treatment of errors…  Input from Lattice QCD B K  Strong dependence on V cb

61. Niels Tuning (61) More hints for new physics? 6) V ub : 2.9 σ ?? BR(B + →τυ)=1.68 ± 0.31 10 -4 Predicted: 0.764± 0.087 10 -4 (If f Bd off, then B Bd needs to be off too, to make Δm d agree) | V ub | from B→τν From: H.Lacker, and A.Buras, Beauty2011, Amsterdam | V ub | from fit |V ub | avg from semi-lep ?

62. A.Buras, Beauty2011: Niels Tuning (62)

63. A.Buras, Beauty2011: Niels Tuning (63)

64. Standard Model: 25 free parameters Strong interaction:  s (m Z )  0.117 e   = 1 2 3 neutrino mixing (4) Electro-weak interaction:  e (0)  1/137.036 m W  80.42 GeV m Z  91.188 GeV m H >114.3 GeV Elementary particle masses (MeV): m e  0.51099890 m   105.658357 m   1777.0 m u  3 m c  1200 m t  174000 m d  7 m s  120 m b  4300 m < 0.000003 m < 0.19 m < 18.2 ee u’ d’ s’ = udsuds quark mixing (4) V ij q V ij l m H >114.3 GeV CMS LHCb Niels Tuning (64)

65. The CKM matrix Couplings of the charged current: Wolfenstein parametrization: Magnitude:Complex phases: b WW u gV ub Niels Tuning (65)

66. The CKM matrix Couplings of the charged current: Wolfenstein parametrization Magnitude:Complex phases: 1) 2) 3) Niels Tuning (66)

67. Complex phases: The CKM matrix Couplings of the charged current: Wolfenstein parametrization: Magnitude:

68. Remember the following: CP violation is discovered in the K-system CP violation is naturally included if there are 3 generations or more –3x3 unitary matrix has 1 free complex parameter CP violation manifests itself as a complex phase in the CKM matrix The CKM matrix gives the strengths and phases of the weak couplings CP violation is apparent in experiments/processes with 2 interfering amplitudes with different strong and weak phase –Often using “mixing” to get the 2 nd decay process Flavour physics is powerful for finding new physics in loops! –Complementary to Atlas/CMS Niels Tuning (68)

69. Remember the following: CP violation is discovered in the K-system CP violation is naturally included if there are 3 generations or more –3x3 unitary matrix has 1 free complex parameter CP violation manifests itself as a complex phase in the CKM matrix The CKM matrix gives the strengths and phases of the weak couplings CP violation is apparent in experiments/processes with 2 interfering amplitudes with different strong and weak phase –Often using “mixing” to get the 2 nd decay process Flavour physics is powerful for finding new physics in loops! –Complementary to Atlas/CMS Niels Tuning (69)

70. 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 (70)

71. Backup Niels Tuning (71)

72. SLAC: LINAC + PEPII PEP-II accelerator schematic and tunnel view LER HER Linac

73. Coherent Time Evolution at the  S  B-Flavor Tagging Exclusive B Meson Reconstruction PEP-2 (SLAC) Vertexing & Time Difference Determination Niels Tuning (73)

74. LHCb: the Detector p T of B-hadron η of B-hadron High cross section LHC energy B s produced in large quantities Large acceptance b’s produced forward Small multiple scattering Large boost of b’s Trigger ↓ Low p T Leptons + hadrons (MUON, CALO) Particle identification (RICH)

75. The well known triangle: γ α β γβ q W q’V q’q CP phases: Measure the CKM triangle to unprecedented precision Measure very small Branching Ratios Measuring the Quark Couplings Niels Tuning (75)