1. 3 The different measurement related to CKM and CP violation

2. from O. Schneider

3. B   +other charmonium radiative decays X s ,X d , X s ll B  DK +from Penguins Charm Physics (Dalitz) ? theo. clean CKM and CP Violation Physics

5.  = a 1 /B 0 > + a 2 /B 0 > It satisfies the (coupled) Schrodinger equation : New interaction which allows the transition between B 0 and B 0 H has to be diagonalised to find the eigenstates of the new interaction Existence of non diagonal terms B 0 / B 0 eigentates of the strong interaction The mass (strong interaction) eigenstates are a linear combination of the eigenstates at the decay (weak interaction) Weak interaction ….General introduction……. (which can change the flavour) (if CPT, B 0 and B 0 have the same mass) As a coupled oscillator If CP is conserved Introduction to the Oscillation and CP Mass difference from weak interaction  m = M long  M short = 2 Re (M 12 )

6. More generally the eigenstates can be written : Solving the eigenvalues equation it follows : For B system useful def. B 0 = bd Eigenstates of flavours def :  =  ’=1 CP Eigenstates If CPT

7. We want now to have the evolution of a meson B 0 (flavour eigenstate) after the time t=0 of its creation (consider ) It follows : MASTER FORMULA

8. Considering only the mixing : If you add  (useful for the discussion on charm) the previous formula become

9. x is a number the mixing frequency in unit of lifetime x>>1 rapid oscillation x<<1 slow oscillation B0dB0d db d b t WW WW B0dB0d t b c u d Slow oscillations BdBd We also define

10. B0sB0s sb s b t WW WW B0sB0s t b c u d Rapid oscillations BsBs D0D0 uc u c d,s WW WW D0D0 c s u d D0D0 K0K0 ds d s c WW WW K0K0 c s u u d K0K0

11.  12 is described by the box diagram, relative to the decay (absorptive part). So only common state to B 0 and B 0 contribute  only light quark appear in the final state b d c d B0B0 b d u d B0B0 d u c d Example of common final states in Bd 0 and Bd 0 decays b d d c u b b d c u B0B0 b d c u B0B0 b d d u b c unit. since modes contributing to   have small Br  to be significant needs   2 to be large

12. b s c s Bs 0 b s c s s c c s b s s c c b  not so small : there are Cabibbo enhanced modes which at the level of quark are common to Bs and Bs (  c u d u D0D0 c u d u D0D0 u d d u c u u d d c BsBs D0D0  small, since we have to look at c  d and not c  s transitions K0K0 Here we can see differently, looking at the CP eigentstates (L,S).  is large ~1 because of the accident of the phase space suppression  vs 

13. x=  m/  y=  K0K0 ~1 D0D0 10 -3 -10 -5 Bd0Bd0 ~0.75~few% Bs0Bs0 ~25(10-15)%

14. Study of the time dependent behaviour of the B 0 - B 0 Oscillation  m q can be seen as an oscillation frequency : 1 ps -1 = 6.58 10 -4 eV In SM  F=2 process GIM mechanism (Rate ~ m 1 2 - m 2 2 ) B 0 d,s d, sb b t,c,u WW WW B 0 d,s t,c,u Dominated by t exchange V ts V td Rate LARGE Allow to access fundamental parameters of the Standard Model The probability that the meson B 0 produced (by strong interaction) at t = 0 transforms (weak interaction) into B 0 (or stays as a B 0 ) at time t is given by :

15. ))1(( 222 2 2    ss dd BB BB s d Bf Bf m m    better know than f B 2 B B  m d /  m s performant constraint for  and   m s oscillations fast Excellent time resolution required Circle around (1,0) in the  plane

16. b/b at the production timeB/B at the decay time Purity of tagging at decay time :  d Purity of tagging at production time:  p As soon as  m s becomes larger the precision on the time measurement becomes crucial Measurement of the decay time All these variables are important and in particular the time resolution Example at LEP/SLD

17. Inclusive Vtx.  m d = 0.531±0.025±0.007 ps -1 LEP NoMix(t)-Mix(t) NoMix(t)+Mix(t) T=2  m ~D~D  m = (0.516  0.016  0.010) ps -1

18. Impressive experimental activity in the last 12 year LEP/SLD/CDF ~ 1993-2002 B-factories ~ 2000  ……

19. Combination using the amplitude method msms Combination using A and  A  m s excluded at 95% CL A + 1.645  A < 1 At given  m s A = 0 no oscillation A = 1 oscillation Sensitivity same relation with A = 0 1.645  A = 1 Measurement of A at each  m s Combine many different analyses which give limits

20. Today : Bit of history :

22. A/  A (17.25 ps –1 ) = 3.5 “In absence of signal, there is a 0.5% probability to see a signature like this” (from toy MC) Threshold set in advance to make measurement was 1%  m s = 17.33 +0.42 (stat) ± 0.07 (syst) ps –1 -0.21

23. Three possible types of CP violation B0B0 B0B0 f CP A1A1 A2A2 A1A1 A2A2 M 12  12 direct mixing Interference mixing-decay And now….the CP violation

24. Analogy: “Double-Slit” Experiments with Matter and Antimatter source In the double-slit experiment, there are two paths to the same point on the screen. In the B experiment, we must choose final states that both a B 0 and a B 0 can decay into. We perform the B experiment twice (starting from B 0 and from B 0 ). We then compare the results.

25. b u BB u u u s  KK V ub b u BB s u  KK u u W W t Direct CP Violation - Generalia In this case :

26. So far the only confirmed case for direct CP violation in B decays Large A CP requires amplitudes of similar order Example : b→u: suppressed tree: charmless decays (competitive channels, as Penguins) A cp (B 0  K     0.095+/- 0.013

27. Observation of direct CP violation in B 0  K +  - BaBar 2004 New Belle Result: -0.113+/- 0.022+/- 0.008 232x10 6 BB’s But angle  cannot extracted from it, since it depends upon weak phase and strong amplitude and phase

28. Direct CP violation occurs because there are two different ways of reaching the same final state b u BB c u u s DD KK V cb W b u BB u u KK c s W D  V ub = |V ub | e -i  Color suppressed also possible GLW (Gronau,London,Wyler) Method ADS (Atwood, Dunietz, Soni) Method In this particular case sensitive to  D 0 and D 0 are involved Look at D 0 (CP) states D 0 and D 0  f D 0 and D 0 give the same final strong phase difference between V ub and V cb mediated transitions strong amplitude (the same for V ub and V cb mediated transitions

29. GLW (Gronau,London,Wyler) Method ADS (Atwood, Dunietz, Soni) Method (only Babar) r B is a crucial parameter. It drives the sensitivity on  (3.62 ± 0.29)10 -3

30. What about r B ? b u BB u u KK c s W D  V ub = |V ub | e -i  b u BB u u KK c s D  V ub = |V ub | e -i  b u BB c u u s DD KK V cb W b u BB c u KK u s W D  V cb + + Evaluation can be done if Annihilation diagram is neglected If |A/C|~0.3 (max?) Beyond this approx. (+- 30% according to the interference between A and C) Conclusions : should be measured on data

31. Interference due to the overlap of large resonances from Cabibbo allowed V cb and V ub transitions Dalitz Method - GGSZ D 0  K S     new technique which make use of the D0 three-body decays K*+ (1430) BaBar angle  K *+ (892)(  s  + )  - ) ADS method K s  (    - ) CP-GLW method Plot of the weights (second derivative wrt 

32. r DK = 0.071 ± 0.024 r comes out to be small. more difficult to get a precise measurement of  RESULTS ON  γ = (83 ± 19) o (up to π ambiguity)

33.  Boost:  = 0.55 Start the Clock Coherent BB pair, L=1 B0B0 B0B0  4S  e + e -   (4S)  B B Exclusive B meson and vertex reconstruction   KSKS B tag B rec  K-K- Flavor tag and vertex reconstruction  At the  (4S) resonance

34. Introducing Similar equations for Here t should be changed in  t=(t (CP-decay) - t tag ) Back to B 0

35. There is some phase convention :  is arbitrary There are phases freedom: Consider the following phase transformation, which has no physical effects Under this phase transformation :

36. Violation in the interference between decay and mixing In general you should study : And fit : Special case : the final state f is a CP eigenstate Only one quantity mixing decay B0B0 B0B0 f ( f ) decay mixing

37. Violation in the interference between decay and mixing decay B0B0 B0B0 f ( f ) decay mixing

38. db d b t,c,u WW WW B0dB0d B decayK mixing b d c c s d J/  K0K0 B0dB0d Is a general result : if the decay is dominated by a single amplitude : Im  is always given by the sine of twice an angle in the Unitarity Triangle

39. For J/ ,K 0 ~only one amplitude Direct CP violation

40. b d s d J/  K0K0 B0dB0d t W Order 4 V ts V * tb 1) The diagram at tree level is dominant 2) The second diagram (Penguin) has the same phase at order 2 since V ts is complex and differs from V cb at order 4 Extraction of sin2  from J/  K 0 theoretically clean at 1% level b d c c s d J/  K0K0 B0dB0d V cb V * cs

41. before tagging and vertexing cuts B decays to flavor-specific final states B decays to CP-eigenstates with charmonium Add Belle D*lnu here Belle BaBar Example of the first significant measurement

42. A cp (t)F(t) t(ps) sin2 D sin2 Everything perfect  Add tag mistakes  Dilution: D=1-2w Add imperfect t resolution Must understand tagging/mistagging and  t resolution !! Experimental aspects of the sin2  measurement: 

43.  t(ps) 535M sin2  gives the best constraint on  plane and the error can still be reduced And now. Very recent results :

44. Example other modes : B 0  D 0 h 0 Babar Many other modes to measure the angle  One example where you can also measure cos2 

45. dd s b WW B0dB0d t s s  K0K0 g s b b s ~ ~ ~ New Physics contribution (2-3 families) sin2  from “s Penguins”…a lot of progress.. Disagreement between sin2  from b  ccs and b  qqs still there and intriguing..

46. Life is not always so simple…. b d u d  B0dB0d  b d u d  B0dB0d  Phase of V ub BUT: b d d d B0dB0d t W u u Order V ub ~ 3 Order V td ~ 3 1)Two kind of diagrams are of the same order 2) and different phases : V ub and V td …the amplitudes of different contributions have to be taken into account to know the total weak phase Tree diagrams(T) Penguin diagrams (P) In fact also Color suppressed diagrams contribute… So in this case we measure both C and S

47. Starting from SU(2) amplitudes :    Uknowns 6 : T, P, T C,,  P,  TC,  Observable 8 : 3Br-fractions, C +-,S +-,A CP(+0),C 00,S 00 The angle  is measured using  and  The way out is to use neutral and charged B and to measured all the possible branching fractions and CP asymmetries in the given system and rely on SU(2)

48.  modes  modes consistent with no CP violation  eff ~90 o (0/180) o Many novelties on the measurement of the angle  Important measurement because it gives the contributions of Penguins diagram

49. α = [81,111] o U [159,171] o @ 95% Prob. (SM solution: α =(93 ± 8) o @ 68% Prob.)

50. D0D0 uc u c d,s WW WW D0D0 c s u d D0D0 As you can notice we did not put the b in the loop since the coupling would have Been |V ub *V cb | 2 ~ 10. Very small. Very important consequence. The D oscillation is a two “family buisness”, the third family is excluded, so the CP violation is very small and the D oscillation is zero in the SU(3) limit (m s 2 -m d 2) =0 c u d u D0D0 c u d u D0D0 u d d u c u u d d c  small, since we have to look at c  d and not c  s transitions

51. Mixing in D 0 -D 0 system Observed !! BaBar Use D 0 from D* to tag the flavour of D 0 D* +  D 0  + DCS decays InterferenceOscillations (1 ± cos  m t) ~ x 2 /2 idem for  ~ y 2 /2 D0D0 D0D0 K K  mixing doubly Cabibbo suppressed(DCS) Cabibbo favoured(CF) Wrong sign : WS  strong phase CF/DCS ampl. rotation (x,y)  (x’,y’) mixing no mixing 3.9  evidence Submitted to PRL (hep-ex/0703020)

52. 2.4  Method using Dalitz ex : D 0  K 0 S     RS and WS occupy the same Dalitz plot. Measurement of strong phase  Constraint on x,y 2 ( also sensitive to sign of x) K  K + (or     ) pure CP D 1 0 K    50% D 1 0 + D 2 0 Constraint on y CP eingenstate lifetimes Two talks tomorrow +theory talk…. Belle : Compare assuming  =0: (x'=x, y'=y) Best fit Within 2  less if  0 Belle life. (1  ) ALL is very exciting. D mixing is Now observed, we need more Measurements with different techniques to get x and y parameters. Belle Dalitz

53. …also radiative and leptonic rare B decays b s,d u,c,t W   q q  →  *(K +  - )  K+K+ -- Loops sensitive to New Physics (heavy “objects” in the loop). ACP one of the best probe of NP in the b  s sector Photon energy spectrum depends on the quark mass and Fermi movement  important for addressing theoretical error for V cb (see later) if b  d  is also measured : Br(b  d  )/ Br(b  s  )  |V td /V ts | 2 same constraint as  m d /  m s Radiative B decays  b  s (d)  B oscillations allow to address V td and V ts CKM elements Inclusive decays are cleaner (excl. depends upon not very well known form factors) V td, V ts

54. Radiative penguin decays of B mesons Observation of B  K*  CLEO II (1993): Loops in B decays Now it’s a physics program!

55. b→s,d: penguins: radiative decays ( dominated by a single amplitude in SM )  small predicted A CP Fantastic probe of NP

56. Observation of the b  d  decays B   Mode10 -6

57. Leptonic B rare decays : B  X s l + l  Sensitive to new physics l l l l  All perfectly agree with theory predictions. -Measurements of Br done -We start to perform A FB measur.

58. BR(B → τ ν) = (0.85 ± 0.13)10 -4 f B = 237 ± 37 GeV from exp+UTfit f B = 189 ± 27 GeV Lattice QCD SM expectation Exp. likelkihood BABAR+BELLE BR(B → τ ν) = (1.31 ± 0.48)10 -4 A milestone in B physics : the measurement of the leptonic decay B   First leptonic decay seen on B meson

59. Determination of V ub and V cb b c l V cb b u l V ub Determined from semileptonic B decays. Decays at the tree level not affected by New Physics Circle around (0,0) in the  plane 1

60. …in fact V cb is the Unitarity triangle normalization. It enters …everywhere ! The precise determination of V cb is primordial

61.  Determination of V cb limited by theoretical uncertainties ….. b c l V cb Determination of V cb b sl theo sl Br Fclb .exp. )(     Inclusive Method f(  2   m b,  s,  D (or 1/m b 3  mbmb (  Fermi movement)( also named  ) 22 cb V 2 Based on OPE Essential point is to control /“measure” the effects of strong interaction

62. Example of single best Inclusive lifetime measurement t b = 1.570  0.005 stat.  0.008 sys. ps World average: Measurement of Br(sl) New ideas came few years ago : Moments of distributions HADRONIC mass, LEPTON Momentum, (Photon energy b  s  Which are sensitive to  2   m b …

63. Precision measurements of |V cb | Inclusive V cb still progress… BaBar/CLEO/CDF/DELPHI Kinetic scheme New technique in b-FACTORIES : full reconstruction of one of the B

64. Exclusive method F(w) is the form factor describing the B  D * transition Based on HQET At zero recoil (w=1), as M Q  F(1)  1 Strategy : Measure d  /dw extrapolate to w=1 to extract F(1) |V cb | BELLE

65. Limiting factor F(1) theo. error > twice the exp. error F(1)*|V cb | = 36.2 ± 0.8  |V cb | = 41.4 ± 2.1 inclusive V cb  |V cb | = 41.6 ± 0.7 ± 0.6

66. Br ~ |V ub | 2 in a limited space phase region… Using Babar E l, (X s  ElEl Progress on V ub.. Inclusive : improving analyses and improving the control of the theory vs cuts B  X u l

67. untagged analysis is the most precise B   l B  (exclusive) l

68. APPENDIX Further Material

69. Appendix Part III a) Note on Hadronic Parameters and on their determination

70. BB bubu W l  Vacuum saturation approx : the matrix element of V-A current is calculated between the vacuum and the pseudoscalar meson, only the axial current contributes (pseudovector*pseudoscalar  vector p   f B translates the probability that the quark and the antiquark meet to decay ( or the size of the B meson wave function at the origin) A new constant B B is inserted to take all possible deviations from vacuum saturation approximation into account Let’s consider the oscillation diagram Gluon exchange between B 0 and B 0 Soft gluon exchange between quark and antiquark in the meson and gluon loops around each quark B B ~ 1 There is a factor 8/3 NON PERTURBATIVE QCD parameter B 0 d,s d, sb b t,c,u WW WW B 0 d,s t,c,u

71. f B is very difficult to be measured experimentally BB bubu Wl For the time being, f B comes from theoretical calculations. Today is most efficiently determined using Lattice QCD calculations Ds Ds  cscs Wl Large Br(D s   )~4.8% V cs well known 1- 2 /2 Excellent experimental method to determine f Ds and to compare its value with theoretical calculations (similar for D    to determine f D+ ) f B enters in many other quantities : for example it governs the B hadron lifetime differences (see later) Charm sector (will be done at B-factories/CLEO-c)

72. Need : improve the precision on theo. determination to impact on UT fit Calculation partially unquenched (N f =2 or 2+1) in agreement 1.09±0.06 Chiral extrapolation : light quarks simulated typically in a range [m s /2 - m s ] from UT fits Some more “seminar like” information

73. The theoretical input on  is crucial for the UT fits.  not determined from data (only limits from  m s ) 1.02±0.02 Important in future : measurement of similar quantities F Ds,F D+ (CLEO-c/WGV) Some more “seminar like” information ξ = 1.15 ± 0.11

74. Consequences : Spectator Model for the weak decays b u The b quark is much heavier than the u quark (5 GeV vs few MeV) The b quark transforming into c quark which recombines with the u quark forming a D meson. The quark u stays as a spectator. W c u B D Example of the importance of controlling and testing the effects due to the strong interaction : The B hadron lifetimes ….parenthesis

75. c b udud cscs l _ W_W_ c b udud cscs l _ W_W_ B bc D X q q WW If this were the only diagram all the B hadron lifetimes would be the same. Important test of B decay dynamics BB b c WW d ( s ) d BB b c s u d BB bc WW u u u Pauli Interference P.I. W.A. c WW b u d d d W.S. Weak annihilation

76. O.P.E. decay widths calculated as series in inverse power of the mass of the b quark The non-spectator diagrams are suppressed because the b quark and the light quarks have to meet (the effect should depend on the wave function at the origin) The effects due to the non-spectator diagrams are:  (H) =  spect + O(1/m b 2 ) +  (P.I.,W.A,W.S) + O(1/m b 4 )

78.  (B 0 d ) = 1.540 ± 0.014 ps ( 0.9%)  (B + ) = 1.656 ± 0.014 ps ( 0.8%)  (B 0 s ) = 1.461 ± 0.057 ps ( 3.9%)  (  B ) = 1.208 ± 0.051 ps ( 4.2%) Averages from LEP/SLD/Tevatron + B-Factories Results on B Lifetimes  (b) = 1.573 ± 0.007 ps ( 0.4%) 1.073 ± 0.014 0.949 ± 0.038 0.797 ± 0.052 0.784 ± 0.034 LIFETIME Working Group

79. (theo. error 50% from Wilson Coeff./Non-Perturbative Operators Example of extraction of f B from the B + /B 0 lifetime difference ….parenthesis

80. Appendix Part III b) CP violation on Mixing + CP violation on K sector (  k,  ’  )

81. Violation in mixing /B H(L) > are not eigenstates of CP  no direct CP Small (  12 <<M 12 ) and require relative phase between M 12 and  12 For instance : semileptonic decays which tags the flavour Look at the events in which the two B have the same flavour: (TODAY : typical error on |q/p| ~ 0.04 (exp. results not discussed in these lectures) For this case we go beyond the leading approx. solving at the first order in  12 Wrong sign

82. CP Violation in Kaon system :  k and  ’ Two CP violating quantities measured in neutral K are : We can define the following amplitude decays : It is clear that in the  00(+-) get contributions from all the different kind of CP violation (since |q/p|  1,Im( )  0 and |Aij/Aij|  1)

83. The final state /  > can be in a isospin state I=0,2 (not =1 for the Bose-stat.) The existence of these two amplitudes allows the CP violation in the decay At zeroth order in A 2 /A 0  A=A  only one amplitude and  =  00 =  (+-) It can occurs only through mixing or interference between mixing and decays The final definition of     = 1/3(  00 +2  (+-) ) or better

84. Calculated from box diagram : top and charm exchanges contribute Overall the top exchange dominates Due to the fact that  k  ImM 12 Hyperbola in the  plane It is not the case for  M K which is 2|M 12 | and

85.  M dominated by top exchange in B sector    dominated by top exchange  M contributions from charm (long distance physics)

86. 1.05±0.15 unquenching factor 1.05±0.05 SU(3) effects factor  K very precisely measured : Theoretical determination of B K crucial  size of the hyperbola band. The theoretical input on B K is crucial for the UT fits. B K determined from data with similar precision than theo. estimate Some more “seminar like” information B K = 0.69 ± 0.10

87. ….and Direct CP Violation : measurement of the relative phase between A 0 and A 2 Used experimentally : better since it is a double ratio. Systematic better under control used as definition

88. WA  ’/  = (16.6±1.6)10 -4 NA31: (23.0±6.5)10 -4 E731: (7.4±5.9)10 -4 KTeV: (20.7±2.8)10 -4 (preliminary) NA48: (14.7±2.2)10 -4

89. Appendix Part III c) Different way of presenting direct CP violation for 

90. b u BB c u u s DD KK V cb W b u BB u u KK c s W DD V ub Color suppressed also possible GLW (Gronau,London,Wyler) Method

91. Triangle in the Complex plane  CP Violation, because : In reality the triangles are squashed because : 6 measurements needed to get  in a clean way, without any hypotesis on the strong phases

92. ADS (Atwood, Dunietz, Soni) Method : D  and D   f Using ~80fb -1 and the world average (Belle and Babar)

93. K L   0 K L decay directly measures  height of unitarity triangle)! SM prediction: Use K +   0 e + measurement to compute hadronic current. E949, PRL 93, 031801 (2004)