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CKM Quark Flavor Mixing

CKM Quark Flavor Mixing. Implications of the Most Recent Results on CP Violation and Rare Decay Searches in the B and K Meson Systems. Sandrine LAPLACE LAL - Orsay. Seminar at the Centro de Física das Interacções Fundamentais Lisbon, Portugal November 26, 2002 .

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CKM Quark Flavor Mixing

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  1. CKM Quark Flavor Mixing Implications of the Most Recent Results on CP Violation and Rare Decay Searches in the B and K Meson Systems Sandrine LAPLACE LAL - Orsay Seminar at the Centro de Física das Interacções Fundamentais Lisbon, Portugal November 26, 2002 Reference for updated plots: http://ckmfitter.in2p3.fr

  2. From the Higgs to the CKM Matrix Quarks: Masses ? Spontaneous Symmetry breaking Scalar Higgs field Yukawa coupling Higgs-quarks from flavour to mass eigenstates Interaction quarks-W (charged currents): 33 unitary matrix

  3. The Cabibbo-Kobayashi-Maskawa Matrix • VCKMunitary and complex • 4 real parameters . (3 angles and 1 phase) Kobayashi, Maskawa 1973 Wolfenstein Parameterization (expansion in  ~ 0.2): CPV phase “Explicit” CPV in SM, if: non-degenerate masses Jarlskog 1985 Link between flavour and CP violation (phase invariant!)

  4. The Unitarity Triangle  g B sector: K sector: Expect large CP-violating effects in B-System b Tree processes Loop processes (mixing, ...) New Physics?

  5. Many Ways Lead to the Unitarity Triangle Wolfenstein-Parameters: = |Vus|  0.2200  0.0025 A = |Vcb| / 2  0.83  0.05 (,) not well known “,”-plane J/2 Can we describe all observables with one unique set of , A, ,  ?

  6. Experimental and Theoretical Input to the Standard CKM Analysis

  7. The CKM Matrix: Impact of non-B physics

  8. D0 Studying CP Violation in the B System 2001 BTEV ? ATLAS 2008 BELLE CLEO 3 1999 1999 A Worldwide Effort:

  9. The CKM Matrix: Impact of B Physics ()Observables may also depend on  and A - not always explicitly noted

  10. Linac Fixed Target Experiments BABAR SLD(& MARK II)

  11. The Asymmetric B-Factory PEP-II: e+ e– • 9 GeV e on 3.1 GeV e+ : • coherentneutral B pair production and • decay (p-wave) • boostof (4S) in lab frame : = 0.56

  12. B0B0Mixing: Principle Schrödinger equation governs time evolution ofB0-B0 System: with mass eigenstates: Defining: One obtains for the time-dependent asymmetry: where: and:

  13. B0B0Mixing (Theory) – – [B=2] d/s – – t B0 B0 W W d/s b t – b FCNC Processes: whose oscillation frequencies md/s are computed by: Perturbative QCD CKM Matrix Elements Non perturbative QCD (lattice) Important theoretical uncertainties: Improved error from ms measurement:

  14. B0B0Mixing (Experiment) Experimental Technique: Exclusive B Recon-struction: Brec (4S) t  z/c z  250m B-Flavor Tagging: Btag (flavor eigenstates) mixing analyses (CP eigenstates) CP analysis

  15. B0B0Mixing using Flavour Eigenstates (simplified picture) Mistag probability Detector Resolution BABAR BABAR BABAR PRD 66 (2002) 032003

  16. Bs0Bs0Mixing Amplitude spectrum: LEP/SLD/CDF msnot yet resolved Prob. of mixing: A=0 for ms(meas)< ms(true) A=1 for ms(meas)= ms(true) Waiting for a ms measurement atTevatron...

  17. Constraints from md and ms Experimental error > 5% CL > 5% CL SM fit SM fit Improvement from ms limit Theoretical uncertainty

  18. Time-dependent CP Asymmetry CP amplitude ratio mixing decay CP eigenvalue Time-dependent CP Observables: CPV if or CPV in decay CPV in interference between Decay with and without mixing CPV in mixing

  19. The Golden Channel: Penguin Tree Diagram (negligible) • Single weak phase: • clean extraction of CP phase • no CPV in decay:

  20. Time-dependent CP Asymmetry: sin2 BABAR 81.3 fb-1 CP = –1 World Average BABAR hep-ex/0207042 sin2 BABAR

  21. |Vcb| and |Vub| exclusive |Vub| |Vcb| Fermi motion b,c = static color source: light degrees of freedom insensitive to spin and flavor of the heavy quark u is light: heavy-quark symmetry does not hold Heavy-quark symmetry • Form factor from quenched lattice • Need unquenching to become • model independant ! b Heavy Quark Effective Theory HQET –1 m b 1/QCD where Isgur-Wise function BABAR In particular: (lattice) Belle Extrapolation to =1 of the d/d  spectrum:

  22. |Vcb| and |Vub| inclusive Heavy Quark Expansion HQE Theoretical tool: nonperturbative corrections free quark decay Measurement: semi-leptonic BXc (Xu) l Coef. 2 = mB* -mB, mc are known theoretical unknowns |Vub| |Vcb| Need to cut bc bkg |Vcb|.103 = 40.81.0exp 2.5th Belle = 40.71.0exp 2.2th LEP CLEO: combined analysis to measure =(mB-mb) and 1 HQE breaks down using mX spectrum moments and b  s photon spectrum cut on El + b  s : |Vub|.103 = 4.080.34exp 0.53th CLEO |Vcb|.103 = 40.40.9exp 1.3th CLEO sensitivity to whole phase space (?): BABAR: spectral moments analysis discrepancies with b  s ? |Vub|.103 = 4.090.38exp 0.54th LEP

  23. The Standard CKM Analysis

  24. status: ICHEP’02 Standard Inputs • |Vud| 0.97394  0.00089 neutron & nuclear  decay • |Vus| 0.2200  0.0025 K   l • |Vcd| 0.224  0.014 dimuon production: N (DIS) • |Vcs| 0.969  0.058 W  XcX (OPAL) • |Vub| (4.09  0.61  0.42) 10–3LEP inclusive • |Vub| (4.08  0.56  0.40) 10–3CLEO inclusive & moments bsg • |Vub| (3.25  0.29  0.55) 10–3CLEO exclusive •  product of likelihoods for |Vub| • |Vcb| (40.4  1.3  0.9) 10–3Excl./Incl.+CLEO Moment Analysis • K (2.271  0.017) 10–3PDG 2000 • md (0.496  0.007) ps–1BABAR,Belle,CDF,LEP,SLD (2002) • ms Amplitude Spectrum’02 LEP, SLD, CDF (2002) • sin2 0.734  0.054 WA, ICHEP 02 • mt(MS) (166  5) GeV/c2CDF, D0, PDG 2000 • fBdBd (230  28  28) MeV Lattice 2000 •  1.16  0.03  0.05 Lattice 2000 BK 0.87  0.06  0.13 Lattice 2000 Tree process  no New Physics Standard CKM fit in hand of lattice QCD + other parameters with less relevant errors…

  25. (,) plane status: ICHEP’02 Standard Constraints (not including sin2) Region of > 5% CL

  26. (,) plane status: ICHEP’02 Standard Constraints (not including sin2) A TRIUMPH FOR THE STANDARD MODEL AND THE KM PARADIGM ! KM mechanism most probably the dominant source of CPV at EW scale

  27. sin2 status: ICHEP’02 BABAR, hep-ex/020707 New CP Results from complemen-tary modes: Belle, hep-ex/0207098 Both decays dominated by single weak phase Tree: Penguin: New Physics ?

  28. (,) plane status: ICHEP’02 Standard Constraints (including sin2) sin2 already provides the most precise and robust constraint • Need new and improved constraints ...

  29. New Constraints: Charmless B Decays [ Constraining ]

  30. CP Violation in B0+– Decays ratio of amplitudes CP eigenvalue Tree diagram: Penguin diagram: For a single weak phase (tree): For additional phases: |  |  1  must fit for direct CP Im ()  sin(2)  need to relate asymmetry to  C = 0, S = sin(2) C  0, S ~ sin(2eff)

  31. Predictions for |– eff| from B0+– • Different Strategies: • Determination of P/T by virtue of flavour symmetries (mild theoretical assumptions, eg, PEW=0) • SU(2): • Gronau-London Isospin Analysis • Grossmann-Quinn bound (also Charles, Gronau et al.) • SU(3): • Fleischer-Buras, Charles (P~ PK) • Using theoretical predictions for P/T • “naive” Factorization (|P/T|2~ BR(B+ p +K 0) / BR(B+ p +p 0) ) • |P/T| and phase from QCD Factorization (Beneke et al.) and pQCD (Li et al.)

  32. sin(2eff) & Isospin Analysis status: ICHEP’02 Using the BRs :+–, ±0,00 (limit) and the CP asymmetries :ACP(±0) , S ,C and the amplitude relations: 2 – 2eff BABAR BABAR

  33. What about More Statistics? Isospin analysis for present central values, but more statistics If central value of BR(00) stays large, isospin analysis cannot be performed by first generation B factories

  34. sin(2eff) & QCD FA • |P/T| and arg(P/T) predicted by QCD FA (BBNS’01) BABAR: (ICHEP’02) Belle: (Moriond’02) BABAR Agreement with SM fit: 1%

  35. Other ways to : B0 Not a CP eigenstate: Time-dependent CP Observables: Asymmetry due to non-CP eigenstate CP violation

  36. CP analysis of B0 and B0K ICHEP’02 BABAR C = 0.45  0.19  0.09 S = 0.16  0.25  0.07 ACP = -0.22  0.08  0.07 ACPK = 0.19  0.14  0.11 C = 0.38  0.20  0.11 S = 0.15  0.26  0.05 Total PDF B + udsc B bkg Systematics dominated by B background B0

  37. Predictions for |– eff| from B0 As for B0, need to know P/T: • Strategies similar to B0: • flavour symmetries • SU(2): • full analysis needs B000 (limit), B+0+ (measured), B++0 (not measured) • bound using B000 • SU(3): from B0K, K* • Using theoretical predictions for P/T: • not mature yet • Additional strategy: Dalitz plot analysis • B0+- , B0-+ , B000 interfere to give B0+-0 • Using interferences provide enough observables to determine P/T • Experimentally very difficult because of backgrounds

  38. CKM and New Physics

  39. Testing New Physics:The Semi-leptonic Asymmetry SL,Z.Ligeti,Y.Nir,G.Perez hep-ph/0202010 Measurements SM NP |12/M12| O(mb2/mW2) arg(12/M12) O(mc2/mb2) O(1) ASL 10-310-2 ( 0.4  5.7 ) x 10-2 ( 1.4  4.2 ) x 10-2 (-1.2  2.8 ) x 10-2 ( 0.48 1.85) x 10-2 ( 0.2 1.4 ) x 10-2 OPAL CLEO ALEPH BABAR WA -1.4 <ASL(10-3)< -0.5 (>10% CL) SM ASL not expected to constrain , but to exhibit / constrain New Physics The present world average already constrains some models…

  40. The Semi-leptonic Asymmetry Including ASL • General NP in mixing amplitude Without ASL • Minimal Flavour Violation model • Conclusion Measurement can discriminate between various NP models ASL not significantly enhanced • <0 allowed

  41. BABAR / Belle Where are we today What brings the future ?

  42. PEP-II Luminosity Projections 3 Similar scenario expected for Belle

  43. Conclusions Summer ’06: (sin2WA) ~ 0.025 for 1000 fb–1 • GlobalCKM fit (CKMfitter) gives consistent picture of Standard Model • sin(2 ) now most accurate constraint • future consistencies:BABAR  Belle ? • J/ KS   KS • ms : constraint on UT angle  from LEP/SLD/CDF limit • expect measurement from TEVATRON soon • Need more constraints on CKM phase: • Charmless B decays: • Conventional isospin analysis in B0 potentially unfruitful to extract sin(2 ) • Significant theoretical input needed • Pursue other ways to measure : B0 Many more results to come from the B-factories

  44. Backup slides

  45. Babar detector

  46. ytheo =(A,,,,mt…) Extracting the CKM Parameters Constraints on theoretical parameters Measurement xexp Theoretical predictions Xtheo(ymodel= ytheo ,yQCD) yQCD=(BK,fB,BBd, …) “2” = –2 lnL(ymodel) L(ymodel) =Lexp[ xexp –xtheo(ymodel)] Ltheo(yQCD) xexp Assumed to be Gaussian « Guesstimates » Frequentist:Rfit Bayesian Uniform likelihoods: “allowed ranges” Probabilities

  47. Three Step CKM Analysis Using Rfit fit package Probing the SM Test: “Goodness-of-fit” Metrology Test New Physics • Define: • ymod = {a; µ} • = {, ,A,,yQCD,...} • Set Confidence Levels in • {a} space, irrespective of • the µvalues • Fit with respect to {µ} • ²min; µ (a) = minµ{²(a, µ) } • ²(a)=²min;µ(a)–²min;ymod • CL(a) = Prob(²(a), Ndof) • If CL(SM) good • Obtain limits on New Physics parameters • If CL(SM) bad • Hint for New Physics ?! • Evaluate global minimum • ²min;ymod(ymod-opt) • Fake perfect agreement: • xexp-opt = xtheo(ymod-opt) • generate xexp usingLexp • Perform many toy fits:²min-toy(ymod-opt)  F(²min-toy) AH, H. Lacker, S. Laplace, F. Le Diberder EPJ C21 (2001) 225, [hep-ph/0104062]

  48. “Direct” CP Violation in the Decay Interfering contributions to the decay amplitude generate direct CPV: Strong phase difference Time-integrated Observable: Weak phase difference =0 and =0  no direct CP Violation For neutral B’s direct CPV competes with other CPV phenomena

  49. Branching Fs. and ACP for B   /K status: ICHEP’02 Agreement among experiments.

  50. Bounds on  status: ICHEP’02 Ratios of CP averaged branching fractions can lead to bounds on : Fleischer, Mannel PRD D57 (1998) 2752 FM bound: no constraint < 1 ? Buras, Fleischer EPJ C11 (1998) 93 BF bound:  1 ? no constraint Neubert, Rosner PL B441 (1998) 403 NR bound:  1 ? some constraint

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