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Implications of the Most Recent Results on CP Violation and Rare Decay Searches

CKM Quark Flavor Mixing. Implications of the Most Recent Results on CP Violation and Rare Decay Searches in the B and K Meson Systems. Andreas H öcker LAL - Orsay. FPCP – Flavor Physics & CP Violation Philadelphia, Pennsylvania, USA May 16-18, 2002.

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Implications of the Most Recent Results on CP Violation and Rare Decay Searches

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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 Andreas Höcker LAL - Orsay FPCP – Flavor Physics & CP Violation Philadelphia, Pennsylvania, USAMay 16-18, 2002 Reference for recent plots: http://www.slac.stanford.edu/~laplace/ckmfitter.html

  2. Determining the CP-Violating CKM Phase CP Violation (CPV) in B and K Systems: CPV in interference of decays with and without mixing CPV in mixing CPV in interference between decay amplitudes  2  1  3 Neutral Bdand BsMixing Precise Determination of the Matrix Elements |Vub| and |Vcb| Detection of Rare Decays: Search for new physics and direct CPV Determination of weak phases

  3. The CKM Matrix Mass eigenstates Flavor eigenstates Quark mixing B and K mesons decay weakly VCKMunitary and complex 4 real parameters (3 angles and 1 phase) modified couplings for charged weak currents:  Kobayashi, Maskawa 1973 Wolfenstein Parameterization (expansion in  ~ 0.2): CPV phase (phase invariant!) “Explicit” CPV in SM, if: Jarlskog 1985

  4. Many Ways Lead to the Unitarity Triangle J/2 Point of Knowledge: SM or new phases (fields)? What is the value of in our world? J Rb Rt  g b Tree Loop (mixing)

  5. The CKM Matrix: Impact of non-B Physics ()Observables may also depend on  and A - not always explicitly noted NA48

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

  7. Extracting the CKM Parameters ytheo =(A,,,,mt…) 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: Ranges Probabilities

  8. Three Step CKM Analysis 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]

  9. Inputs Before FPCP’02 (status: Moriond 2002) • |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| (4.08  0.61  0.47) 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 0.78  0.08 WA, Updates Moriond’02 BABAR • and Belle included • 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 + other parameters with less relevant errors… Tree process  no New Physics Standard CKM fit in hand of lattice QCD

  10. B0B0Mixing – – [B=2] d/s – – t B0 B0 W W d/s b t – b Effective FCNC Processes (CP conserving): whose oscillation frequencies md/s are computed by: Perturbative QCD CKM Matrix Elements Lattice QCD (eff. 4 fermion operator) Important theoretical uncertainties: Improved error from ms measurement:

  11. Using ms Experimental error > 5% CL > 5% CL SM fit SM fit Improvement from ms limit Theoretical uncertainty Waiting for a ms measurment atTevatron...

  12. Probing the Standard Model Test of goodness-of-fit Toy MC 2 distribution 2min Confidence Level of Standard Model: CL(SM) = 57%

  13. Metrology (I) Standard Constraints (not including sin2) Region of > 5% CL

  14. Metrology (I) Standard Constraints (not including sin2) A TRIUMPH FOR THE STANDARD MODEL AND THE KM PARADIGM ! KM mechanism most probably dominant source of CPV at EW scale

  15. Metrology (I) Standard Constraints (including sin2) sin2 already provides one of the most precise and robust constraints • How to im-prove these con-straints? • How to mea-sure the missing angles ? ...

  16. Metrology (II): the sin(2) - sin(2) Plane Standard Constraints (not including sin2) Be aware of ambiguities !

  17. Metrology (II): the sin(2) -  Plane Standard Constraints (not including sin2)

  18. Metrology (III): Selected Numerical Results CKM and UT Parameters Rare Branching Fractions Theory Parameters() ()Without using a priori information

  19. Constraint from Rare Kaon Decays: K+ + Box: u u + K+ c,t s d W W l   Penguin: u u + K+ W s d c,t Z0   Buchalla, Buras, Nucl.Phys. B548 (1999) 309 top contribution charm contribution ellipse Main theoretical uncertainty comes from charm contribution Experiment: Two events observed at BNL (E787), yielding: E787 (BNL-68713) hep-ex/0111091

  20. Constraint from Rare Kaon Decays: K+ + At present dominated by experimental errors. However: uncertainties on |Vcb|4=8A4 will become important for constraints in the - plane

  21. Rare Charmless B Decays We distinguish two Categories: Box • Semileptonic (FCNC) and radiative decays • (GF)2 increased compared to loop-induced non- radiative decays  (GF )2 • Sensitive sondes for new physics (SUSY, right-handed couplings, ...) • Determination of |Vtd| and |Vts| • Determination of HQET parameters • Search for direct CP asymmetry • Hadronic b  u(d) decays • Measurement of CPV • Determination of UT angles  and  • Test der B decay dynamics (Factorization) Penguin Tree

  22. Radiative B Decays The ratio of the rates B   to B  K*can be predicted more cleanly than the individual rates: determines |Vtd| Ali, Parkhomenko, EPJ C23 (2002) 89 see also : Bosch, Buchalla, NP B621 (2002) 459 For demonstrating purpose only Rough estimate of the theoretical uncertainties !

  23. Charmless B Decays into two Pseudoscalars [ Constraining  and  ?! ]

  24. BK and the Determination of  Interfering contributions of tree and penguin amplitudes: Potential for significant direct CPV CP averaged BRs and measurements of direct CPV determine the angle Fleischer, Mannel (98) Gronau, Rosner, London (94, 98) Neubert, Rosner (98) Buras, Fleischer (98) Beneke, Buchalla, Neubert, Sachrajda (01) Keum, Li, Sanda (01) Ciuchini et al. (01) ...list by far not exhaustive! • Theoretical analysis deals with: • SU(3) breaking • Rescattering (FSI) • EW penguins The tool is: QCD Factorization...  see contributions at this conference • ... based on Color Transparancy • Large energy release • soft gluons do not interact with small qq-bar color dipole of emitted mesons • non-fact. contributions are calculable in pQCD perfect for mb. • Higher order corrections: (QCD/mb) Soft scattering Vertex corr., penguins Hard scattering (pQCD)

  25. Branching Fractions for B  /K Updated Belle (La Thuile’02) Updated BABAR (Moriond EW’02) World average CLEO 9 fb–1 BABAR up to 56 fb–1 Belle 32 fb–1 5.4  0.7  0.4 5.1  1.1  0.4 5.17  0.62 21.8  1.8  1.5 18.6  1.1 17.8  1.1  0.8 < 0.5 (90%) < 1.1 (90%) 5.9  1.4 5.1  2.0  0.8 7.0  2.2  0.8 11.5  1.5 10.8  2.1  1.0 12.5  2.4  1.2 18.2  3.3  2.0 18.8  3.0  1.5 8.2  3.1  1.2 7.7  3.2  1.6 8.9  2.3 < 5.7 (90%) < 3.4 (90%) < 5.6 (90%) Agreement among experiments. Most rare decay channels discovered

  26. Direct CP Asymmetries in K Modes BABAR CLEO Belle +1 -0.5 0 +0.5 BABAR: BABAR Moriond’02 ACP(K+–) = –0.05  0.06  0.01 ACP(K+0) = +0.00  0.18  0.04 ACP(K0+) = –0.21  0.18  0.03 Belle: BELLE La Thuile’02 ACP(K+–) = –0.06  0.08  0.08 ACP(K+0) = –0.04  0.19  0.03 ACP(K0+) = +0.46  0.15  0.02 CLEO: CLEO PRL 85 (2000) 525 -1 ACP(K+–) = –0.04  0.16 ACP(K+0) = –0.29  0.23 ACP(K0+) = +0.18  0.24 Are annihilation contributions important? World averages: Agreement among experiments. No significant deviation from zero. ACP(K+–) = – 0.05  0.05 ACP(K+0) = – 0.09  0.12 ACP(K0+) = + 0.18  0.10

  27. Bounds on  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 ? no constraint See also recent Bayesian analysis: Bargiotti et al. hep-ph/0204029

  28. Neubert-Rosner Bound Tree a) Penguin QCD FA: small relative strong phases b) a) b)

  29. CP Violation in B0+– Decays mixing decay CP 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)

  30. sin(2eff) & Gronau-London Isopin Analysis Using the BRs :+–, ±0,00 (limit) and the CP asymmetries :ACP(±0) , S ,C and the amplitude relations: sign convention changed! BABAR Belle 2min=0.7 2min=2.8

  31. BABAR: sin(2eff) & Theory (QCD FA) & QCD FA (BBNS) Input: S & C Input: S & C& sin(2WA)

  32. Belle: sin(2eff) & Theory (QCD FA) Zoom Input: S & C Input: S & C

  33. The Reverse: sin(2eff , 2) & SM fit THEORY • The theory provides tree und penguin contributions and their relative phases • The global fit determines the agreement between experiment and theory, using all measured BRs and CP asymmetries (also time-dependent) • Determine also the free parameters of the theory (i.e., the CKM elements) GR: Gronau, Rosner, Phys.Rev.D65:013004,2002 BBNS: Beneke et al., Nucl.Phys.B606:245-321,2001

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

  35. The Standard Model holds the castle: We know the center already quite well… but it is too large! A better understan-ding of long distan-ce QCD opens the shrine to a full ex-ploitation of the huge data samples currently produced at KEKB and PEPII. ...and the incredible data quantities that will be produced at the Tevatron & LHC

  36. And in the far future ? In 2010 we will need a zoom, to see the overlap region...

  37. And in the far future ? Will there still be an overlap region ? v

  38. And in the far future ? ? ... maybe we can es-tablish new physics before the LHC finds it ???

  39. Backup Material

  40. Using ms msnot yet measured. How to use the available experimental inform.? Amplitude spectrum: LEP/SLD/CDF Following a presentation of F. Le Diberder at the CERN CKM workshop (Feb. 02) • compute the expected PDF for the • current prefered value • compute the CL • infer an equivalent 2 Preferred value: 17.2 ps-1

  41. Determination of the Matrix Elements |Vcb| and |Vub| 1/mQ Symmetry of heavy quarks [=SU(2nQ)]: in the limit mQ of a Qq system, the heavy quark represents a static color source with fixed 4-momentum. The light degrees of freedom become insensitive to spin and flavor of the quark. 1/QCD Compton wavelength For both, |Vcb| and |Vub|, exist exclusive and inclusive semileptonic approaches. The theoretical tools is Heavy Quark Effective Theory (HQET) and the Operator Product Expansion (OPE) • |Vub| ( 2+2) is important for the SM prediction of sin(2) • |Vcb| ( A) is crucial for the interpretation of kaon decays (K, BR(K), …)

  42. Exclusive Semileptonic BDl Decays • Measurement of rate as fct. of momentum transition  • Determination of |Vcb| from extrapolation to  1 (theory is most restrictive) Bigi, Uraltsev; Neubert; ...; Lattice QCD Belle  =1  =1.5 in B rest system is  = (D) Belle, PLB 526, 247 (2002)

  43. Inclusive Semileptonic BXc l Decays • OPE: expansion of decay rate in und • Model-independent results for sufficiently inclusive observables: Bigi, Shifman, Uraltsev; Hoang, Ligeti, Manohar • Identify by tagging one of the Bs: • Full reconstruction of the high energetic lepton • Select leptons from the semileptonic decay of the other B Experimental strategy Fast e+: „right-sign“ Cascade e–: „wrong-sign“

  44. BABAR BR(BX l(e)): BABAR: (10.82  0.21  0.38) % Belle: (10.86  0.14  0.47) % CLEO: (10.49  0.17  0.43) % LEP: (10.65  0.23) % ARGUS : ( 9.7  0.5  0.4 )% BABAR preliminär: z.B.: |Vcb|(BABAR)  (40.8 1.7 1.5)10–3 0.1 1 A promising approach for a theoretically improved analysis is the combined fit of the HQET parameters  und 1 (CLEO) by means of b  s. Allows to test Quark-Hadron Duality. (See also spectral moments analysis of hadronic Tau decays). 0 –0.1 –0.2 –0.3 |Vcb|(CLEO)  (40.4 1.3)10–3 –0.4 –0.5 CLEO, Phys. Rev. Lett. 87, 251808 (2001)

  45. |Vub| from exclusive Decays (I) Pure tree decay. The decay rate is proportional to the CKM element |Vub|2 Problem: form factor is model dependent

  46. |Vub| from exclusive Decays (II) CLEO BABAR other bul bcl und andere cross feed stat mod sys CLEO, Phys.Rev.D61:052001,2000 BABAR preliminary (Moriond’02)

  47. |Vub| from inclusive Decays CLEO Suppression of the dominant charm background by cutting on the BXullepton momentum beyond the kinematic limit of BXcl Problem: strong model dependence of|Vub| B Xs Reduction of model dependence by using HQE and the “shape function“ measured in B Xs CLEO, hep-ex/0202019 > 5% CL stat fu 1/mb HQE SM fit Possible “violation“ of quark-hadron duality? Measurement of the whole spectrum ( Theorie under control) BXul (Neural Net for Signal) LEP B Working group exp bc bu b HQE Knowledge of bcbackground, incl. measurement ?

  48. BR(B  /K) & ACP & Theory (QCD FA) Beneke, Buchalla, Neubert, Sachrajda (BBNS) Nucl.Phys.B606:245-321,2001 • Theoretical uncertainties: • ms, mc, B, RK • Renorm. scale  • Gegenbauer moms: • a1(K), a2(K), a2() • F(B), fB • XH, XA This means: error estimation not settled yet !!!

  49. Frequentist Approach: Rfit the package Three main analysis steps: AH, H. Lacker, S. Laplace, F. Le Diberder EPJ C21 (2001) 225, [hep-ph/0104062] 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)

  50. And in the far future ? ? ? In 2010 we will need a zoom, to see the overlap region... Will there still be an overlap region ? v ... maybe we can es-tablish new physics before the LHC finds it ???

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