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Measurement of |Vcb| in B Decays at DELPHI Experiment: Theory and Analysis

This Ph.D. thesis explores the determination of the |Vcb| parameter in B decay processes using theoretical models and data analysis from the DELPHI experiment. The study covers exclusive and inclusive decay processes, heavy quark expansions, event reconstruction, systematics, and comparison with other measurements.

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Measurement of |Vcb| in B Decays at DELPHI Experiment: Theory and Analysis

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  1. A. Oyanguren Ph.D. thesis. 26/03/2004

  2. Contents Introduction Theory The DELPHI experiment Analysed data samples |Vcb| from Eur. Phys. J. C33 (2004) 213 Phys.Lett. B556 (2003) 41 DELPHI Paper 340/draft 1 |Vcb| from inclusive decays Summary and Conclusions Contents 2

  3. Vud Vus Vub Vcd VcsVcb Vtd Vts Vtb l nl CKM = q2 b c Vcb The CKM matrix , A, ,  Vcb is a fundamental parameter of the SM From tree level processes DeterminesA =sinC  0.22 PDG ’02 5%accuracy Introduction 3

  4. Measurement of |Vcb| by means of: Exclusive processes Inclusive processes Introduction 4

  5. Expected small ( no term 1/mb) Heavy quark expansions sl = |Vcb|2f (theory) Exclusive decays: Heavy Quark Effective Theory (HQET) Decoupling of heavy quark spin (doublets) Universal form factors F(q2max)=1 Inclusive decays: Operator Product Expansion (OPE) Non perturbative corrections in inverse powers of mb Theory 5

  6. DELPHI TPC magnet RICH ToF ID HPC OD VD Muon chambers HCAL The DELPHI experiment 6

  7. B decays @ DELPHI Z →qq  3.4 M bb / hadrons 22% EB  0.7 Ebeam  30 GeV c 3mm Missing energy HPC + muon chambers l- l D*+ + K- B0 RICH D0 + Other B Tracking (VD)  3mm Fragmentation particles Analysed data samples 7

  8. Event reconstruction Exclusive reconstruction: Analysed data samples 8

  9. |Vcb| from |Vcb| from D* From the s.l. decay width: Known function (Phase space) Form factor of the B D* transition Normalized by HQET (mQ  ) at q2max (w= 1)  (1/ mQ )n and QCD corrections  FD*(1)=1 FD*(1)= 0.91  0.04* * PDG ‘02 9

  10. |Vcb| from Selected candidates D*+ - l- candidates 1688  48 B  D*l- m= m(D0) -m(D0) ~ m(soft) D0 soft D0  K-+ D0  K- + - + D0  K-+(0) 10

  11. |Vcb| from q2 measurement From decay products Efficiency  (q2): From missing energy E, p conservation, vertex info... Measured q2 resolution: (q2s) = (0.9850.026) + (0.00240.0043)q2s 11

  12. 1 2 3 3 |Vcb| from Sample composition Real or fakeD*+ candidates can come, apart from signal Bd→D*+l- events, from : •bD**l- l Discriminant variables based on the event topology Main source of background (d±) D*+X •bD*+DX (Cascade) l- lY Isospin •bD*+-X QX< 0 l- lY QX= 0 • Z  cc •Events with fake leptons •Combinatorial background m distribution 12

  13. |Vcb| from Fit  Event by event likelihood: q2 m d+ d- dN   |Vcb|2F2(w)K(w)  eff(q2) res(q2) dq2 meas. F(w) as function of other form factors: R1and R2, and the slope 2 (I.Caprini, L. Lellouch, M. Neubert, [Nucl. Phys. B530(1998)153]) Fit F(1)|Vcb| and 2 13

  14. |Vcb| from Results on real data  Fitted D** contribution: 14

  15. |Vcb| from Systematic uncertainties 15

  16. |Vcb| from DELPHI average Goals: Increased statistics( 4) Improvements in the reconstruction(Eb, mD*) Control on background DELPHI average: 16

  17. |Vcb| from Comparison with other measurements (excl.) World average |Vcb|=0.0402  0.0009  0.0018 17

  18. 1+O(1/mb) 2 |Vcb| from inclusive decays Inclusive s.l. decay width: Measured  sl=(0.434  0.008)×10-10 MeV Error on |Vcb| ~ 1 % Theory: O.P.E. ci=f(mb,mc,s) sl=|Vcb|2 Non-perturbative corrections5% Perturbative corrections 10% |Vcb| from inclusive decays 18

  19. 3 3 D,LS 3 3 2 rLS G rD 2 2 , G 2  OPE formalism Phys.Lett. B556 (2003) 41 Kinetic mass scheme (=1GeV) Not rely on mc expansion sl=|Vcb|2 mb, mc Quark masses  Kinetic energy of the b quark inside the meson : chromo-magnetic exp. value  (MB*-MB) Darwin term: Spin-orbit term: Can be measured? |Vcb| from inclusive decays 19

  20. l nl q2 b c Moments of the D** distribution Inclusive observables  O  b cl- nl  50% D** properties ? Known  22% D* Moments of the total hadronic mass distribution inbcl-l  28% Measurements of OPE parameters D D** Inclusive |Vcb| determination |Vcb| from inclusive decays 20

  21. D** spectroscopy In addition to resonant states, D** includes non resonantD(*) D** decays into D and D* possible D** D(*) (not measured) Broad resonances Narrow resonances Ground state D** properties 21

  22. D** signal Definition of signal and background regions D** properties 22

  23. D** production rates **, 1ary and 2ary vertices, and other topological info signal Fit to right sign candidates: Fit to wrong sign candidates: D** properties 23

  24. Results on production rates Main systematics:discr. variables & cascade modelling (RS BR’s 4% each) From wrong sign candidates D** D(*) limits: Comparison with other measurements: Increased statistics Improved systematics D** properties 24

  25. D** mass distribution From right sign candidates Fit to m = m(D(*)**) - m(D(*)) and R(>0.25) Considering D** 11 parameters (19±13)% D** properties 25

  26. D** mass distribution m = m(D(*)**) - m(D(*)) D0+ D+- D*+- D** properties 26

  27. First measurement of D* properties in B semileptonic decays 1 D** production characteristics Compatible results with measure- ments from B →D**  decays : CLEO Total D** rate: BELLE Main systematics due to the possible D(*) contribution D** properties 27

  28. Moments of the mass distribution From previous results: Moments 28

  29. Combining information from moments DELPHI hadronic mass + lepton energy moments + Constraining Fixing Moments 29

  30. 3 D small  0.1 GeV3 2 2   G (BPS limit) Fit results Unconstraining the b quark mass: The c quark mass corresponds to: Moments 30

  31. mb, mc, , D,G, LS 2 3 2 3 |Vcb| determination In the kinetic mass scheme, mqkin(1GeV) Including electroweak, (s)2and (1/mb)3 corrections: s (mb/2, 2mb) LEP tb, Moments 31

  32. Comparison with other measurements Amsterdam, ICHEP ‘02 Aachen, ICHEP ‘03 New theoretical calculations: hadron + lepton moments within the kinetic mass formalism. First measurement at low pl BABAR result seems not to fit with theoretical expectations New analysis from BABAR Moments 32

  33. Summary and conclusions |Vcb| from exclusive BdD*+l-nl 0 Measurement of BR(bD*+Xl- nl) |Vcb| from inclusive decays D** properties, measurements of: -production rates -production characteristics -hadronic mass moments Development of a new OPE formalism: -measurement of non-perturbative parameters up to O(1/mb) 3 Precise |Vcb| determination -Measured sl.~ 1% -Non-pert. parameters ~ 1.4% -Theory ~ 1-1.4% Summary and conclusions 33

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