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Measurements of V cb and Form Factors

Measurements of V cb and Form Factors. Elisabetta Barberio University of Melbourne Beauty 2006: Oxford September 2006. Standard Model Consistency Tests. V cb provide a test of CP violation in the Standard Model comparing the measurements on the (  ,  ) plane. Semileptonic B decays.

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Measurements of V cb and Form Factors

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  1. Measurements of Vcband Form Factors Elisabetta Barberio University of Melbourne Beauty 2006: Oxford September 2006

  2. Standard Model Consistency Tests Vcb provide a test of CP violation in the Standard Model comparing the measurements on the (, ) plane E. Barberio

  3. Semileptonic B decays Vcb u + long distance: ,u tree level, short distance: decay properties depend directly on |Vcb|,mb perturbative regime (sn) But quarks are bound by soft gluons: non-perturbative (QCD) long distance interactions of b quark with light quark E. Barberio

  4. heavy quark symmetry heavy quark: the energy of soft gluon QCD~250 MeV << mb,c heavy quarkspin and mass (flavour) are good symmetry as mQ/QCD∞ departure from theheavy quarksymmetry can be expressed as (QCD/mQ)n corrections Two methods to extract Vcb Inclusive b + Br(b cl) + shapes Exclusive E. Barberio

  5. Inclusive semileptonic decays Many theorists love inclusive semileptonic decays Short distance is calculable Long distance leading orderand short distance contribution are cleanly separated Most accurate Vcb determination from inclusive decays: precision limited by theory error Operator Product Expansion predictions: integration over neutrino and lepton full phase space provides smearing over the invariant hadronic mass of the final state E. Barberio

  6. Vcb from inclusive semileptonic decays exp. |Vcb|<1% sldescribed by Heavy Quark Expansion in (1/mb)n and sk non perturbative parameters need to be measured The expansion depend on mb definition: non-perturbative terms depend on the choice of mb definition Theory error is dominated by 1/mb3terms and above E. Barberio

  7. Parameters of HQE Decay rate in are express in terms of OPE up to 1/mb3 • Calculations available in different renormalization schemes (mb definition): • Kinetic running mass (P. Gambino, N.Uraltsev, Eur. Phys. J. C 34, 181 (2004)) • 1S mass (C.Bauer, Z.Ligeti, M.Luke, A.Manohar, M.Trott PRD 70 094017) • Pole mass not used anymore: not well behaved, irreducible error on mb

  8. Inclusive SL decays rate |Vcb| shape mc, mG, mb, m2 shape 1.5 Difficulty to go from measured shape to true shape: e.g. QED corrections, accessible phase space, resolution, background E. Barberio

  9. moments in semileptonic decays non-perturbative parameters are extracted from the spectral moments Xn are evaluated either on the full lepton spectrum or part of it: p > pmin in the B rest frame E : lepton energy spectrum (BaBar BelleCLEODelphi) MX: hadronic mass spectrum (BaBar Belle CDFCLEODelphi) E. Barberio

  10. Υ(4S) π ν Full reconstruction 0 γ K l- γ π BXc  fully reconstruct the tag-side B meson by searching the decay modes e.g. B→D(*), B→ D(*)ρ, and B→D(*)a1 flavour - charge - momentum Bsig→Xlν Btag→DX B+ and B0 decays studied separately B B 0 But low efficiency < 1%

  11. moments in BXc  Most recent measurements from Belle 140 fb-1 sample P*l (GeV) P*l (GeV) Plmin = 0.4 GeV from the moments of these distributions we get Vcb and HQ parameters E. Barberio

  12. Moments with threshold (statistical errors only) Belle unfolded spectrum: B0 and B+ combined 0.4 GeV electron energy threshold Measure up to 4th moment! E. Barberio

  13. Electron energy moments and partial BR Increase of the mean Decrease of the width Decrease of truncated BR Belle final results Belle-Conf-0667 Br(B+)0.4GeV=(10.79±0.25±0.27)% Br(B0)0.4GeV=(10.09±0.30±0.22)% Systematics: b->c model, background, electron detection E. Barberio

  14. Hadronic Xc system 54% 21 % ~25% BR(B→Xcl) ~ 10.5% Grounds states Broad states Narrow states Important to understand the shape and branching fractions of each hadronic contribution: B→D**l not measured well E. Barberio

  15. Υ(4S)  ν 0 γ K l- γ  Belle hadronic mass moment analysis Select (4S) decays with fully reconstructed hadronic B decays “Btag” Select events withone identified lepton (electron or muon) Bsig→Xlν Measure Mx masson signal side of the event: Mx pX = pbeam-pBtag-pl-pν Btag→DX Constrain neutrino mass to zero: B B 0 M2miss < 3 GeV2/c4

  16. Hadronic-Mass Spectrum Measured Mx2 spectrum for different El*cut Belle ICHEP06 Main systematics: b→c model, background subtraction E. Barberio

  17. Unfolded Mx2 spectrum Belle D* El*cut D D** 0.7 GeV 1.5 GeV decrease in higher mass final states Results and systematic uncertainties The moments are derived from the unfolded spectrum down to 0.7 GeV minimum lepton energy in the B rest frame Mx2 (GeV2/c4) E. Barberio

  18. Vcb extraction • well behaving renormalization schemes are used: • Kinetic running mass • 1S mass both schemes have 7 free parameters: higher moments are sensitive to 1/mb3 terms  reduce theory error on Vcb and Heavy Quark parameters

  19. Yellow band: theory error Filled circles: used in fit Ee,1 BR Mx4 Mx2 Ee,3 Eγ,1 Eγ,2 Ee,2 Kinetic Scheme Preliminary Belle Belle ICHEP06 |Vcb|= (41.93 ± 0.65fit ± 0.48αs ± 0.63th )×10-3 mb = 4.564 ± 0.076 GeV, mc = 1.105 ± 0.116 GeV Contours =1 /dof =17.8/24

  20. Red band: Theory + Fit Yellow band: fit error Filled circles: used in fit Ee,1 BR Mx2 Mx4 Eγ,1 Ee,3 Eγ,2 Ee,2 20 20 1S Scheme Preliminary Belle ICHEP06 |Vcb|= (41.5 ± 0.5fit ± 0.2τ)×10-3 mb1s= 4.73 ± 0.05 GeV 1 = -0.30 ± 0.04 GeV Contours =1 /dof =6/17 E. Barberio

  21. Vcb and HQ parameters Exp HQ sl Global fit Kinetic scheme expansion - all experiments (Buchmuller, Flasher PRD73:073008 (2006)) Belle new measurements missing |Vcb|=(41.96±0.23exp±0.35HQE±0.59SL)10-3 Vcb @ 2% mb < 1%  crucial for Vub mc @ 5% E. Barberio

  22. HQET and B D*l l  -  q2 b c w=1 Vcb -  c c w>1 q q Heavy Quark Effective Theory (HQET): simplified description of processes involving heavy  heavy quark transitions B D(*)l transitions non-perturbative effects are described by one form factor , Isgur-Wise function, as a function of w q2  4-momentum transfer w=1  D* produced at rest in B rest frame E. Barberio

  23. Vcb from B D*l Delphi F(1)Vcb w when mQ∞(1)=1 Vcb extraction K(w): phase space (known function) F(w):unknown form factor F(1)•g(w) in the heavy quark limitF(1)=(1)=1 measure d/dw and extrapolate at w=1 the slope is important fit for both intercept F(1)|Vcb| and slope 2 E. Barberio

  24. signal and w reconstruction Signal region CLEO B  D*lD* +slowD0: m(D*)-m(D0)~m(+): + is almost at rest in the B rest frame  difficult to reconstruct when the B is almost at rest Main physics background BD**l, D**resonant and non resonant E. Barberio

  25. extrapolation: form factor shape expansion around w=1 up to second order: use dispersive relations to constraint the shape Caprini,Lellouch,Neubert NP B530(98)153 and Boyd,Grinstein,Lebed PRD56(97)6895 R1,R2 calculated using QCD sum rules R1(w)1.27-0.12(w-1)+0.05(w-1)2 R2(w) 0.80+0.11(w-1)-0.06(w-1)2 measured by CLEO: R1(1)=1.18±0.30±0.12 R2(1)=0.71±0.22±0.07 used in the old world average For long time R1,R2 uncertainty was the major source of systematic onA2 E. Barberio

  26. form factor shape one-dimension projection of fitted distributions: Fit w and 3 angles E. Barberio

  27. form factor and Vcb Simultaneous fit of the Form factors and Vcb F(1)|Vcb|=(34.680.321.15)10-3 Br(B0 D*+l)=(4.840.39)% E. Barberio

  28. F (1)|Vcb| 2=1 CL=37% New HFAG average uses R1, R2 from Babar: this decrease F(1)|Vcb| 2/dof = 38.7/14 F(1)|Vcb|=(36.20.8)10-3A2 =1.190.06 E. Barberio

  29. F(1) and Vcb +0.030 F(1) =0.919 -0.035 non-perturbative QCD calculations F(1) =0.9070.0070.0250.017 F(1) =0.9000.0150.0250.025 from lattice and sum rule |Vcb|excl=(39.40.9exp1.5theo)10-3 E. Barberio

  30. Vcb from Bd0D+- decays BELLE large combinatorial background but very good prospective on the theory side for G(1) Worth to measure as it will may cross-check Vcb excluisve G(1)|Vcb|=(42.64.5) x 10-3 G2=1.17  0.18 E. Barberio

  31. (BD*,**-)/(BDX-) Measurement There is disagreement between inclusive and exclusive b cl branching fractions (BD*,**-)/(BDX-) is sensitive to non resonant states Measure simultaneously D, D* and D** components using the fully reconstructed events 211 fb-1 E. Barberio

  32. (BD*,**-)/(BDX-) Measurement This measurement is not solving the puzzle … E. Barberio

  33. Conclusions Vcb is now a precision measurement: |Vcb|inc=(41.96±0.23exp±0.35HQE±0.59SL)10-3 Inclusive and exclusive analyses give consistent results |Vcb|excl=(39.40.9exp1.5theo)10-3 The measurement of mb from the inclusive spectrum are crucial for the precise extraction of Vub BD**- are still a puzzle and a concern…. E. Barberio

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