1. Elisabetta Barberio University of Melbourne Beauty 2006: Oxford September 2006 Measurements of V cb and Form Factors

2. September 2006 E. Barberio 2 Standard Model Consistency Tests V cb provide a test of CP violation in the Standard Model comparing the measurements on the (  ) plane

3. September 2006 E. Barberio 3 Semileptonic B decays tree level, short distance: decay properties depend directly on |V cb |,m b perturbative regime (  s n ) V cb u + long distance:,u But quarks are bound by soft gluons: non-perturbative (  QCD ) long distance interactions of b quark with light quark

4. September 2006 E. Barberio 4 heavy quark symmetry heavy quark: the energy of soft gluon  QCD ~250 MeV << m b,c heavy quark spin and mass (flavour) are good symmetry as m Q /  QCD  ∞ departure from the heavy quark symmetry can be expressed as (  QCD /m Q ) n corrections Two methods to extract V cb Inclusive  b + Br(b  cl ) + shapes Exclusive

5. September 2006 E. Barberio 5 Inclusive semileptonic decays Short distance is calculable Long distance leading order and short distance contribution are cleanly separated Operator Product Expansion predictions: integration over neutrino and lepton full phase space provides smearing over the invariant hadronic mass of the final state Many theorists love inclusive semileptonic decays Most accurate V cb determination from inclusive decays: precision limited by theory error

6. September 2006 E. Barberio 6 V cb from inclusive semileptonic decays  sl described by Heavy Quark Expansion in (1/m b ) n and  s k The expansion depend on m b definition: non-perturbative terms depend on the choice of m b definition exp.  |V cb |<1% non perturbative parameters need to be measured Theory error is dominated by 1/m b 3 terms and above

7. Parameters of HQE Decay rate in are express in terms of OPE up to 1/m b 3 Calculations available in different renormalization schemes (m b 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 m b

8. September 2006 E. Barberio 8 Difficulty to go from measured shape to true shape: e.g. QED corrections, accessible phase space, resolution, background Inclusive SL decays rate shape |V cb | m c,   G, m b,  2  1.5

9. September 2006 E. Barberio 9 non-perturbative parameters are extracted from the spectral moments moments in semileptonic decays X n are evaluated either on the full lepton spectrum or part of it: p > p min in the B rest frame E : lepton energy spectrum ( BaBar Belle CLEO Delphi ) M X : hadronic mass spectrum (  BaBar Belle CDF CLEO Delphi )

10. 10 Full reconstruction flavour - charge - momentum B + and B 0 decays studied separately fully reconstruct the tag-side B meson by searching the decay modes e.g. B → D (*) , B → D (*) ρ, and B → D (*) a 1 B sig → X    K   l-l-  B B 0 0  (4S) B tag → DX B  X c But low efficiency < 1%

11. September 2006 E. Barberio 11 Most recent measurements from Belle moments in B  X c P l min = 0.4 GeV P * l (GeV) from the moments of these distributions we get V cb and HQ parameters 140 fb -1 sample

12. September 2006 E. Barberio 12 Moments with threshold Belle unfolded spectrum: B 0 and B + combined (statistical errors only) 0.4 GeV electron energy threshold Measure up to 4th moment!

13. September 2006 E. Barberio 13 Electron energy moments and partial BR Decrease of truncated BR Increase of the mean Decrease of the width Belle-Conf-0667 Belle final results Systematics: b->c model, background, electron detection Br(B + ) 0.4GeV =(10.79±0.25±0.27)% Br(B 0 ) 0.4GeV =(10.09±0.30±0.22)%

14. September 2006 E. Barberio 14 BR(B → X c l ) ~ 10.5% 21 % 54% ~25% Grounds statesBroad statesNarrow states Hadronic X c system Important to understand the shape and branching fractions of each hadronic contribution: B → D**l not measured well

15. Select  (4S) decays with fully reconstructed hadronic B decays “B tag ” Select events with one identified lepton (electron or muon) Constrain neutrino mass to zero: p X = p beam -p Btag -p l -p ν   K γ γ l-l- ν B B 0 0 Υ (4S) MxMx M 2 miss < 3 GeV 2 /c 4 Belle hadronic mass moment analysis B sig → Xl ν B tag → DX Measure M x mass on signal side of the event:

16. September 2006 E. Barberio 16 Hadronic-Mass Spectrum Measured M x 2 spectrum for different E l * cut Main systematics: b → c model, background subtraction Belle ICHEP06

17. September 2006 E. Barberio 17 Results and systematic uncertainties The moments are derived from the unfolded spectrum down to 0.7 GeV minimum lepton energy in the B rest fram e 0.7 GeV E l * cut 1.5 GeV decrease in higher mass final states D* D** D Belle Unfolded M x 2 spectrum M x 2 (GeV 2 /c 4 )

18. V cb extraction m kin b, m kin c ( m 1S b ) - mass of b and c quarks Λ QCD 2 /m b 2 μ  2 ( λ 1 ) - kinetic energy of b quark, μ G 2 ( λ 2 ) - chromomagnetic coupling Λ QCD 3 /m b 3 ρ D, ρ LS ( ρ 1, τ 1-3 ) well behaving renormalization schemes are used: Kinetic running mass 1S mass both schemes have 7 free parameters: higher moments are sensitive to 1/m b 3 terms  reduce theory error on V cb and Heavy Quark parameters

19. Kinetic Scheme Belle    /dof =17.8/24 m b = 4.564 ± 0.076 GeV, m c = 1.105 ± 0.116 GeV Contours     =1 |V cb | = (41.93 ± 0.65 fit ± 0.48 α s ± 0.63 th )×10 -3 BR E e,1 E e,2 E e,3 Mx2Mx2Mx2Mx2 E γ,1 Mx4Mx4Mx4Mx4 E γ,2 Yellow band: theory error Filled circles: used in fit Preliminary Belle ICHEP06

20. September 2006 E. Barberio 20 |V cb | = (41.5 ± 0.5 fit ± 0.2  )×10 -3 1S Scheme m b 1s = 4.73 ± 0.05 GeV 1 = -0.30 ± 0.04 GeV Belle ICHEP06 E e,3 Mx2Mx2Mx2Mx2 E γ,1 Mx4Mx4Mx4Mx4 E γ,2 20 Yellow band: fit error Red band: Theory + Fit BR E e,1 E e,2 Filled circles: used in fit   /dof = 6/17 Contours     =1 Preliminary

21. September 2006 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  V cb @ 2% m b < 1%  crucial for V ub m c @ 5% |V cb |=(41.96±0.23 exp ±0.35 HQE ±0.59  SL )10 -3

22. September 2006 E. Barberio 22 c q - w=1 HQET and B  D * l w=1  D * produced at rest in B rest frame l V cb bc q2q2 q 2  4-momentum transfer 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 c q - w>1

23. September 2006 E. Barberio 23 V cb from B  D * l measure d  /dw and extrapolate at w=1  the slope is important fit for both intercept F (1)|V cb | and slope  2 when m Q  ∞  (1)=1  V cb extraction F(1)V cb w Delphi K(w): phase space (known function) F (w): unknown form factor F (1)g(w) in the heavy quark limit F (1)=  (1)=1

24. September 2006 E. Barberio 24 signal and w reconstruction B  D*l  D *   + slow D 0 : m(D * )-m(D 0 )~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 CLEO Signal region

25. September 2006 E. Barberio 25 extrapolation: form factor shape expansion around w=1 up to second order: Caprini,Lellouch,Neubert NP B530(98)153 and Boyd,Grinstein,Lebed PRD56(97)6895 use dispersive relations to constraint the shape R 1,R 2 calculated using QCD sum rules R 1 (w)  1.27-0.12(w-1)+0.05(w-1) 2 R 2 (w)  0.80+0.11(w-1)-0.06(w-1) 2 measured by CLEO: R 1 (1)=1.18±0.30±0.12 R 2 (1)=0.71±0.22±0.07 For long time R 1,R 2 uncertainty was the major source of systematic on  A 2 used in the old world average

26. September 2006 E. Barberio 26 form factor shape one-dimension projection of fitted distributions: Fit w and 3 angles

27. September 2006 E. Barberio 27 form factor and Vcb Simultaneous fit of the Form factors and Vcb F (1)|V cb |=(34.68  0.32  1.15)10 -3 Br(B 0  D* + l )=(4.84  0.39)%

28. September 2006 E. Barberio 28 F (1)|V cb |  2 /dof = 38.7/14  2 =1 CL=37% New HFAG average uses R 1, R 2 from Babar: this decrease F (1)|V cb | F (1)|V cb |=(36.2  0.8)10 -3  A 2 =1.19  0.06

29. September 2006 E. Barberio 29 non-perturbative QCD calculations F (1) = 0.907  0.007  0.025  0.017 F (1) = 0.900  0.015  0.025  0.025 F (1) = 0.919 -0.035 +0.030 |V cb | excl = ( 39.4  0.9 exp  1.5 theo )10 -3 F (1) and V cb from lattice and sum rule

30. September 2006 E. Barberio 30 V cb from B d 0  D +  decays BELLE G (1)|V cb |=(42.6  4.5) x 10 -3  G 2 =1.17  0.18 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

31. September 2006 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

32. September 2006 E. Barberio 32  (B  D *,**  )/  (B  DX  ) Measurement This measurement is not solving the puzzle …

33. September 2006 E. Barberio 33 Conclusions |V cb | inc =(41.96±0.23 exp ±0.35 HQE ±0.59  SL )10 -3 |V cb | excl = ( 39.4  0.9 exp  1.5 theo )10 -3 V cb is now a precision measurement: The measurement of m b from the inclusive spectrum are crucial for the precise extraction of V ub B  D **  are still a puzzle and a concern…. Inclusive and exclusive analyses give consistent results