1. measurements of V cb, branching fractions, form factors E.Barberio University of Melbourne FPCP: Daegu October 2004

2. October 2004 E. Barberio 2 Semileptonic B decays V cb tree level, short distance: decay properties depend directly on fundamental Standard Model parameters: - |V cb |: essential ingredient in tests of CKM unitarity - m b, m c : predictions of B decay rates, precision electroweak observables

3. October 2004 E. Barberio 3 Extracting V cb, m b, m c precise determination of V cb m b m c ! quarks are inside hadrons bound by soft gluons  both perturbative (higher order QCD (  s n ) corrections) and non-perturbative (  QCD ) long-distance interactions of b quark with light quark tools: Heavy quark symmetry and lattice QCD + higher order & long distance:

4. October 2004 E. Barberio 4 Heavy Quark Symmetry when the energy of soft gluon  QCD ~250 MeV << m b,c  heavy quark heavy quark is ‘invisible’ to gluon probes with de Broglie wavelegnth g >>1/m c,b : - 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 Exclusive Inclusive

5. October 2004 E. Barberio 5 HQET and B  D * l in m Q  ∞  (1)=1  V cb extraction with little model dependence bonus: B  D (*) l largest branching fraction of B decay modes 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 non-perturbative effects described by form factors all B  D (*) l transitions are described by one form factor  (Isgur-Wise function) as a function of w: the D* boost in B rest frame c q n - w>1 c q n - w=1

6. October 2004 E. Barberio 6 V cb from B  D * l F(1)V cb w DELPHI (unfolded data) K(w): is the phase space (known function) F (w): unknown form factor= F (1)g(w) in the heavy quark limit m Q  ∞ F (1) =  (1)=1 in HQET measure d  /dw(w) and extrapolate at w=1  g(w) slope important fit for both intercept F (1)|V cb | and slope (  2 ) [ Caprini, Lellouch, Neubert, Nucl.Phys.B530(98) ]

7. October 2004 E. Barberio 7 B  D * l : signal and w reconstruction Belle D*  D  D  K  (  ) D *   + slow D 0 : m(D * )-m(D 0 )~m(  + ): the  + is almost at rest close to K(w=1) in the B rest frame  + difficult or impossible to reconstruct if the B is produced at rest or has little boost w  p and E : need good resolution for E +p, easy if the B is produced at rest of with little boost B  D*l l V cb bc q2q2

8. October 2004 E. Barberio 8 B  D (*) l  signal efficiency LEP Z  bb: B 0 large variable momentum ~30 GeV good efficiency at w~1: less extrapolation uncertainty at w=1  (4S)  B 0 at rest or almost large data sample, good w resolution, low D** background poor efficiency at w~1 w CLEO poorer w resolution large background from higher D ** B   D* 0  B d 0  D *+ 

9. October 2004 E. Barberio 9 B  D (*) l : background B  D ** l with D **   D * /  D 0 resonant (narrow and wide) and non resonant LEP: resonant D ** :different form factors depending on assumption on quark decay dynamics [Leibovich,Ligeti,Stewart,Wise] D ** shape from constraints on D ** rates: Br(B  D * 2 l )/ Br(B  D 1 l  <0.4  (4S): CLEO

10. October 2004 E. Barberio 10 B  D (*) l : 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 measured by BaBar R 1 (1)=1.128±0.060±0.025 R 2 (1)=0.920±0.048±0.013 R 1,R 2 uncertainty is the major source of systematics on  A 2 used in the world average

11. October 2004 E. Barberio 11 Extracting F (1)V cb BELLE w CLEO B d 0  D * - and B -  D* 0 - w OPAL w h A1 (w) |V cb | x 10 -3 B A B AR

12. October 2004 E. Barberio 12 F (1)|V cb | world average F (1)|V cb |=(37.8  0.9)x10 -3  A 2 =1.54  0.14

13. October 2004 E. Barberio 13 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) = 0.913 -0.017 -0.030 +0.024 +0.017 F (1)=0.91  0.04 future error reduction from unquenched calculations |V cb | excl =(41.5  1.0 exp  1.8 theo ) 10 -3 F (1) and V cb from lattice and sum rule

14. October 2004 E. Barberio 14 V cb from B d 0  D +  decays BELLE G (1)|V cb |=(42.0  3.7) x 10 -3  G 2 =1.15  0.16 consistency check and test of the theory: from Belle D* and D + results  2 D -  2 D * =-0.23  0.29  0.20 G (1)/ F (1)=1.16  0.14  0.12 compatible with expectations large combinatorial background non-zero 1/m Q corrections to G (1)

15. October 2004 E. Barberio 15 B d 0  D *  and B d 0  D +  The B d 0  D *  and B d 0  D +  branching fraction are derived from the same analyses used for V cb

16. October 2004 E. Barberio 16 V cb from inclusive semileptonic decays  1 2 or   2  G 2 at 1/m b 2  D 3,  LS 3 or  1,  2, T 1-4 at 1/m b 3  sl described by Heavy Quark Expansion in (1/m b ) n and  s k expansions depend on m b definition: different expansions different non- perturbative terms, but they related low scale running quark masses exp.  |V cb |<1% non perturbative parameters need to be measured and arise at each order pole mass

17. October 2004 E. Barberio 17 inclusive V cb rate shape |V cb | m b,m c  2 G,  2  non-perturbative parameters though the shape ‘moments’ b Difficulty to go from the measured shape to the true shape: shape in B rest frame, QED corrections, detector resolution, accessible phase space, etc

18. October 2004 E. Barberio 18 Rate: b  X c  branching fraction  (4S) experiments traditionaly use di-lepton technique: e sig e-e-e-e- e+e+e+e+ B tag B sig ν e tag To reduce the error due to the experimental spectrum cut-off (modelling)

19. October 2004 E. Barberio 19 B-factoies more data  new tecknique: B-meson fully reconstructed B  X   K   l-l- B B 0 0  S  Belle The inclusive B + and B 0 semileptonic branching fractions measured separately : B (B 0  X ) = (10.32  0.32  0.29)% B (B +  X ) = (11.92  0.26  0.32)% Rate: b  X c  branching fraction

20. October 2004 E. Barberio 20 Inclusive semileptonic branching fractions LEP: BR(B  X c - ) = (10.42  0.26) 10 -2 main sys from modelling Partial BF

21. October 2004 E. Barberio 21 Shape: moments of kinematics variables how much is there? (area) how wide is it? (width) where is it? (mean) skewness

22. October 2004 E. Barberio 22 E : lepton energy spectrum in B  X c (BaBar Belle CLEO DELPHI) M X 2 : hadronic mass spectrum in B  X c  (BaBar CDF CLEO DELPHI) E  : photon energy spectrum in B  X s  (Belle CLEO) O n=1,2,.. : different sensitivities to non-perturbative parameters evaluated on the full spectrum or part of it (p > p min ) in the B rest frame OPE predictions can be compared with experiments after smearing  integration over neutrino and lepton phase space provides smearing over the invariant hadronic mass of the final state: test of OPE predictions, quark-hadron duality higher moments used to get sensitivity to 1/m b 3 parameters: reduced uncertainty on |V cb | from inclusive semileptonic decay moments in semileptonic decays

23. October 2004 E. Barberio 23 photon energy spectrum photon energy spectrum in B  X   not sensitive to new physics and give information on B structure E  >2 GeV Belle E  >1.8 GeV u, c, t CLEO

24. October 2004 E. Barberio 24 CLEO: hadronic moments hadronic mass spectra M x Mx from l : M X 2 = m B 2 +m n 2 -2E B E n fit relative contributions of D,D *,D ** MX2MX2 CLEO 3.2 fb -1 P* min = 1.5 GeV  = 0.35  0.07  0.1 GeV 1 =-0.238  0.071  0.078 GeV 2 photon and hadronic mass spectrum evaluated at 1/m B 3 and  s 2  o [Ligeti,Luke,Manohar,Wise] [Falk,Luke,Savage]

25. October 2004 E. Barberio 25 Belle preliminary BaBar Belle: hadronic moments fit relative contributions of D,D *,D ** lepton cutoff P*>0.9 GeV for both BABAR 51 fb -1 Events/0.5 GeV 2 high mass charm states M x 2 [GeV 2 /c 4 ] B A B AR D, D* Belle 140 fb -1 B-factories, lower lepton momentum cutoff in the B rest frame: small B boost, larger statistics, fully reconstructed sample

26. October 2004 E. Barberio 26 CDF: hadronic moments hadronic mass spectra M x M(D *+  ) P*>0.7 GeV D and D* well measured  determine contribution to moments from high mass components B  D B  D* B  D** B  D  n.b. details of resonances not included in parton level calculation CDF fixes D,D * contribution and measures the D ** rate: CDF  = 0.39 + 0.0750 stat + 0.026 exp + 0.064 BR + 0.058 theo GeV 1 =-0.182 + 0.055 stat + 0.016 exp + 0.022 BR + 0.077 theo GeV 2

27. October 2004 E. Barberio 27 LEP: hadronic moments large momentum of b-hadron ~30 GeV: full lepton energy spectrum in B rest frame  non-truncated spectra  M=M(D (*)  )-M(D (*) ) fits with resonant and non resonant states D **  D 0  + D **  D *+  - D **  D +  - B d 0  D ** - decays exclusively reconstructed

28. October 2004 E. Barberio 28 First and second hadronic moment preliminary Belle preliminary BaBar measure also the 3rd and 4th moment DELPHI the third

29. October 2004 E. Barberio 29 spectra background subtracted ee ratios of truncated lepton spectra CLEO: lepton moments Gremm,Kapustin Cleo photon, hadronic mass and lepton energy spectrum evaluated at 1/m B 3 and  s 2  o from 1/m B 3 +  s 1  theo.  =0.39+0.03 stat +0.06 sys +0.12 th GeV 1 =-0.25+0.02 stat +0.05 sys +0.14 th GeV 2

30. October 2004 E. Barberio 30 BaBar: lepton moments B-factories, lower lepton momentum cut in the B rest frame: small B boost and larger statistics B A B AR 47+9 fb-1 156,000 e ± E cut =0.6 GeVM 1 (MeV)M 2 (10 -3 MeV 2 )M 3 (10 -3 MeV 3 ) B + +B 0 1432.8  3.9  7.8 148.0  2.2  3.1-12.05  0.88  0.46 BaBar uses the di-lepton sample

31. October 2004 E. Barberio 31 Belle: lepton moments E cut =0.6 GeVM 1 (MeV)M 2 (10 -3 MeV 2 ) B+B0B+B0 1432.1  4.3  3.614 44.9  5.5  2.8 150.1  1.8  1.2 144.0  2.1  1.0 P* [GeV] unfolded spectra preliminary B0B0 B+B+ Belle fully reconstructed sample: B + & B 0 studied separately P* >0.6 GeV 140 fb -1 5054±145 B0B0 B+B+ 8371±209

32. October 2004 E. Barberio 32 LEP: lepton energy spectrum large momentum of b-hadron ~30 GeV: full lepton energy spectrum in B rest frame  non-truncated spectra unfolded spectrum background subtracted e+  lepton spectrum First three moments: M 1 = 1.383  0.012 stat  0.009 sys GeV M 2 = 0.192  0.005 stat  0.008 sys GeV 2 M 3 =-0.029  0.005 stat  0.006 sys GeV 3

33. October 2004 E. Barberio 33 DELPHI: parameter extraction  = 0.40 + 0.10 fit + 0.02 sys GeV 1 =-0.15 + 0.07 fit + 0.03 sys GeV 2  1 =-0.01 + 0.03 fit + 0.03 sys GeV 3  2 = 0.03 + 0.03 fit + 0.01 sys GeV 3 similar results with m b 1S - 1 formalism Bauer, Ligeti, Luke, Manohar pole mass expansion: (compatible with CLEO)   2 (GeV 2  m b (GeV   D 3 (GeV 3  m b (GeV  M 1 (M x ) M 2 (M x ) M 3 (M x ) M 1 (E ) M 2 (E ) M 3 (E ) input:  G 2 = 0.35 +0.05 GeV 2  LS 3 = -0.15 +0.15 GeV 3  c = 1.05  0.30 GeV  b = 4.57  0.10 GeV equivalent to B  X s  m b,kin (1GeV)= 4.59 +0.08 fit +0.01 sys GeV m c,kin (1GeV)= 1.13 +0.13 fit +0.03 sys GeV  p 2 (1GeV) = 0.31 +0.07 fit +0.02 sys GeV 2  D 3 (1GeV) = 0.05 +0.04 fit +0.01 sys GeV 3 present accuracy: no need of higher order terms m b (m b )= 4.233 GeV m c (m c )= 1.245 GeV  2 /d.o.f.=0.96 multi-parameter  2 fit to determine relevant 1/m b 3 parameters Phy.Lett B556(2003)41

34. October 2004 E. Barberio 34 BaBaR: parameters extraction BABAR: up to 1/m b 3 : fit all parameter and V cb at the same time M X moments o= used, = unused in the nominal fit B A B AR   2 /ndf =20/15 M1xM1x M2xM2x M3xM3x M4xM4x M0lM0l M1lM1l M2lM2l M3lM3l Red line: HQE fit Yellow band: theory errors P.Gambino, N.Uraltsev hep-ph/0401063 hep-ph/0403166

35. October 2004 E. Barberio 35 Another parameters extraction Fit with all data in (except Belle) from Bauer, Ligeti, Luke, Manhoar, Trott (hep-ph/040800) Using the expansion in m b 1S : V cb =(41.0  0.4  0.1  )10 -3 m b 1S =(4.68  0.03) GeV B A B AR m b from Babar fit (fifferent m b scheeme):

36. October 2004 E. Barberio 36 Conclusion |V cb | from exclusive B decays Limited by the error on F (1)=1: will reduce by lattice calculations, not soon We need to understand the “experimental” spread of F (1)V cb B d 0  D (*) - precision systematics limited: slow , D’s BR, D**? |V cb | from inclusive B decays Constraints on non-perturbative parameters reduce the uncertainty to ~2.% BR(B  X c - ) and  B are very precise Quark-hadron duality violation? no evidence with the present sensitivity. Different experiments are now providing many measurements: they are all consistent. Belle measures B + and B 0 separately. |V cb | excl =(40.1  0.9 exp  1.8 theo )  10 -3

37. October 2004 E. Barberio 37 Summary of BABAR Results on |V cb | B A B AR Conversion to MS scheme (N. Uraltsev) Exp. Determination of Quark Masses BABAR (D* l ) Recent Measurements of |V cb | inclusive exclusive

38. October 2004 E. Barberio 38  (b  X c  LEP: BR(B  X c - ) = (10.42  0.26) 10 -2  b = (1.573  0.01) ps  B  Xc - = (0.436  0.010  0.006)10 -10 MeV  B  X c - = (0.441  0.008) 10 -10 MeV  (4S): BR(B  X c - ) = (10.83  0.25) 10 -2  B = (1.598  0.01) ps  B  Xc - = (0.446  0.010  0.003)10 -10 MeV Word average

39. October 2004 E. Barberio 39 derivation of inclusive V cb |V cb | = |V cb | 0 {1 -0.65[ m b (1)-4.6 GeV] + 0.4 [m c (1)-1.15 GeV] + 0.01[   2 - 0.4 GeV 2 ] + 0.10 [  D 3 -0.12 GeV 3 ] + 0.05[  G 2 - 0.35GeV 2 ] - 0.01 [  LS 3 + 0.15 GeV 3 ] } using  sl (world) and Babar: |V cb | = 41.9  [1±0.009 G sl ±0.010 fit ±0.005 pert ]  10 -3 m b,m c,   2,  G 2,  D 3,  LS 3  s scale N.Uraltsev hep-ph/0302262 V cb dependence on non-perturbative parameters in running quark mass scheme:

40. October 2004 E. Barberio 40 CLEO BELLE Systematics

41. October 2004 E. Barberio 41 Systematics LEP

42. October 2004 E. Barberio 42 E cut (GeV) B + M 1 (GeV)M 2 (GeV 2 ) B 0 M 1 (GeV) M 2 (GeV 2 ) 0.61432.1  4.3  3.6150.1  1.8  1.21444.9  5.5  2.8144.0  2.1  1.0 0.81487.2  3.9  2.2118.4  1.4  0.71488.0  5.1  1.8119.0  1.8  0.6 1.01554.1  3.6  1.388.1  1.1  0.31551.5  4.7  1.090.7  1.4  0.3 1.21631.7  3.3  0.761.7  0.8  0.11632.6  4.3  0.864.1  1.1  0.2 1.51774.8  2.8  0.730.6  0.5  0.11778.2  3.8  0.732.3  0.7  0.1

43. October 2004 E. Barberio 43 CKM mixing matrix Wolfenstein parameterization: unitarity (A † A = 1)