1. Precise Determination of |V cb |, |V ub |, and the b-quark mass from inclusive B decays |V cb | at the ~1% level - The new BABAR result as an example Towards a ~5% measurement of |V ub | - what can we lean from b  cl and b  s  b  s  and its senitivity to „new physics“ - how tight are the constraints really? |V cb | at the ~1% level - The new BABAR result as an example Towards a ~5% measurement of |V ub | - what can we lean from b  cl and b  s  b  s  and its senitivity to „new physics“ - how tight are the constraints really? DESY TUESDAY SEMINAR 21/09/2004 Oliver Buchmüller CERN

2. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 2 CP Violation in the Standard Model(SM) CKM Matrix Unitarität The elements of the CKM matrix are the only source of CP violation in the SM The area of the triangle is proportional to the CP violation in the SM Measurements of the angles and sides of the triangle represent a fundamental test of the SM! N(q)/N(anti-q) ~ 10 -20 much to small! The expected size of CP violation in the SM is much too small The expected size of CP violation in the SM is much too small to explain N(q)/N(anti-q)~10 -9

3. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 3 The sides of the triangle |V ub /V cb | describes a circle in the ( ,  ) plane A measurement of a length of a triangle is as good as a measurement of an angle!

4. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 4 The Trinagle Today sin2  has become a precision measurement and is now the best know quantity of the triangle! If we want to sufficiently over constrain the triangle we need to improve the other measurements as well!  |V cb | and |V ub |

5. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 5 |V cb | und |V ub | from semilleptonic B decays Why semileptonic B decyas? B  Xl mit l=e,  b  cl No „colour activity“ between W  l and c quark b c W 1.For |V xb | we need to have a b  x transition (trivial) 2.Need a precise theoretical framework to translate the measurements on “meson level” into “quark level” (not trivial)  semileptonic decays are theoretical necessity!

6. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 6 The Inclusive Approach The advantage of being inclusive!  QCD «m b : inclusive decays admit systematic expansion in  QCD /m b Non-pert corrections are generally small and can be controlled Hadronization probability =1, approximately insensitive to details of meson structure as  QCD «m b (at least far from perturbative singularities)  s and can be expressed as double series in  s and  QCD /m b (OPE) with parton model as leading term No 1/m b correction!

7. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 7 The Heavy Quark Expansion (HQE) Short-distance physics encoded in coefficients of operator products (to some order in  s ). Calculable! Long-distance physics encoded in exp. values of products of quark operators (to some order in 1/m b ). NOT calculable! Must be determined empirically.  Need to get access to the not very well know HQE parameters!

8. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 8 Access to the HQE Parameter The HQE not only predicts the inclusive decay rates but also inclusive differential decay distributions for semileptonic decays (e.g. moments of the lepton energy spectrum). Measure (a lot) moments of inclusive kinematic distributions Extract HQE parameters (e.g. m b ) from a fit to all moments Compare predicted inclusive decay rate with its measurement  sl =  sl (  B, BR sl ) |V cb |

9. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 9 Pioneering Work M 1 (M x ) M 2 (M x ) M 3 (M x ) M 1 (E ) M 2 (E ) M 3 (E ) m b,kin  (  GeV  = 4.58 + 0.06 fit +0.05 sys GeV m c,kin  (  GeV  = 1.15 + 0.09 fit +0.08 sys GeV   2 (  GeV  = 0.41 +0.04 fit +0.04 sys GeV 2  D 3 (  GeV  = 0.05 +0.02 fit +0.01 sys GeV 3 Input constraints: m b = 4.57  0.10 GeV m c = 1.05  0.30 GeV DELPHI CLEO Multi parameter fits to moments but sensitivity was limited …

10. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 10 The B Factory BABAR and PEPII LINAC BABAR SLD

11. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 11 BABAR AND PEPII 9 GeV 3.1 GeV e+e-   4s (10.58 GeV)  BB (96%, 4% non-BB)  4s (10.58 GeV) BB production threshold

12. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 12 A Tough Race RUNI RUNII RUNIII RUNIV Competition is important: Both B factories perform very well (15/06/2004)  BABAR 227 fb -1  BELLE 275 fb -1   500 fb -1 Better than expected and gives hope for the future. (ca. 550 Mio BB events) BABAR results of this talk are based on 82 fb -1  ca. 90 Mio BB events

13. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 13 Semileptonic B Events: Access to V cb and V ub A theoretical necessity … V cb b c W (V ub ) “Tree Level” “Detector Level” No color interaction between W and c-quark “CKM Matrix” … but an experimental challenge! D*D*D*D* l e-e-e-e-  e+e+e+e+ B reco B recoil XcXcXcXc ν  Need to fully reconstruct the semileptonic B Event in order semileptonic B Event in order to get access to the kinematic to get access to the kinematic information of the signal B decay information of the signal B decay “Neutrino Reconstruction”

14. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 14 Kinematic of Semileptonic B Events Reco. B: 4 measured quantities X-System 4 gemessene Größen (e.g. M x ) Lepton 3 measured quantities (e.g. E l ) Energy and Momentum Conservation E breco + E X + E l + E - E PEPII = 0 P breco + P X + P l + P - P PEPII = 0  4 Constraints + Mass Constraint M(Breco)=M(X,l, )  + 1 Constraint Neutrino 3 unmeasured quantities 5 Constarints – 3 unmeasured quantities = 2 times overconstraint System „2C kinematic fit“ Use fulll reconstructed B sample:  „Tag“ B is full reconstructed and the signal B is identified via the lepton. P e- P e+ Incomming momentum of the two beams are well measured (E PEPII,P PEPII ) bekannt!  full reconstruction of the entire semileptonic event (especially M x und E l )

15. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 15 1. Fully reconstructed hadronic B-decay 2. Semileptonic decay of other B o Identify Lepton (e or  ) o reaming tracks and neutral objects define the X-System 3. M x determined by 2C kinematic fit 4. Sideband subtraction of the combinatoral B background. Hadron Moments signal background 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 m ES [GeV/c 2 ] 2250 2000 1750 1500 1250 1000 750 500 250 0 Events / 1.8 MeV/c 2 BABARBABAR Y(4S) 7114 signal events, 2102 combinatoral bg.  Out of 90 Mio BB events! high mass final states M x 2 [GeV 2 /c 4 ]

16. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 16 Lepton Moments BABAR e sig e-e-e-e- e+e+e+e+ B tag B sig ν e tag “e + e - ” unlike sign “e ± e  ” like sign “double lepton tag” Subtract irreducible bg. and unfold the number of primary electrons from the two samples (“ARGUS method”). Select events with two identified electrons: e + e - and e ± e  Unfolded primary electron spectrum for B  Xl

17. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 17 (E L CUT ) and (E L CUT ) Measure moments over a large rage in phase space  as function of a cut in the lepton energy A cut in the lepton energy will restrict the phase space for high mass states production (D**, D*  ). Thus (E L CUT ) and (E L CUT ) will probe the underlying “decay dynamic” of B  X c l events. Mx High mass states

18. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 18 (E L CUT ) and (E L CUT ) Increase of the mean Decrease of truncated BR BABAR E cut Phys.Rev.D69:111103,2004 Phys.Rev.D69:111104,2004 Reduction of high mass final states

19. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 19 HQE Fit  i-th central E l moment for E l >E 0 :  i-th M x moment and E l >E 0 :  |V cb | „master“ formula :  : Use dedicated HQE for every measured observable:  clv (BR, lifetime)  Hadron Mass Moments (E cut )  Lepton Energy Moments (E cut ) (Fit parameters are in red)  i-th E  moment and E  >E 0 : From B  X s   Extract the HQE parameter m b,m c,   2,  G 2,  D 3,  LS 3 and |V cb | as well as BR clv from a simultaneous fit to all moment measurements (27+1*). Experimental and theoretical errors and their correlations are all accounted for in the fit. * Only external input to the fit is: B lifetime  B+B0 =1.608  0012 ps

20. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 20 Combined Fit to E e and M x Moments  i-th central E l moment for E l >E 0 :  i-th M x moment and E l >E 0 :  |V cb | „master“ formula :  : Calculations taken from Gambino and Uraltsev, hep/ph 0401063 high correlation between measurements :  this fit uses solid points only

21. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 21 Fit Results Strong correlation between m b and m c : m b (1 GeV) – m c (1 GeV) = (3.44±0.03 exp ±0.02 HQE ±0.01 α s ) GeV kinetic mass scheme Phys. Rev. Lett. 93:011803,2004 hep-ex/0404017 BABAR  2 =1 ellipses 2D projections of the fit result: BABAR

22. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 22 |V cb | and BR(B  Xl ) But comparison is not on “equal footing” because the input (e.g. B lifetime and BR ) as well as the theoretical error assumption are not the same  job of HFAG A better comparison is the total semileptonic BR. The from the HQE Fit extracted BR is roughly 30% more accurate than the HFAG average.  sets roughly the scale of improvement

23. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 23 b-quark and c-quark mass Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262 See also report from CKM WS hep-ph/0304132 m c (m c ) = 1.33 ± 0.10 GeVm b (m b ) = 4.22 ± 0.06 GeVBABAR

24. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 24 New Moment Measurements ICHEP04 has surprised us with a lot more moment measurements from various collaborations: BABAR: hep-ex/0403031 (Phys.Rev.D69,2004)  Hadron Moments from semileptonic B decays hep-ex/0403030 (Phys.Rev.D69,2004)  Lepton Moments from semileptonic B decays BELLE: hep-ex/0408139 (preliminary)  Hadron Moments from semileptonic B decays hep-ex/0409015 (preliminary)  Lepton Moments from semileptonic B decays B  X s  decayshep-ex/0403004 (Phys.Rev.Lett.93,2004)  Photon Energy Moments from B  X s  decays CDF: http://www-cdf.fnal.gov/physics/new/bottom/040428.blessed-bhadr-moments/  Hadron Moments from semileptonic B decays CLEO: hep-ex/0403052 (Phys.Rev.D70:,2004)  Hadron Moments from semileptonic B decays hep-ex/0403053 (Phys.Rev.D70:,2004)  Lepton Moments from semileptonic B decays B  X s  decayshep-ex/0108032 (Phys.Rev.Lett.87,2001)  Photon Energy Moments from B  X s  decays DELPHI: hep-ex/0210046  Hadron Moments from semileptonic B decays hep-ex/0210046  Lepton Moments from semileptonic B decays More than 100 single moment measurements!  perfect playground for consistency tests …

25. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 25 Include Additional Moments in the HQE Fit BABAR moments only All Moments  2 /NDF 0.75 0.55 |V cb |x10 -3 41.39  0.59(  0.62)41.38  0.45(  0.62) m b [GeV] 4.611  0.067 4.610  0.053 m c [GeV] 1.18  0.09 1.17  0.08 BR clv [%] 10.61  0.17 10.64  0.14 Very consistent results and the inclusion of the additional moments leads to significant improvements of the extracted fit parameters (e.g. m b ~25%) Include all moment measurements in the fit that are given with a full covariance matrix.  Use the extracted HQE parameters as base for the theoretical predictions!

26. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 26 Comparison: Hadron Moments Y-axis: HQE prediction - Measurement Best fit Total Error Exp. Error Very good agreement! Also the moments not included in the fit agree well with the HQE prediction based on the fit results!

27. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 27 Comparison: Lepton Moments Y-axis: HQE prediction - Measurement Very good agreement for lepton moments from BABAR, BELLE and DELPHI.  Under investigation. Need to properly take into account common systematics, all correlations, etc … but looks like a ~3  difference Keep in mined that the moments are highly correlate. Typical  between the two extreme values is ~50% Best fit Total Error Exp. Error But the results from CLEO fit not too well …

28. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 28 Comparison with other (independent) determinations In hep-ph/0408002 Bauer et al. have carried out an independent |Vcb| determination based on calculations in the 1s scheme (and other schemes). m b, m c  Leading order defined in different schemes (   2,  G 2 ) 1, 2  O(1/m b 2 ) & (  D 3,  LS 3 )  1,  2  O(1/m b 3 ) &  Gremm,Kapustin  A simultaneous fit to all data yields: (hep-ph/0408002 - 1s scheme) |Vcb|=41.9  0.6(fit)  0.1(  B ) x10 -3 m b 1s =4.68  0.4(fit) GeV 1 =-0.23  0.06(fit) GeV 2 (our results - kinetic scheme) |Vcb|=41.4  0.5(fit) [  0.6(theo)] x10 -3 m b kin =4.61  0.5(fit) GeV   2 =0.40  0.04(fit) GeV 2 Comparison:   2 = - 1 + O(  s )  - 1 + 0.17 GeV 2 translate m b into MS: m b (m b ) —— |Vcb|: 41.9 vs.. 41.4 [x10 -3 ]  0.4 vs. 0.4 [GeV 2 ]  4.19 vs. 4.22 [GeV] -  Leading HQE parameters are consistent but |Vcb| differs by 1.2% - too much?

29. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 29 Inclusive |V cb | Moment measurements from various experiments as well as improved theoretical calculations in the HQE framework allow the extraction of the O(1/m b 3 ) parameters without any external constraints. Example BABAR analysis: Phys. Rev. Lett,2004 hep-ex/0404017 Or hep-ph/0408002 1S scheme Bauer et al.  The determination of |V cb | from inclusively defined moments of semileptonic kinematic distributions has entered the phase of a precision measurement. Still a few outstanding issues: Consistency of CLEO lepton moments Compatibility of extracted |V cb | values (inconsistently applied QED corrections?!) Uncertainty of calculations for the non-integer moment and >2% measurement of |V cb | + extraction of all HQE parameters to O(1/m b 3 ) But the general picture looks very encouraging ….

30. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 30 Unitarity Triangle and |V cb | What have we learned … 5% vs. 2%

31. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 31 |V ub | today … and its (current) limitations |V ub | has crossed the ~10% error barrier! Already quite an accomplishment but we want more (target ~5% error) Error Budget  |V ub |  |V ub |  [  0.09(exp)  0.1(SF)  0.05(HQE)]  10% - experimental error:  With increasing statistic BABAR and BELLE will be able to significantly improve this error!  10% - “shape function” error:  Limited knowledge of the shape function leads to the largest theoretical uncertainty. Currently the shape function parameter are obtained from the BELLE photon energy spectrum from b  s   5% - “HQE” error:  OPE based translation of the measured Br ulv into |v ub |. The limiting factor is the uncertainty of the b quark mass! Need to work hard on the extraction of the shape function parameter and a better determination of m b

32. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 32 Photon Energy Spectrum  Besides “new physics” the radiative penguin decay b  s  probes also very important SM quantities such as the b-quark mass and the “Fermi motion”. s  b bsbs  m b ) 2 > Fermi Motion (   2 ) Heavy Quark Limit m b  8 =m b /2 and ) 2 >=   2 /12  Probes directly m b while b  cl is most sensitive to m b -m c  Gives access to the shape function (b quark distribution function) for the heavy to light quark transition Complementary information to semileptonic decays

33. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 33 The experimental challenge Schnitt b  s  BR ~ 10 -4 BB udsc Before all cutsAfter almost all selection cuts  The very difficult background situation requires a lower cut on the photon energy to measure relevant quantities like BR b  s  or the moments of the spectrum. How far can we go down …?

34. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 34 The Measured Spectrum BELLE 2004 CLEO 2001 E  >1.8 GeV E  >2.0 GeV E  cut =1.8 GeV: BELLE =2.292  0.043 GeV - 2 =0.0305  0.0100 GeV 2 E  cut =2.0 GeV: CLEO =2.346  0.034 GeV - 2 =0.0226  0.0070 GeV 2

35. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 35 Shape Function Parameter The shape function from b  s  and b  ul are related and it is possible to use the photon energy spectrum to extract the shape function parameter valid for b  ul decays (Caveat: 1/m b corrections) HFAG: Use the BELLE photon energy spectrum to determine the shape function (hep-ex/0407052) Fit true underlying photon spectrum via a Monte Carlo simulation to the measured spectrum (similar to an unfolding)

36. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 36 HQE Prediction for and ) 2 > New HQE calculation from Benson, Bigi and Uraltsev (soon to be published) in the kinetic scheme [O(1/m b 3 ); O(  )] (soon to be published)  Comparable to those for clv moments.  i-th E  moment and E  >E 0 : Caveat: For tight cutoffs the expansion scale Q  M B -2E  cut (“hardness”) becomes to small for a reliable 1/Q expansion  Bias in the leading HQE parameters m b am   2 Benson et al provide also predictions for the bias effect as a function of the cutoff Expected bias at 2E  cut =2.0 GeV:  m b  40 MeV ;   2  0.1 GeV 2 In the following consider both scenarios: 1.HQE prediction only 2.HQE prediction & bias correction

37. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 37 Consistency between b  s  and b  cl Use extracted HQE parameters from the clv moment fit to predict the moments of the photon energy spectrum. “HQE only” “bias corrected HQE” Moment measurements agree well with HQE prediction obtained from the clv moment fit. Evidence that bias correction is needed for moments above E  >1.8 GeV But we can do more …  Use the shape function parameter which ft the BELLE spectrum to obtain the moments as a function of the cut. ( Test: agrees nicely at E  =1.8 GeV with the direct measurement from BELLE ) Remarkable agreement with HQE prediction Strong evidence, especially from the second moment, that bias corrections are needed above above E  >1.8 GeV.

38. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 38 What can we learn from this? 1. The HQE parameter extracted from b  cl events are the same as the one obtained from b  s  events (e.g. m b from clv =m b from s  )  We can use the enormous potential of our clv moment measurements to predict the moments of the photon energy spectrum and to extract the shape function parameter from it! … very important for |V ub | 2.There is compelling evidence that for E  >1.8 GeV the HQE prediction have to be bias corrected (as claimed in hep-ph/0308165)  We need more moment measurements as a function of E  to to established this bias effect … but the current evidence is already strong.

39. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 39 Moment Predictions E  cut =1.8 GeV: =2.312  0.024 GeV - 2 =0.0329  0.0026 GeV 2 E  cut =2.0 GeV: =2.341  0.025 GeV - 2 =0.0222  0.0024 GeV 2 E  cut =1.8 GeV: BELLE =2.292  0.043 GeV - 2 =0.0305  0.0100 GeV 2 E  cut =2.0 GeV: CLEO =2.346  0.034 GeV - 2 =0.0226  0.0070 GeV 2 Experimental Results Predictions for the HQE fit based on cl moments  The HQE fit results would constrain the moments of the photon energy spectrum by a factor ~2 better than the current experimental measurements. Using this information for the extraction of the shape function parameters will significantly improve the theoretical uncertainties on Vub!  |V ub |  |V ub |  [  0.09(exp)  0.05(SF)  0.04(HQE)]  |V ub |  |V ub |  [  0.09(exp)  0.1(SF)  0.05(HQE)] Getting much closer to a 5% theoretical error

40. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 40 Unitarity Triangle - The Future?! Vcb ~ 1% and Vub ~5%(theo) 5% (exp)

41. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 41 b  s  : very sensitive to “new physics” b s “New physics” can contribute in the loop … …and would lead to an increase of BR( b  s  ) Tight constraints on “new physics parameter” which are especially important for the search at the LHC/LC.

42. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 42 BR(B  X s  ) Today Slide from the ICHEP04 Plenary Talk of Ahmed Ali (DESY). BR HFAG =3.54  0.3 BR SM =3.70  0.3 However, a new paper (hep-ph/0408179) from M. Neubert claims that perturbative uncertainties have been underestimated in the theoretical calculations of BR SM :  BR SM  0.6 100% increase of the uncertainty for the SM prediction!

43. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 43 Potential Impact on “New Physics” Constraints tan  BR(b  s  ) MHMH ICHEP2004 BR(b  s  )  BR(b  s  ) Since the b  s  decay is very sensitive to certain contributions from „new physics“ a significant incraese of the theoretical uncertainties would soften a lot of rather tight (indirect) limits on „new physics“ processes (e.g. 2HDM). For illustrative purpose only - the TYPEII Two Higgs Doublet Model 0.65 200 Neubert - hep/ph 0408179

44. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 44 How can we validate the prediction? hep-ph/0408179 According to hep-ph/0408179, also the prediction of the first moment of the photon energy spectrum must suffer from large perturbative uncertainties:  ~  0.06 GeV (  m b ~  120 MeV) The prediction from hep-ph/0408179 are compatible with the data (E  =[1.6,2.0]) but the HQE prediction in the kinetic scheme from Bigi et al. describe the data over the entire cut range much better than the claimed  ~  0.06 GeV (  m b ~  120 MeV).  Evidence that perturbative (and non-perturbative) uncertainties are under control? In any case, the multitude of moment measurements represent a tool to scrutinize the prediction power of the theory  important for b  s  and its sensitivity to new physics.

45. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 45 Today 2007?

46. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 46 BACKUP - UT Fits ---------------------------------------------------------- Vcb_err : 0 ( 0.2% ) | 2% | 5% ---------------------------------------------------------- ===> Lmax (flat Likelihood) ---------------------------------------------------------- rho_bar : 0.21 +- 0.05 eta_bar : 0.35 +- 0.02 ---------------------------------------------------------- ===> L*e^{-1/2} ---------------------------------------------------------- rho_bar : 0.22 +- 0.12 | 0.22 +- 0.12 | 0.21 +- 0.14 eta_bar : 0.34 +- 0.05 | 0.34 +- 0.06 | 0.35 +- 0.07 ---------------------------------------------------------- ===> L*e^{-2} ---------------------------------------------------------- rho_bar : 0.21 +- 0.17 | 0.20 +- 0.18 | 0.19 +- 0.20 eta_bar : 0.35 +- 0.08 | 0.35 +- 0.08 | 0.36 +- 0.11 ---------------------------------------

47. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 47 Backup - RESULTS m b (m b ) = 4.22 ± 0.06 GeVm c (m c ) = 1.33 ± 0.10 GeV Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262 See also report from CKM WS hep-ph/0304132

48. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 48 Backup Lepton Moment Measurement

49. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 49 Selecting B  X e Decays  Based on events with one high energetic electron  p * > 1.4 GeV/c, J/  -veto „ tag electron “, ?originates predominantly from semileptonic B-decays  Look for oppositely charged electrons : J/  Backgrounds (MC) Signal (MC) p e [GeV/c] B‘s at rest : no angular correlation between e + & e  cut e + & e  „back-to- back“ 1.0 0.5 0.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 „ARGUS-Method“ 0 0.5 1.0 1.5 2.0 2.5

50. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 50 Raw Spectra & Backgrounds  Sizable contribution of „upper Vertex“ processes : ?dominant source of syst. uncertainties at low energies mostly Electrons / 50 MeV/c

51. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 51 Inclusive e Spectrum  Correction for electron efficiency  e and B 0 B 0 mixing  Bremsstrahlung corrections ?full detector simulation ?checked appropriate modeling of detector material  Compare E e distribution of e  e   e  e  events in data with simulation  Partial branching fraction : Consistent with previous result ( Phys. Rev. D 67, 031101)

52. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 52 Inclusive e Spectrum : Moments  Subtraction of contribution from B  X u e  decays  Br(B  X u e  from BABAR-measurement (  this talk)  Correction for QED-radiative effects ?PHOTOS  Moments estimated from histogram ?small corrections due to finite binning and boost into B-restframe  Results (E e > E cut ) :

53. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 53 Backup Hadron Moment Measurements

54. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 54  M x n  Analysis : Event Selection  Fully reconstructed hadronic B-decay  Semileptonic decay of other B ?lepton with  : missing energy E mis & momentum p mis ?completeness of X H : E mis  p mis  M x determined by 2C kinematic fit ?energy conservation, p 2 miss = 0  signal background 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 m ES [GeV/c 2 ] 2250 2000 1750 1500 1250 1000 750 500 250 0 Events / 1.8 MeV/c 2 high mass final states M x 2 [GeV 2 /c 4 ] BABARBABAR Y(4S) 7114 signal events, 2102 combinatoral bg.

55. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 55 Determination of  M x n  (n=1,2,3,4)  Measured  M x n  differs from true  M x n   For each interval in M x n, full detector simulation delivers  M x n  and  M x n  ?calibration curve which is applied to data event-by-event ?weak dependence on decay model ?validated on data with decays ?function of multiplicity and  Event selection efficiency ?depends on decay mode ?influence on  M x n  determined with MC, systematic error estimated by variation of individual exclusive decay modes 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 p min [GeV/c] 4.5 4.4 4.3 4.2 4.1 4.0  M x 2  [GeV 2 /c 4 ] ~ calibration (D,D *, D **,D (*)  mix) verification with excl. modes 3 4 5 6 7 8 9 10 11 12  M x 2  [GeV 2 /c 4 ] 12 11 10 9 8 7 6 5 4 3  M x 2  [GeV 2 /c 4 ] ~ ~

56. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 56 Hadron Moments: and Bauer et al. 1s scheme (hep-ph/0408002)Our results - kinetic scheme Not in the fit While the lepton energy moments lead to very similar results, especially the non-integer hadron mass moments and are different …

57. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 57 Scale Dependence of the Kinetic Scheme Check scale dependence on the level of the physical observables (moments) that are supposed to be scale independent! Valuable input from Paolo Gambino and Nikolai Uraltsev Vary the scale dependent HQE parameters simultaneously between  =[0.5-1.5] GeV. However, to maintain the physical meaning of the c quark mass  =[0.8-1.2] GeV is a more appropriated choice for a reasonable scale variation. Red Band: Propagated theoretical uncertainty from the extracted HQE parameters in the BABAR analysis. Yellow Band:  10% variation of the O(1/m b 2 ) and O(1/m b 3 ) contribution. This variation corresponds to an 0.1x10 -3 uncertainty in |V cb |

58. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 58 Scale Dependence of the Kinetic Scheme  The observed scale dependence of the predicted moments in the kinetic scheme is very small and even for the large scale variation of  =[0.5-1.5] GeV (default  =1GeV), the observed moment shifts are already covered by an uncertainty of the O(1/m b 2 ) and O(1/m b 3 ) contributions of  10%. Such an uncertainty would manifest itself in an error on |V cb | of 0.1x10 -3. Following the suggestion for the theoretical error evaluation in hep-ph/0401063, the final theoretical errors of the BABAR analysis on |V cb | and the extracted HQE parameters fully cover the small effect of the observed scale dependence: Example:  |V cb | (theo-BABAR) =0.7x10 -3 to be compared with  |V cb | (scale) <0.1x10 -3

59. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 59 BSG MOMENT PREDICTION I------------------- Eg=1.8 EG 2.31394725 0.0183035162 VEG 0.0329645342 0.0026 RHO 0.759208181 I------------------- Eg=2.0 EG 2.34259823 0.0190865906 VEG 0.0222734452 0.0024 RHO 0.694841549 CLV + BSG BELLE + BSG CLEO + BSG BABAR I------------------- Eg=1.8 EG 2.31247747 0.0243168435 VEG 0.0328578215 0.0026 RHO 0.845508417 I------------------- Eg=2.0 EG 2.34107022 0.0253493739 VEG 0.0221826394 0.0024 RHO 0.795027137 CLV + BSG BELLE E  cut =1.8 GeV: BELLE =2.292  0.043 GeV - 2 =0.0305  0.010 GeV 2 E  cut =2.0 GeV: CLEO =2.346  0.034 GeV - 2 =0.0226  0.007 GeV 2 Experimental Results

60. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 60 Yet another “triangle” to be tested … b  s , X s ll BR ~10 -4  m b b  ul b  ul BR ~10 -3  V ub b  cl b  cl BR ~10 -1  V cb, m b,   m b,    “shape function” HQE link established? HQE link not yet established b  s  : b  s  : Large potential for new physics but still the issue of the rather high photon energy cutoff. b  X s ll: b  X s ll: “Flag ship analysis” for future b exp. (LHCB, BTEV,10 35-36 ) Theoretical uncertainties on X s ll will dependent on the knowledge of the b quark mass and its fermi motion in B meson. Vub/Vcb: Vub/Vcb: The largest uncertainty is due to the imperfect knowledge of the b quark mass and its fermi motion (Vub).  We need Theory and Experiment to not only establish the missing links in the “HQE triangle” but also to check its consistency! in the “HQE triangle” but also to check its consistency! The measurement of the moments is one step in this direction …

61. Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004 61 The three requirements from Andrei Sacharow (1967): 1.Baryon number violation 2.C und CP violation 3.Abkehr vom thermodynamischen Gleichgewicht Somewhere here