1. Inclusive B Decays - Spectra, Moments and CKM Matrix Elements Presented by Daniel Cronin-Hennessy (CLEO Collaboration) Feb 24, 2004

2. Outline  Motivation and discussion of moments  Overview of CESR/CLEO  Moments Measurements and |V cb |  E  spectrum in inclusive decays B  X s   M X 2 spectrum in inclusive decays B  X c l  E l spectrum in inclusive decays B  X c l  Extraction of |V ub |  More from E  spectrum and lepton energy endpoint ( | V ub | )  Summary

3. Motivation

4.  CKM matrix relates quark mass eigenstates to weak eigenstates  Fundamental Standard Model parameters. Must be measured.  Describes math of CP Violation.  May not describe observed matter- antimatter asymmetry.

5. Overview  CKM matrix relates quark mass eigenstates to weak eigenstates  Fundamental Standard Model parameters. Must be measured.  Describes math of CP Violation.  May not describe observed matter- antimatter asymmetry. Motivation

6. B Meson Decay & The Heavy Quark Expansion

7. c u d b  c d u b W b  c Decay Still need QCD corrections Perturbative Hard gluon (Short distance)  s Non-Perturbative Soft gluon (Long distance) , 1 & 2 B  D e W e ]D]D c B[B[ b Just right? W bc u d ]] ]D]DB[B[ B  D  Very difficult

8. Not always 3-body Gluons in final state. Quark Motion Rate of decay modified by motion of quark in B meson. b quark lives longer. ~p 2 /E 2 ~ (.5/5) 2 Challenges: Quark Hidden We know M B well. m b not so well. Semileptonic Rate Goal Rate of semileptonic decay of beauty quark  CKM element(s)

9.  HQET+OPE allows any inclusive observable to be written as a double expansion in powers of  s and 1/M B : HQET O(1/M)  energy of light degrees of freedom (M B ~ m b +  ) O(1/M 2 )  1 -momentum squared of b quark  2 hyperfine splitting (known from B/B * and D/D *  M) O(1/M 3 )             ~(.5 GeV) 3 from dimensional considerations   sl = |V cb | 2 ( A(  s,,  o  s 2 )+B(  s )  /M B + C 1 /M B 2 +… )   1 combined with the  sl measurements  better |V cb | 2

10. Semileptonic Decay Width   sl (B Meson Semileptonic Decay Width) –Calculated from B meson branching fraction and lifetime measurements (CLEO, CDF, BaBar, Belle …) –It is the first approximation to the b quarks decay width Free quark decay width b quark motion – increased b lifetime  M hyperfine splitting

11. Observables B  X s  : 1 st and 2 nd moments of Photon energy B  X c : 1 st and 2 nd moments of hadronic recoil mass B  X c : lepton energy moments

12. Moments How much is there? (area) How wide is it? (width) Where is it? (mean)

13. b  s   Moments u, c, t

14. b  s   Moments u, c, t

15. b  s   Moments radiative tail u, c, t

16. Hadronic Mass Moments  Monte Carlo model shown  Measure moments of recoil mass  D and D* well measured  Need to determine contribution to moments from high mass components  Details of resonances not included in parton level calculation 2 B  D B  D* B  D** B  D  B  X c

17. Strategy  At least two inclusive measurements needed in addition to the B branching fraction and B lifetime in order to extract V cb.  Measure:  1 st and 2 nd moments of Photon energy (b  s  )  1 st and 2 nd moments of hadronic recoil mass (B  X c )  lepton energy moments (B  X c )  Many measurements are needed to verify  Convergence of Expressions  Quark-Hadron Duality

18. CESR/CLEO

19. LEPP Cornell Electron-positron Storage Ring  ~ ¾ km circumference  e + e - collisions  E beam : 1.5-5.6 GeV  Most data collected near  (4S) resonance.

20. Operating Energies  2/3 data collected ON  (4S)  e + e -   (4S)  BB (  ~ 1.0 nb)  e + e -  qq (  ~ 3.0 nb)  1/3 data collected OFF  60 MeV below Resonance  Continuum only  Almost perfect qq background sample  (4S)

21. CLEO Photons: XtalCal (res=1.8%) Electrons: XtalCal, Tracking Muons: MuCh, Tracking p K  e  : ToF+DeDx

22. Measurements I Moments & V cb

23. Hadronic  Mass Moments  Want from B  X c   but can not use hadronic daughters  Reconstruct mass with B,, and four-vectors X smallunknown XcXc  Lepton: Select events with very high lepton momentum (1.5 GeV)  above lower momentum secondaries (eg D decays)  Neutrino: Use all observed energy-momentum to calculate neutrino 4-vector  fakes arise from non-interacting neutrals (K long, secondary neutrinos, neutrons)

24. –Fit spectrum with B  D B  D * B  X H (various models for X H ) –Find moments of true M X 2 spectrum Hadronic Mass Moments PRL 87 251808, 2001

25. Hadronic Mass Moments If we believed the second moment expansion, we could get V cb from this Use first moments from b  s  and hadronic b  c instead...

26. Photon Energy Moments  Always require high energy photon 2.0 < E  < 2.7 GeV |cos  | < 0.7  Naïve strategy: Measure E  spectrum for ON and OFF resonance and subtract  But, must suppress huge continuum background! [veto is not enough]      and    Three attacks:  Shape analysis  Pseudoreconstruction  Leptons

27. Photon Energy Moments

31. Hadronic Mass and Photon Energy CLEO PRL 87 251807, 2001

32. V cb In MS scheme, at order 1/M B 3 and  s 2  o  = 0.35 + 0.07 + 0.10 GeV 1 = -.236 + 0.071 + 0.078 GeV 2 |V cb |=(4.04 + 0.09 + 0.05 + 0.08) 10 -2  sl , 1 Theory

33. Lepton Energy Moments in B  X l  Muons  Electrons Unfolded Lepton Energy Spectrum for leptons from B  X l R 0 = 0.6187+0.0014 +0.0016 R 1 = 1.7810+0.0007+0.0009 GeV CLEO Measure lepton energy From energy spectrum: PR D67 072001, 2003

34. Consistency Among Observables   and  ellipse extracted from 1 st moment of B  X s  photon energy spectrum and 1 st moment of hadronic mass 2 distribution( B  X c l ). We use the HQET equations in MS scheme at order 1/M B 3 and  s 2  o.  Expressions:  A. Falk, M. Luke, M. Savage, Z. Ligeti, A. Manohar, M. Wise, C. Bauer  The red and black curves are derived from the new CLEO results for B  X l lepton energy moments.  Expressions:  M.Gremm, A. Kapustin, Z. Ligeti and M. Wise, I. Stewart and I. Bigi, N.Uraltsev, A. Vainshtein  Gray band represents total uncertainty for the 2 nd moment of photon energy spectrum. CLEO

35. Consistency Among Experiments CLEO B A B AR Preliminary CLEO OPE (Falk, Luke) , 1 free param. OPE (Falk, Luke) , 1 using CLEOs photon energy moment.

36. Interpretation of Data B A B AR Preliminary CLEO OPE (Falk, Luke) , 1 free param. OPE (Falk, Luke) , 1 using CLEOs photon energy moment.  Expect average hadronic mass to increase with lowering lepton momentum cut  Increase observed much larger than expected  Suspects Heavy Quark Expansion BaBar measurement(s) CLEO measurement(s) Repeat BaBar’s measurement (underway) Suspect photon energy moments Did we miss a contribution at low photon energy? Need to have missed a strange quark state with high mass.  Baryon (our Neural Networks were never informed of this possibility)

37. Mechanism for baryon production in B decay Internal W EmissionExternal W Emission Di-quark popping providing a mechanism for baryon production in B semileptonic decays will also allow for the same in B radiative decays.

38. Limits on Baryon Production (External W Emission) Br(B  X s  <3.8 x 10 -5 90% CL (E  >2.0 GeV, X s containingBaryons ) PR D68:011102, 2003 Semileptonic Case Radiative Case Br(B  pe - X)< 5.9 x 10 -4 90% CL PR D68:012004, 2003 Strong Limit but not enough.

39. Recent Moments Results  Current standing from CLEO and BaBar. ( Extrapolates well to DELPHI measurement )  Good agreement between analyses.  Tolerable agreement with theory.

40. Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke & Manohar |V cb |=(4.08 + 0.09) 10 -2 PR D67:054012, 2003

41. Measurements II V ub

42. |V ub | from Lepton Endpoint (using b  s  )  |V ub | from b  u –We measure the endpoint yield –Large extrapolation to obtain |V ub | –High E cut leads to theoretical difficulties (we probe the part of spectrum most influenced by fermi momentum)  GOAL: Use b  s   to understand Fermi momentum and apply to b  u  for improved measurement of |V ub | Kagan-Neubert DeFazio-Neubert

43. Convolute with light cone shape function. b  s  (parton level) B  X s  (hadron level) B  lightquark shape function, SAME (to lowest order in  QCD /m b ) for b  s   B  X s  and b  u l  B  X u l. b  u l (parton level ) B  X u l (hadron level) Fraction of b  u spectrum above 2.2 is 0.13 ± 0.03

44.  Method for partial inclusion of subleading corrections: Neubert Published With subleading corrections  Subleading corrections large C. Bauer, M. Luke, T. Mannel A. Leibovich, Z. Ligeti, M. Wise M.B. Voloshin |V ub | from Lepton Endpoint (using b  s  ) |V ub | = (4.08 + 0.34 + 0.44 + 0.16 + 0.24)10-3 The 1 st two errors are from experiment and 2 nd from theory PRL 88 231803 2002 CLEO

45. Summary

46.  V cb :  Bound state corrections to the semileptonic width, predicted by HQET and measured by a number moments analyses have permitted the extraction of V cb to a level of a few %.  The precision has a minimal impact on  constrains but we can view as stringest test of HQE methods used for V ub.  Many new measurements now available (some overlapping)  Recent measurements of hadronic mass moments with lower cut on lepton momentum. More inclusive. Hints at trend that may be incompatible with theory but experimental and theoretical uncertainties are still large.  CLEO: Soon to publish lepton moments at lower lepton energy cut.  Enough data available for a global fit (with correlations properly accounted for). Need more input from theory on best method of including theory uncertainties.

47. Summary  V ub :  Important to reduce uncertainties for test of standard model  The photon energy spectrum in b  s  provides a quantitative model for the bound state effects in b  u l   This approach has not yet reached its full potential  We expect improved measurements from B factories (in progress at CLEO).  Current work is to improve shape extraction particulalry at low photon energy  The method does require additional theoretical refinements.  Can theory calculate differences in the b  light quark processes or provide reliable estimate of this difference.

49. Improved Photon Energy Spectrum Original analysis optimized for Br Measurement. Motivation for improving spectrum particularly in the low photon energy region. Backgrounds are numerous in low energy region.  0      electrons (with no track matching) anti-neutrons K Long -More efficient  0 /  veto -CC simulation of non-photon showers constrained by data Calorimeter Lateral Shape

50. Improved Photon Energy Spectrum Repeat entire analysis without a cut on the Calorimeter cluster shape. MC does not model data well either due to incorrect simulation of shower shape or wrong Klong and anti-neutron rates.

51. Improved Photon Energy Spectrum Require enriched anti-neutron sample Select events with L baryon if no anti-proton found look at “photons” in the event. The antineutron calorimeter response is extracted from this sample.

52. B  X l with Neutrino Reconstruction  Neutrino four-momentum inferred from hermeticity of detector.  Maximum likelihood fit over full three dimensional decay distribution  Contributions from B  X c l  (D,D*,D**and NR) and B  X u l  |V ub | =(4.05 + 0.18 + 0.58 + 0.25 + 0.21 + 0.56) 10 -3 stat syst b->c b->u theory model model Cos  w l q 2 M X 2 M X 2 <2.25 GeV 2 Q 2 >11 GeV 2 CLEO CONF 02-09 ICHP02 ABS933 Preliminary M X 2 <2.25 GeV 2 Q 2 >11 GeV 2

53. Inclusive B Decays CLEO II&IIV 37 M hadronic 9.7 M BB Pairs 3.8 M B   X c 34 k B  X u 7 k B  X s  Observables

54. Consistency Across Schemes- 1S Mass v. MS   and  ellipse extracted from 1 st moment of B  X s  photon energy spectrum and 1 st moment of hadronic mass 2 distribution ( B  X c l ). We use the HQET equations in 1S scheme at order 1/M B 3 and  s 2  o. 1S Expressions(recent): C. Bauer, M. Trott (hep- ph/0205039) C. Bauer, A. Manohar, Z.Ligeti and M. Luke private communication In 1S mass scheme, at order 1/M B 3 and  s 2  o |V cb |=(4.05 + 0.09 + 0.04 + 0.10) 10 -2 (recall MS: |V cb |=(4.04 + 0.09 + 0.05 + 0.08) 10 -2 )

55. Vcb Results

57. BaBar at ICHEP B A B AR Preliminary CLEO OPE (Falk, Luke) , 1 free param. OPE (Falk, Luke) , 1 using CLEOs photon energy moment. DELPHI 0.0 0.4 0.534 Lepton Cut (GeV)

58. Inclusive? CLEO moments analysis reduce background with cuts on variables of interest (but no explicit mass cut on mass moments) semileptonic: e.g. leptons from charm decay radiative: eg: photons from  0 decay model dependence of course but even more fundamental concerns Assumption that the average value of observable is the same at the hadron and quark level relies on a truly inclusive analysis.  Must lower cuts in all analyses. BaBar (and later CLEO) measures mass moments with various lepton momentum cuts. Lower lepton momentum correlates with higher mass hadronic state. Moments expected to increase but how much? Preliminary results indicate larger increases than expected if one uses the HQET parameter (  ) derived from photon energy spectrum.

59. MomentCLEODELPHI(prelim) B A B AR(prelim) 0.251±0.023±0.062 (E l >1.5GeV)0.534±0.041±0.074 Later ) 2 >.576±0.048±0.163 (E l > 1.5GeV)1.23±0.16±0.15 ) 3 >2.97±0.67±0.48 <E   2.346  0.032  0.011  (E    E   ) 2  0.0226  0.0066  0.0020 <E  1.7810+0.0007+0.0009 (E l > 1.5 GeV)1.383  0.012  0.009  (E   E  ) 2  0.192  0.005  0.010  (E   E  ) 3  0.029  0.005  0.005 R0R0 0.6187+0.0014 +0.0016 (E l > 1.5 GeV) Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke & Manohar

60. Overview Unitarity Algebra 0,0  1,0   CP

61. Moments Summary  CLEO has measured six moments, two each from 1) the photon energy distribution in B  X s  2) the hadronic mass 2 distribution in B  X c l 3) most recently the lepton energy spectrum in B  X c l  The allowed values for HQET parameters  and 1 are in agreement for all measurements.  |V cb | extracted at the level of 3%