1. Inclusive B Decays - Spectra, Moments and CKM Matrix Elements Presented by Daniel Cronin-Hennessy University of Rochester (CLEO Collaboration) Dec 16, 2003

2. Outline  Overview of CESR/CLEO  The B Meson and HQET  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. CESR/CLEO

4. 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.

5. 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)

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

7. Overview: The Standard Model & The Heavy Quark Expansion

8. Overview  CKM matrix relates quark mass eigenstates to weak eigenstates  Fundamental Standard Model parameters – must be measured.  Measurement of these electro-weak parameters complicated by QCD (we observe hadrons not quarks)  The formalism that provides a viable framework for extracting CKM elements is Heavy Quark Effective Theory HQET.

9. Overview  CKM matrix relates quark mass eigenstates to weak eigenstates  Fundamental Standard Model parameters – must be measured.  Measurement of these electro-weak parameters complicated by QCD (we observe hadrons not quarks)  The formalism that provides a viable framework for extracting CKM elements is Heavy Quark Effective Theory HQET.

10. 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

11.  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 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

12. 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 : Semileptonic Width (  sl ) B  X c : lepton energy moments

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 Quark  Hadron 2 B  D B  D* B  D** B  D  B  X c

17. 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 P fermi  M hyperfine splitting

18. 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

19. Measurements I Moments & V cb

20. 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)

21. –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

22. 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...

23. 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

24. Photon Energy Moments

28. Hadronic Mass and Photon Energy CLEO

29. 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

30. 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:

31. 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.  MS 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.  MS Expressions: M.Gremm, A. Kapustin, Z. Ligeti and M. Wise, I. Stewart (moments) and I. Bigi, N.Uraltsev, A. Vainshtein(width)  Gray band represents total uncertainty for the 2 nd moment of photon energy spectrum. CLEO

32. 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%

33. 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

34. 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.

35. Mechanism for baryon production in B decay (not completely understood) 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.

36. Limits on Baryon Production Search Limits: Br(B  X s  X s (containingBaryons)) 2.0 GeV) 90% CL Semileptonic Case Radiative Case Search Limits: Br(B  pe - )< 5.9 x 10 -4 90% CL

37. Recent Moments Results  Current standing from CLEO and BaBar. ( Extrapolates well to DELPHI measurement )  Good agreement between analyses.  Tolerable agreement with theory.  Are we living on borrowed time?

38. Measurements II V ub

39. |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

40. 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

41.  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 |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 ‘02 CLEO

42. Conclusions

43. Summary  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.  Several experiments contributing to the body moments knowledge. Endpoint |V ub | = (4.08 + 0.63) 10 -3 Moments |V cb | = (4.04 + 0.13) 10 -2  V ub :  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).  The method does require additional theoretical refinements.