1. 1 Inclusive B Decays - Spectra, Moments and CKM Matrix Elements Presented by Daniel Cronin-Hennessy University of Rochester (CLEO Collaboration) ICHEP July 2002 Amsterdam, Ne

2. 2 Outline  Motivation for measuring moments of various spectra.  Measurements:  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  |V cb |  Moments Summary  More from E  spectrum and lepton energy endpoint ( |V ub | )  Exclusive decays and CKM matrix extraction  Using more than one kinematic variable ( B  X l ) at a time.  Summary

3. 3 Motivation  Extremely naïve model for B  X s   Two body decay ( b  s  ) yields photon energy spike at half the b quark mass. 1 st moment = m b /2 2 nd moment = 0  A better model (spectator)  Parameterizes B meson structure with average masses (1 st ) and fermi momentum (2 nd ). Some include QCD.  A theory (HQET)  Expressions for observables in increasing powers of 1/M B GOOD  Introduces increasing number of non- perturbative parameters – NOT SO GOOD  1/M B 1, 2 1/M 2 B       1/M 3 B

4. 4 Motivation  Similar expressions for the moments of M X 2 and E  spectra.  The 1/M 3 B parameters are estimated from dimensional considerations to be (0.5GeV) 3.  Extracting  and  requires two measurements  These are used to extract |V cb | HQET plus OPE allows inclusive observables to be written as double expansions in powers of  s and 1/M B. To order  o  2 s and 1/M 3 B in the scheme.

5. 5 Hadronic Mass and Photon Energy 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 PRL 87 251807 ’01 PRL 87 251808 ’01

6. 6 Lepton Energy Moments (CLEO Preliminary )  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 CONF 02-10 ICHEP02 ABS932 M.Gremm, A. Kapustin, Z. Ligeti M. Wise, I. Stewart CLEO Preliminary

7. 7 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 Preliminary

8. 8 Consistency Across Schemes   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 )

9. 9 Moments Summary  CLEO has measured six moments, two each from 1) the photon energy distribution in B  X s  events 2) the hadronic mass2 distribution in B  X c l events and 3) most recently the lepton energy spectrum in B  X c l  events.  The allowed bands for HQET parameters  and 1 are in agreement for all measurements.  Additionally, CLEO has used the HQET expressions from the 1S mass renormalization scheme and has extracted a value of |V cb | in excellent agreement with that derived from the MS scheme.  There remains some ambiguity on the treatment of uncertainties due to the higher order HQET terms.

10. 10 |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

11. 11 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

12. 12  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  ) |Vub| = (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

13. 13 |V ub | from B ( B   l ) with Reduced Model Dependence  Use missing four-momentum in full B reconstruction.  Sample of 9.7 M BB pairs.  Sample size allows parsing into 3 bins of q 2 ( reduces dependence on modeling of q 2 shape) CLEO CONF 02-09 ICHP02 ABS931

14. 14  Three b  u models of q 2 distribution.  Averaging detection efficiency over smaller q 2 range => smaller variation in fits to width.  Shown are the best fits to d  /dq 2 for SPD, B all’01 & ISGW2 Branching fractions in restricted q 2 bins

15. 15 | V ub | from B ( B   l ) with Reduced Model Dependence B ( B   l )= (1.376 + 0.180 + 0.008 + 0.102 + 0.021)10 -4 stat syst ff  ff  model |V ub | = (3.32 + 0.21 + 0.12 + 0.07)10 -3 +0.17 -0.19 +0.116 -0.135 Preliminary +0.55 -0.39

16. 16 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 model theory 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

17. 17 Summary  CLEO has measured the yield of B  X u l  above the lepton energy endpoint of B  X c l  The total rate is extrapolated by using our photon energy spectrum in b  s  for which the spectrum is known over most of the kinematically allowed range. |V ub | is extracted from the total rate. Additional subleading correction are currently being investigated.  CLEO presented an updated B   l Branching ratio and a new (exclusive) extraction of |V ub |.  CLEO has also performed a log likelihood fit to the B  X l in three independent kinematic variable. A preliminary value of |V ub | was presented. The weight of events in the endpoint region is currently not fully understood – do not average the inclusive results.

18. 18 Backup I