2. Vcb and Vub Determinations Changhao Jin University of Melbourne BEACH 2002, Vancouver

3. June 26, 2002Changhao Jin2 How to measure |V cb | and |V ub |? Leptonic B decays Semileptonic B decays Nonleptonic B decays I will talk about inclusive semileptonic B decays.

4. June 26, 2002Changhao Jin3 observable=|V c(u)b | 2 T Routine observable branching fraction,lifetime Theory-motivated observable “theoretically clean”, “model-independent” in some sense theory Theory may be involved in it.

5. June 26, 2002Changhao Jin4 Theory of inclusive semileptonic B decays Hadronic tensor Five structure functions W 1-5, a priori independent, incorporate non-perturbative QCD effects.

6. June 26, 2002Changhao Jin5 Light-Cone (LC) Approach M B >>  QCD Starting point: light-cone expansion At leading twist, structure functions are related to a single universal distribution function: y 2  0

7. June 26, 2002Changhao Jin6 What is known about the distribution function? Normalization because b-quark number conservation Shape Free quark limit Mean Variance The distribution function is sharply peaked around m b /M B. Narrow width   QCD /M B

8. June 26, 2002Changhao Jin7 Comparison with heavy quark expansion (HQE) approach Starting point HQE: local operator product expansion (y  0) LC: non-local light-cone expansion (y 2  0)

9. June 26, 2002Changhao Jin8 Comparison with HQE (continued) Assumption of quark-hadron duality HQE: Yes. Using quark phase space LC: No. Using hadron phase space Singularity in lepton energy spectrum HQE: Yes LC: No Distribution function HQE: partial resummation of heavy quark expansion  a different distribution function (“shape function”) ~  QCD /m b correction to leading contribution in terms of shape function LC: ~ (  QCD /M B ) 2 correction to leading contribution in terms of distribution function f(  )

10. June 26, 2002Changhao Jin9 A manifestation of quark-hadron duality violation HQE uses quark phase space LC uses hadron phase space HQE misses rate due to phase space extension B  X u l

11. June 26, 2002Changhao Jin10 Significant duality violation in HQE Important to include phase space effect Non-perturbative QCD corrections change sign For B  X c l For B  X u l

12. June 26, 2002Changhao Jin11 Conventional methods Routine observables: Problems in theoretical calculations of  c and  u HQE: quark-hadron duality LC: detailed shape of distribution function unknown

13. June 26, 2002Changhao Jin12 Particular problem in |V ub | determination Kinematic cutFraction of events E l > (M B 2 -M D 2 )/(2M B )  10% q2 > (M B -M D ) 2  20% M X < M D  80% Very large B  X c l background Use kinematic cut to suppress background M X cut is most efficient  small extrapolation

14. June 26, 2002Changhao Jin13 Better method for |V ub | Model-independent Without relying on quark-hadron duality No free parameters (such as m b ) No perturbative QCD corrections b-quark number conservation  semileptonic sum rule observabl e Advantages:

15. June 26, 2002Changhao Jin14 Apply cut M X < M D (or other realistic cuts) Measure weighted spectrum  u -5 d  /d  u Extrapolate it to entire phase space to obtain integral S Determine |V ub | from observable S using theoretically clean relationship (sum rule) between them However, large B  X c l background Strategy:  u spectrum

16. June 26, 2002Changhao Jin15 Theoretical uncertainties Higher twist correction to the sum rule: ~ 1% error on |V ub | Shape of the distribution function for extrapolation: ~ 6% error on |V ub | Improvements: Constraints from experimental data (distribution,moment) Universal distribution function from B  X s  Lattice QCD

17. June 26, 2002Changhao Jin16 Summary |V cb | from inclusive semileptonic width  (B  X c l ) can be more reliable and accurate if fundamental uncertainty due to assumption of quark-hadron duality is avoided and phase space effect is included. This is achievable with light-cone approach to inclusive B decays. More precise |V ub | can be extracted using semileptonic sum rule.