Vcb and Vub Determinations

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

2. How to measure |Vcb| and |Vub|? • Leptonic B decays • Semileptonic B decays • Nonleptonic B decays I will talk about inclusive semileptonic B decays. Changhao Jin

3. observable=|Vc(u)b|2 T theory Theory may be involved in it. • Routine observable • branching fraction,lifetime • Theory-motivated observable • “theoretically clean”, “model-independent” in some sense Changhao Jin

4. Theory of inclusive semileptonic B decays Hadronic tensor Five structure functions W1-5, a priori independent, incorporate non-perturbative QCD effects. Changhao Jin

5. Light-Cone (LC) Approach Starting point: light-cone expansion y2 0 MB>>QCD At leading twist, structure functions are related to a single universal distribution function: Changhao Jin

6. 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 mb/MB. Narrow width  QCD/MB Changhao Jin

7. Comparison with heavy quark expansion (HQE) approach Starting point • HQE: local operator product expansion (y0) • LC: non-local light-cone expansion (y20) Changhao Jin

8. 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/mb correction to leading contribution in terms of shape function • LC: ~ (QCD/MB)2 correction to leading contribution in terms of distribution function f() Changhao Jin

9. HQE uses quark phase space LC uses hadron phase space HQE misses rate due to phase space extension A manifestation of quark-hadron duality violation B  Xul Changhao Jin

10. For B  Xcl • Significant duality violation in HQE • Important to include phase space effect • Non-perturbative QCD corrections change sign For B  Xul Changhao Jin

11. Conventional methods Routine observables: • Problems in theoretical calculations of c and u • HQE: quark-hadron duality • LC: detailed shape of distribution function unknown Changhao Jin

12. Particular problem in |Vub| determination Very large B  Xcl background Use kinematic cut to suppress background MX cut is most efficient  small extrapolation Changhao Jin

13. Better method for |Vub| b-quark number conservation  semileptonic sumrule observable Advantages: • Model-independent • Without relying on quark-hadron duality • No free parameters (such as mb) • No perturbative QCD corrections Changhao Jin

14. However, large B  Xcl backgroundStrategy: • Apply cut MX < MD (or other realistic cuts) • Measure weighted spectrum u-5d/du • Extrapolate it to entire phase space to obtain integral S • Determine |Vub| from observable S using theoretically clean relationship (sum rule) between them uspectrum Changhao Jin

15. Theoretical uncertainties • Higher twist correction to the sum rule: ~ 1% error on |Vub| • Shape of the distribution function for extrapolation: ~ 6% error on |Vub| • Improvements: • Constraints from experimental data (distribution,moment) • Universal distribution function from B  Xs • Lattice QCD Changhao Jin

16. Summary • |Vcb| from inclusive semileptonic width (B  Xcl) 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 |Vub| can be extracted using semileptonic sum rule. Changhao Jin