Heavy Quark Effective Field Theory -- An Effective Theory in Large Components of Heavy Quarks

1. Heavy Quark Effective Field Theory--An Effective Theory in Large Components of Heavy Quarks Y. L. Wu, Y. A. Yan, M. Zhong,W. Y. Wang (speaker) KITPC Beijing, July 1, 2008

2. HQS and HQET • HQEFT as a Large Component QCD motivation and derivation on some comments to HQEFT weak matrix elements and Luke’s Theorem differences between HQET and HQEFT some features of HQEFT • |Vcb| extraction in HQEFT • Heavy-to-Light Decays and |Vub| 5. B Decays to Excited Heavy Mesons 6. Summary

3. 1. HQS and HQET • Heavy quark symmetry In the limit the characters of the heavy hadron are irrelevant to the heavy quark spin and flavor. Momentum of the heavy quark: HQS is only an approximate symmetry ! For many processes, the finite mass corrections should be considered carefully .

4. The starting point of HQET is separating the quark field into large and small component fields • Heavy quark effective theory (HQET) HQET Lagrangian: Quark and antiquark fields are completely decoupled at the beginning of deriving HQET !

5. 2. HQEFT as a Large Component QCD Y. L. Wu, Mod. Phys. Lett. A 8, 819 (1993). Motivation : Particles and antiparticles can not decouple completely in finite mass case. When consider 1/mQ corrections, neglecting particle-antiparticle coupling effects may affect the precision of calculation. Integrate in the higher scale physics to get effective theories

6. Derivation For field Q in QCD, with Taking v=(1,0,0,0), one has large components small components

7. To get an effective field theory for heavy hadrons containing one heavy quark: Comparison:

8. Integrate out the small components, with

9. For making 1/mQ expansion, it is useful to introduce Integrate out the heavy antiquark fields,

10. Some comments on this Lagrangian • Could the above Lagrangian recover the case for the free quark fields ? • How to perform the power counting ? For a free quark on mass-shell, taking v=(1,0,0,0) for simplicity, In the coordinate space,

11. In the coordinate space, Substituting this into the Lagrangian, one has ------ self-consistent with the on mass-shell condition

12. HQE in the Large component QCD of heavy quarks Power counting in HQE depends on the physical state under consideration. 1. Nonrelativistic case (such as a heavy-heavy bound state) Taking v=(1,0,0,0), one has which does result in a NRQCD.

13. 2. Slightly off mass-shell case( such as a hadron containing a single heavy quark ) and for the operators ---Operators corresponding to longitudinal and transverse momenta are taken to be at the same order in HQE. So, -------- differs from the usual HQET.

14. HQE of Weak Matrix Elements (Transitions between heavy hadrons as example)

15. Nomalization of states In the full theory, one has the conventional normalization: In the effective theory, it is better to introduce an effective hadron state exhibiting a manifest spin-flavor symmetry: Which should be related to |H〉by with ----- a heavy flavor-independent binding energy that reflects the effects of the light degrees of freedom in the heavy hadron.

16. Form factors and wave functions (heavy hadrons as examples)

17. Comparison HQET HQEFT Only operators with even powers of • Fewer independent functions (parameters) are needed in HQEFT. • It is not surprising to get up to O(1/mQ2) in the new formulation of HQEFT.

18. Some features of HQEFT • No difference between HQEFT and HQET in limit • Effective Lagrangian automatically preserves the velocity reparametrization invariance as well as Lorentz invariance without the need of summing over the velocity. • Luke’s theorem naturally holds in HQEFT, without the need of imposing the on-shell condition • Unlike the usual HQET, one has in HQEFT • Relations between hadron masses and zero recoil values of wave functions

19. Funtions (parameters) at 1/mQ order : • Fewer independent functions (parameters) are needed in the HQEFT than in the usual HQET. Weak transition wave functions Decay constants HQET HQEFT

20. 3. |Vcb| Extraction from B decays • Exclusive decays where with

21. HQET: B→D*lv is more favorable for |Vcb| extraction, because its decay rate receives no corrections of 1/mQ order. • HQEFT: h-(ω)=0, both the differential decay rates of channels B→D*lv B→D*lv receive no order 1/mQ corrections. • Relations exist between meson masses and transition • wave functions :

22. Heavy quark as a dressed particle: PH=mQv+k+k’ with k’ being the momentum depending on the heavy flavor and suppressed by the inverse of the heavy quark mass. • Inclusive decays Then the B→Xclν decay rate is found to be with • Effects of light degrees of freedom are explicitly taken into account in the picture of dressed heavy quark • 1/mQ order contribution vanishes, and order contributes only -0.7~5% correction • Dressed quark mass instead of mb and separately

23. |Vcb| :

24. Important for extraction of Vub, Vcs ,Vcd , Vts 4. Heavy-to-Light Decays and |Vub|

25. HQS does not reduce the number of independent form factors needed for an individual semileptonic decay. • HQS provides relations between different decay channels. • HQS provides relations between penguin form factors and semileptonic ones.

31. B→π(ρ)lν to NLO and |Vub| extraction Including 1/mQ correction: NLO: inclusive B decays

32. 5. B Decays to Excited Heavy Mesons

34. HQET: The magnitudes of 1/mQ corrections might be comparable with or even several times of the leading order results .[110-113] • HQEFT: Both the LO and NLO wave functions are kinematically suppressed near zero recoil. The 1/mQ corrections are not likely to be as large as the leading order contributions.

36. An effective theory with heavy quark-antiquark coupling effects “integrated in”. • Favorable features • Measurable effects from heavy quark-antiquark couplings 6. Summary

37. Thank You !