Review of QCD Introduction to HQET Applications Conclusion

1. Introduction to HQET (Heavy Quark Effective Theory) Yoon yeowoong(윤여웅) Yonsei Univ. 2004.04.30 • Review of QCD • Introduction to HQET • Applications • Conclusion Paper: M.Neubert PRPL 245,256(1994)

2. Confinement Barrier Color charge Distance from the bare quark color chage High Energy probe Asymtotic freedom 1 fermi • Introduction to HQET - Review of QCD Bjorken scaling : structure function only depend on . (1969) → Point-like structure inside proton, Asymtotic freedom → Non-Abelian gauge field theory. Yang, Mills → Asymtotic freedom in Non-Abelian gauge field theory. t’Hooft(1973) → Gell-Mann propose extra symmetry of non-Abelian color symmetry(1972) QCD was born → Quark confinement( Only colorless states are physically observable) is explained in QCD by infrared divergences due to the massless gluons

3. Introduction to HQET - Review of QCD Summary of Non Abelian Gauge theory SU(3)

4. q q Q Q • Introduction to HQET - physical picture Heavy Quark : m Q > ΛQCD Heavy Quark limit : mQ→∞ Heavy Quark + light quark system Comptom wavelength of Q : λQ~ To resolve the quantum number of Heavy quark, need a hard probe with “Brown muck” light quark q cannot see the quantum numbers of Heavy Quark

5. v v • Introduction to HQET - physical picture The configuration light Degree of freedoms with different heavy quark flavor, spin system of hadron does not change if the velocity of heave quark is same. We can regard heavy quark velocity as conserved quantity Heavy Quark velocity ≒ Meson velocity Momentum transfer ~ ΛQCD ⇒ velocity change ~ ΛQCD /mQ ~ 0 Therefore this picture gives spin – flavor symmetry in QCD under mQ→∞ limit. Nh heavy quark flavor → SU(2Nh) spin-flavor symmetry group It provide the relations between the properties of hadrons with different flavor and spin of heavy quark. Such as B, D, B*,D*, ΛbΛc

6. Introduction to HQET - details with elementary field theory Heavy quark momentum almost on-shell Divide quark field by large and small component respectively QCD Lagrangian where

7. Introduction to HQET - details with elementary field theory On a classical level, DOF of H v can be eliminated by EOM of QCD Variation of Lagrangian with respect to Considering order of 1/mQ (n=0) And using the relation

8. Chromo-magnetic momentum interaction (Halzen Ex6.2) • Introduction to HQET - details with elementary field theory It can be shown by Kinetic term From residual momentum k PQ=mQv+k hv=eimQv·xP+Qv Inserting gluon field strength tensor and, Then the effective Lagrangian of order 1/mQ is

9. Introduction to HQET - details with elementary field theory Now we consider heavy quark limit mQ→∞ 1. It has spin symmetry Associated group is SU(2) symmetry group under which Leff is invariant An infinitesimal SU(2) transformation On-Shell condition satisfied

10. Introduction to HQET - details with elementary field theory 2. It has flavor symmetry When there are Nh heavy quark flavor Because this Lagrangian do not contain heavy quark mass, It is invariant under rotations in flavor space Combined with spin symmetry the effective Lagrangian belong to SU(2Nh) symmetry group.

11. Introduction to HQET - details with elementary field theory Now consider Feynman rules Feynman propagator, and vertex factor can be derived by effective Lagrangian Propagator Vertex It can be also derived by taking the appropriate limit of the QCD Feynman rules

12. Introduction to HQET - details with elementary field theory For the heavy quark gluon vertex Using the relation Therefore vertex factor in Heavy quark limit become

13. Application - Spectroscopy Strong Interaction dynamics is independent of the spin and mass of the heavy quark by heavy quark symmetry. Therefore hadronic states can be classified by the quantum number of the light DOF such as flavor, spin, parity, etc. Spin-flavor symmetry in HQET predict some relations of properties of hadron states, typically mass spectrum of different Hadrons states

14. Application - Spectroscopy 1. Ground state mesons degenerate states Experimentally Need a hyperfine correction of order 1/mQ Quite small as expected So we can expect

15. Application - Spectroscopy 2. Excited state mesons degenerate states It is small mass splitting supporting our assertion One can expect also 3. Excitation energy

16. Hadronic matrix element parameterized by several form factors. • Application - Weak decay form factors Physical picture of weak decay

17. q q q q Q Q’ Q Q’ • Application - Weak decay form factors Kinematical picture Maximum q2=(mM’-mM)2 ; minimum w=1 Zero recoil Q Q’ Minimum q2=0 ; maximum w

18. Application - Weak decay form factors Typical hadronic matrix element M.Wirbel ZPHY C29,637(1985)

19. Why not • Application - Weak decay form factors Now in HQET Is called Isgur-Wise function Using flavor symmetry Normalized at zero recoil as explained by following For equal velocity is conserved current

20. Application - Weak decay form factors Using spin symmetry In the rest frame of the final state meson

21. HQET Typical • Application - Weak decay form factors Summarize parameterization

22. Application - Weak decay form factors Relations between form factors and Isgur-Wise function.

23. Application - Weak decay form factors

24. Conclusion - more study • Renormalization group equation • Model independent Vcb • Inclusive decay with HQET • Study hard !