Heavy hadron phenomenology on light front

1. Heavy hadron phenomenology on light front Zheng-Tao Wei Nankai University 2012年两岸粒子物理与宇宙学 研讨会，重庆，5.7—5.12。

2. Introduction • Light front QCD and quark model • Phenomenologies: • 1. ηb • 2. Λb decay • 3. fDs puzzle • Summary

3. Introduction • The theory to describe the strong interaction is • quantum chromodynamics (QCD). It is a beautiful • but difficult theory. • Asymptotic freedom: weak coupling at short distances, • perturbation theory, 2004 Nobel prize • Confinement: non-perturbative at long distance, • hadron structure, spectrum, chiral symmetry breaking…

4. Non-perturbative methods: 1. Lattice 2. Effective field theories 3. QCD sum rules 4. Light-fone method 5. AdS/QCD 6. …

5. Light front method • For a relativistic Hamiltonian system, the definition of time • is not unique. There are three forms. Dirac’s three forms of Hamiltonian dynamics (1949)

6. Why light-cone framework? 1. A relativistic particle looks like non-relativistic if viewed on the light-cone. 2. Simple vacuum: vacuum is trivial. k+=k0+k3>0 The LC framework is the most possible way to reconcile the high energy parton model and the non-relativistic constitute quark model.

8. Advantage of LF framework • LF Fock space expansion provides a convenient description • of a hadron in terms of the fundamental quark and gluon • degrees of freedom. • The LF wave functions is Lorentz invariant. Ψ(xi, k┴i ) is independent of the bound state momentum. • The vacuum state is simple, and trivial if no zero-modes. • Only dynamical degrees of freedom are remained. for quark: two-component ξ, for gluon: only transverse components A┴. Disadvantage • In perturbation theory, LFQCD provides the equivalent results • as the covariant form but in a complicated way. • It’s difficult to solve the LF wave function from the first principle.

9. LF Fock space expansion • LF bound state equation It is impossible to solve the equation for all Fock states. Some theorists assumes valence quark dominance and a linear potential to solve the equation.

10. Basic assumptions of LF quark model • Valence quark contribution dominates. • The quark mass is constitute mass which absorbs • some dynamic effects. • LF wave functions are Gaussian. Choose Gaussian-type wave function The parameter β determines the confinement scale.

11. Melosh rotation

12. The pseudoscalar meson decay constant is with • The physical form factors are expressed by convolution • of hadron LC wave functions.

13. ηb study • ηb was not observed until 2008. C. Hwang, Wei, JPG (2007)

14. Conventional harmonic oscillator model • Adopting different β parameters will break the orthogonality • among the nS states.

15. LF wave function for Υ(nS) H. Ke, X. Li, Wei, X. Liu, PRD (2010) The harmonic oscillator model shows a discrepancy for Y(nS) decay constants . The LF wave function is questionable. A modified wave function

16. Orthogonality, normalization

18. Λb decay • Diquark picture for baryon • Two quarks in a color-antitriplet state can form a diquark. • Baryon looks like a meson. • Diquark approximation simplifies greatly the calculation of • baryon decays.

19. H. Ke, Li, Wei, PRD (2008) • Λb→Λc decays

20. Λb→p, Λ decays Wei，Ke，Li， PRD (2009) Definition of form factors

23. Symmetry relations We propose that there are three independent form factors. Large energy limit relations: C. Chen, C. Geng, hep-ph/0106193, HQET T. Feldman, M. Yip, 1111.1184; T. Mannel, Y. Wang, 1111.1189.

24. fDS Puzzle? • Most model predictions are smaller than exp. • 3σ deviations between experiment and lattice results.

25. It is easy to adjust parameters β to fit the data. • One prediction is that D->τν is 1.2*10^{-3 }, • which will be observed soon.

26. With the new parameters, theory predictions are closer • to experimental data.

27. Rosner, 1201.2401 No puzzle?

28. Summary • LC quark model provides a convenient non-perturbative • method to study the decay constants, form factors, etc. • We proposed a modified LC wave functions for Y(nS) states. • The study of heavy baryon in LC quark model indicates the • reliability of the diquark approximation. • Within the standard model, “fDs puzzle” can be explained.