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

 Introduction  Light front QCD and quark model  Phenomenologies: 1. η b 2. Λ b decay 3. f Ds puzzle  Summary 2

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… 3

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 + =k 0 +k 3 >0 The LC framework is the most possible way to reconcile the high energy parton model and the non-relativistic constitute quark model.

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8  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(x i, 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 ┴. Advantage of LF framework 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 with  The pseudoscalar meson decay constant is  The physical form factors are expressed by convolution of hadron LC wave functions.

13 C. Hwang, Wei, JPG (2007) η b study  η b was not observed until 2008.

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

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

16 Orthogonality, normalization

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18 Λ b 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  Λ b →Λ c decays H. Ke, Li, Wei, PRD (2008)

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

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

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

 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. 25

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

27 Rosner, 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, “f Ds puzzle” can be explained.