heavy hadron phenomenology on light front zheng-tao wei nankai university 1 2012...
DESCRIPTION
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… 3TRANSCRIPT
Heavy hadron phenomenology on light front
Zheng-Tao Wei
Nankai University
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2012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. ηb
2. Λb decay 3. fDs puzzle Summary
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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…
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Non-perturbative methods: 1. Lattice 2. Effective field theories 3. QCD sum rules 4. Light-fone method 5. AdS/QCD 6. …
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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)
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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.
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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┴.
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.
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1
/ ),,(,,:][)(n
iiiMniiiiin kxPxkPxndPM
LF Fock space expansion
2MPPHLF
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.
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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.
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Melosh rotation 22
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meson. for vector
),,()(),(~21
meson;ar pseudoscalfor
),,(),(~21
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with
The pseudoscalar meson decay constant is
)1(21 xmxmA
The physical form factors are expressed by convolution of hadron LC wave functions.
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C. Hwang, Wei, JPG (2007)
ηb study ηb was not observed until 2008.
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Adopting different β parameters will break the orthogonality among the nS states.
Conventional harmonic oscillator model
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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)
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Orthogonality, normalization
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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.
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Λb→Λc decays H. Ke, Li, Wei, PRD (2008)
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Wei ， Ke ， Li ， PRD (2009) Λb→p, Λ decays
Definition of form factors
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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.
Symmetry relations
fDS Puzzle?
Most model predictions are smaller than exp. 3σ deviations between experiment and lattice results.
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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.
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With the new parameters, theory predictions are closer to experimental data.
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Rosner, 1201.2401
No puzzle?
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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.