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。
1
 Introduction
 Light front QCD and quark model
 Phenomenologies:
1. ηb
2. Λb decay
3. fDs 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
Non-perturbative methods:
1.
2.
3.
4.
5.
6.
Lattice
Effective field theories
QCD sum rules
Light-fone method
AdS/QCD
…
4
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)
5
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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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.
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
LF Fock space expansion

M ( P )    d [ n ] n : xi P  , ki  xi Pi , i n / M ( xi , ki , i )
n 1
 LF bound state equation
H LF   P  P    M 2 
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
( RM ) s ' s  uD ( pi , s' )u( pi , s)
 2mi

 
mi  xi M 0  i s ' s  ( p  n )
( mi  xi M 0 ) 2  p
2
R SSz 12 constructs a state of of spin ( S , S z ) out of
LC helicity eigenstate s (1 , 2 ) :
R
00
12
1

~ u ( k1 , 1 ) 5v ( k2 , 2 ),
2M 0
for pseudoscal ar meson;
R
1S z
12

1
  (k1  k2 ) 

v ( k2 , 2 ),
~ u ( k1 , 1 )  

wV
2M 0


for vector meson.
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 The pseudoscalar meson decay constant is
with
A  m1x  m2 (1  x)
 The physical form factors are expressed by convolution
of hadron LC wave functions.
12
ηb study
 ηb was not observed until 2008.
C. Hwang, Wei, JPG (2007)
13
Conventional harmonic oscillator model
 Adopting different β parameters will break the orthogonality
among the nS states.
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
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
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Orthogonality,
normalization
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17
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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 Λb→p, Λ decays
Wei，Ke，Li， PRD (2009)
Definition of form factors
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 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.
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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.
26
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.
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