1. Factorization in some exclusive B meson decays
Zheng-Tao Wei
(NCTS and Institue of Physics)
Introduction
SCET factorization
Heavy-heavy decays in FA
Summary
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2. I. Introduction 1. The direct CP asymmetry 
strong phase difference (FSI).
Exclusive B decays 
hadronic matrix elements.
Perturbative and non-perturbative QCD are
necessary.  Factorization
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3. Concept of factorization
Semi-leptonic decay amplitude separates into
Apply similar idea to hadronic decay,
decay constant
Naïve factorization approach
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form factors

4. Naïve factorization approach neglects non-factorizable QCD effects.
(parton model in exclusive B decays)
The decay amplitudes are scale and scheme dependent when using the effective theory.
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5. Mechanism of factorization
Large Nc theory
A. Buras, J. Gerard, R. Ruckl, Nucl. Phys. B 268, 16 (1986).
Large Nc expansion is not favored in B->D pi decays (Cheng 1994)
Color transparency
J. Bjorken, Nucl. Phys. Proc.
Suppl 11, 325 (1989).
Small size color-singlet quark-antiquark
pair decouples from soft gluons.
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6. II. SCET factorization framework (a language) from the view of scales.
The soft-collinear effective theory provides a systematic
framework (a language) from the view of scales.
It simplifies the analysis with multi-scales: proof of factorization
to all orders, Sudakov resummation.
The factorization in effective theory refers to integrating
out the heavy degrees of freedom scale by scale.
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7. Degrees of freedom Power counting Field Momentum
Reproduce the full IR physics
Power counting
Field
Momentum
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8. The effective interaction is non-local in position space.
Lagrangian:
The effective interaction is non-local in position space.
Two different formulae: momentum-space and
position-space representation.
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9. Wilson line No interaction with soft gluons
Gauge invariant operators: (basic building blocks)
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10. The factorization in B->DKK decays
Recently, Belle Collaboration observed three body decays.
The kaon pair mass spectrum peaks the mass threshold.
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11. (Form factor suppression)
Kinemics:
(Form factor suppression)
Collinear
approximation
Where
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12. The factorization of decays
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13. Factorization
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14. The non-locality of factorization formulae in position space is
because the collinear momentum is of the same order as the
hard loop momentum.
The coefficients C are infrared finite because it is obtained from
the matching.
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15. The final factorization formulae
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16. III. Heavy-heavy decays in GFA
Factorization
The momentum of D meson is not
much larger than c quark mass.
 not energetic as light meson
Color transparency is not applicable.
Non-factorizable soft interactions exist.
We will employ GFA .
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17. General features
Most decay modes are color-allowed dominated. There is no
color-suppressed diagrams.
Non-factorizable hard QCD corrections are suppressed by
C2/Nc~0.1.
The form factors and decay constants are governed by HQS in
the heavy quark limit.
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18. Polarization in B->VV
HQS + factorization hypothesis
heavy-heavy
power law
light-light
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19. provides clear measurement of
Form factor A2 decouples up to 10%.
provides clear measurement of
HQS breaking effect.
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20. Weak annihilation contribution
Estimation on the order of magnitude
PQCD approach
H. Li, S. Mishima, Phys. ReV. D 71, (2005).
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23. Summary
The study of exclusive processes indicate that factorization is a central and successful concept.
In order to obtain a precise prediction of direct CP asymmetry and exclusive decays, To generalize the factorization into non-perturbative region is a challenging task.
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24. Thank you !
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