Factorization in some exclusive B meson decays Zheng-Tao Wei (NCTS and Institue of Physics) Introduction SCET factorization Heavy-heavy decays in FA Summary 2019/5/24

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 2019/5/24

Concept of factorization Semi-leptonic decay amplitude separates into Apply similar idea to hadronic decay, decay constant Naïve factorization approach 2019/5/24 form factors

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. 2019/5/24

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. 2019/5/24

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. 2019/5/24

Degrees of freedom Power counting Field Momentum Reproduce the full IR physics Power counting Field Momentum 2019/5/24

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. 2019/5/24

Wilson line No interaction with soft gluons Gauge invariant operators: (basic building blocks) 2019/5/24

The factorization in B->DKK decays Recently, Belle Collaboration observed three body decays. The kaon pair mass spectrum peaks the mass threshold. 2019/5/24

(Form factor suppression) Kinemics: (Form factor suppression) Collinear approximation Where 2019/5/24

The factorization of decays 2019/5/24

Factorization 2019/5/24

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. 2019/5/24

The final factorization formulae 2019/5/24

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 . 2019/5/24

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. 2019/5/24

Polarization in B->VV HQS + factorization hypothesis heavy-heavy power law light-light 2019/5/24

provides clear measurement of Form factor A2 decouples up to 10%. provides clear measurement of HQS breaking effect. 2019/5/24

Weak annihilation contribution Estimation on the order of magnitude PQCD approach H. Li, S. Mishima, Phys. ReV. D 71, 054025 (2005). 2019/5/24

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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. 2019/5/24

Thank you ! 2019/5/24