QCD factorization at twist-3: the two parton contributions

In this paper, the twist-3 two parton corrections in charmless \(B\to PP\) decays are shown to be factorizable under the QCD factorization approach. The factorizability of the twist-3 two parton corrections is constructed on the following findings. Under the energetic meson limit, the pseudoscalar d...

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Bibliographic Details
Published inarXiv.org
Main Author Tsung-Wen Yeh
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.03.2008
Subjects
Amplitudes
Divergence
Equations of motion
Factorization
Quarks
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Summary:In this paper, the twist-3 two parton corrections in charmless \(B\to PP\) decays are shown to be factorizable under the QCD factorization approach. The factorizability of the twist-3 two parton corrections is constructed on the following findings. Under the energetic meson limit, the pseudoscalar distribution amplitude for a light pseudoscalar meson is allowed to be non-constant by the equations of motion for the quark. The non-constant pseudoscalar distribution amplitude is then used to regularize the end-point divergences in the hard spectator corrections at twist-3 order. By retaining the momentum fraction variable of the spectator quark of the \(B\) meson in the propagators, the end-point divergence in the weak annihilation corrections at twist-3 order is resolved. The factorization of the \(O(\alpha_s)\) corrections under the two parton approximation is shown valid up-to \(O(1/m_b)\) . The hard scattering kernels of order \(O(\alpha_s)\) and \(O(\Lambda_{QCD}/m_b)\) are explicitly given and found to be infrared finite. The results are applied for making predictions for the branching ratios of \(B\to \pi K \) decays.
ISSN:2331-8422