Improvements to the Method of Dispersion Relations for B Nonleptonic Decays

Details Improvements to the Method of Dispersion Relations for B Nonleptonic Decays Improvements to the Method of Dispersion Relations for B Nonleptonic Decays

1999-10-11

arxiv.org/abs/hep-ph/9910297v2

Phys.Rev. D62 (2000) 034016

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, 4 new figures. modifications of the dispersion representation

Scientific paper

10.1103/PhysRevD.62.034016

We bring some clarifications and improvements to the method of dispersion relations in the external masses variables, that we proposed recently for investigating the final state interactions in the B nonleptonic decays. We first present arguments for the existence of an additional term in the dispersion representation, which arises from an equal-time commutator in the LSZ formalism and can be approximated by the conventional factorized amplitude. The reality properties of the spectral function and the Goldberger-Treiman procedure to perform the hadronic unitarity sum are analyzed in more detail. We also improve the treatment of the strong interaction part by including the contributions of both t and u-channel trajectories in the Regge amplitudes. Applications to the $B^0\to \pi^+\pi^-$ and $B^+\to \pi^0 K^+$ decays are presented.

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