Improvements to the Method of Dispersion Relations for B Nonleptonic Decays

Abstract

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.

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

References in corpus (6)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• Final State Interactions and New Physics in B -> pi K Decays
• Model-Independent Analysis of B -> pi K Decays and Bounds on the Weak Phase gamma
• Annihilation, Rescattering, and CP Asymmetries in B Meson Decays
• Final State Interaction Phases in $B\to K\pi$ Decay Amplitudes
• Dispersion Relations and Rescattering Effects in B Nonleptonic Decays

Cited by in corpus (1)

• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states