Dispersion Relations and Rescattering Effects in B Nonleptonic Decays

TL;DR

This paper develops a dispersion relation formalism for nonleptonic B decays, revealing a discrepancy in spectral functions and applying the approach with Regge theory and SU(3) symmetry to constrain decay amplitudes.

Contribution

It introduces a novel dispersion relation derivation for B decays and clarifies the role of spectral functions in final state interactions.

Findings

Discrepancy identified between spectral function and dispersive variable.

Constraints on tree and penguin amplitudes in B0→π+π− decay.

Formalism combines unitarity, dispersion relations, Regge theory, and SU(3) symmetry.

Abstract

Recently, the final state strong interactions in nonleptonic B decays were investigated in a formalism based on hadronic unitarity and dispersion relations in terms of the off-shell mass squared of the $B$ meson. We consider an heuristic derivation of the dispersion relations in the mass variables using the reduction LSZ formalism and find a discrepancy between the spectral function and the dispersive variable used in the recent works. The part of the unitarity sum which describes final state interactions is shown to appear as spectral function in a dispersion relation based on the analytic continuation in the mass squared of one final particles. As an application, by combining this formalism with Regge theory and SU(3) flavour symmetry we obtain constraints on the tree and the penguin amplitudes of the decay $B^0\to \pi^+\pi^-$.