Quark-Hadron Duality, Factorization and Strong Phases in $B_d^0\to {\pi }^{+}{\pi }^{-}$ Decay

Abstract

We consider the hadronic description of the $B_d^0\to {\pi }^{+}{\pi }^{-}$ decay, with the aim to investigate the strong phases generated by the final state interactions. The derivation of the dispersion relations using the Lehmann-Symanzik-Zimmermann formalism and the Goldberger-Treiman method to include inelastic effects in the spectral function are presented. We discuss the problem of quark-hadron duality and estimate in the hadronic formalism the corrections to the factorized amplitude in the heavy quark limit.

Comments: 16 pages, revised version, introduction of a scale dependence