  We consider the hadronic description of the $B^0_d\to \pi^+\pi^-$ 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.
