Quark–hadron duality, factorization and strong phases in $B^0_d\to \pi^+\pi^-$ decay

Abstract.

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.