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Particles and Fields

Eur. Phys. J. C 21, 145-153 (2001)
DOI: 10.1007/s100520100717

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

I. Caprini1, L. Micu1 and C. Bourrely2

1  National Institute of Physics and Nuclear Engineering, P.O. Box MG 6, 76900 Bucharest, Romania
2  Centre de Physique Théorique (Laboratoire propre au CNRS-UPR 7061) , CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France

(Received: 19 March 2001 / Revised version: 25 May 2001 / Published online: 29 June 2001 -© Springer-Verlag / Società Italiana di Fisica 2001)

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.

© Società Italiana di Fisica, Springer-Verlag 2001