Eur. Phys. J. C **10**, 639-661

DOI 10.1007/s100529900054

## SU(*N*) elastic rescattering in *B* and *D* decays

**Ch. Smith**

Institut de Physique Théorique, Université Catholique de Louvain-la-Neuve, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium (smith@fyma.fyma.ucl.ac.be)

Received: 17 December 1998 / Revised version: 17 February 1999 / Published online: 28 September 1999

**Abstract**

The treatment of elastic final-state interactions (FSIs) under
a symmetry
group is presented. The proposed model is based on Watson's
theorem, i.e.
on symmetry properties of the -matrix and on its unitarity.
This
theorem provides an easy way to introduce rescattering effects
by defining
final-state interactions mixing matrices. A symmetry group fixes
the
structure of such mixing matrices, and the passage from one group
to another
is studied (for example, SU(2) to SU(3)). Mixings among two charmless
pseudoscalar decay product states will be systematically analyzed.
Finally,
these mixing matrices will be used on quark diagram parametrizations
of *B*
and *D* decay amplitudes. This will have some important consequences
on the
definition of quark diagrams. It will be argued that these diagrams
should
not contain any FSI effects, i.e. they should be real (except
for CKM
factors). FSIs are then introduced at the hadronic level, by
mixing
basic
quark diagram topologies.

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