Seminars IFIC
# Topical Seminar: Isospin symmetry and three-body rescattering in $D\to \bar{K}\pi\pi$ amplitudes

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1001-Primera-1-1-1 - Paterna. Seminario (Universe)
### 1001-Primera-1-1-1 - Paterna. Seminario

#### Universe

60

Description

In non-leptonic weak decays the strong-interaction phases are necessary ingredients for extracting information on the CP violating phases. In this talk, we discuss an approach for calculating these strong phases, for a class of three-body D decays: $D\to\bar{K}\pi\pi$. The mode $D^0\to K_S\pi+\pi^-$ is of particular interest for the measurement of the CKM parameter $\gamma$. At first, isospin symmetry is rather predictive here due to the simple isospin transformation of the relevant weak hamiltonian, and eventually allows to describe simultaneously all the $D\to\bar{K}\pi\pi modes. Going beyond the popular isobar model three-body rescattering effects (which could be more significant for $D$ decays than for $K$ or $B$ decays) are taken into account by deriving a set of dispersive Khuri-Treiman (KT) integral equations. The outcome, based on KT solutions which use experimental inputs on $\pi\pi$ and $\pi K$ scattering, is compared with some experimental results concerning, in particular, the strong phases, which are available for some $D^+\to\bar{K}\pi\pi$ and $D^0\to\bar{K}\pi\pi$ modes.

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