### Speaker

Ms
Patricia Magalhães, C.
(University of São Paulo, Brazil)

### Description

The last decade provided important advances on light scalar resonances sector in the D decays. In particular, different analyses showed the evidence for $\sigma$ and $\kappa$ mesons close to the threshold.
Decays of charmed meson, however, are still poorly understood theoretically. The $K^-\pi^+$ phase shift extracted from $D^+\to K^- \pi^+\pi^+$[1] and from $K^-\pi^+$ scattering[2] are significantly different. Our main purpose is to understand this discrepancy.
We investigate $D^+\to K^- \pi^+\pi^+$ exploring two gaps in the theoretical models. The first one is the weak vertex, which we know very little about. The other is the final state interactions.
We focus our work on the low energy part of $K\pi$ spectrum making two assumptions: the contribution of $\pi^+\pi^+ $ interaction is small and can be neglected; the $K$ interacts with only one pion at a time.
The basic building block in the calculation is a $K\pi$ amplitude based on unitarized chiral perturbation theory[3], and with parameters determined by a fit to elastic LASS data.
For the weak vertex, three different topologies are considered.
The perturbative solution involve the sum of diagrams with different numbers of loops. We found that each term in this series is systematically related to the previous one and a ressummation of the whole series was performed.
The analysis shows that corrections to the ressummed series are important at threshold and converge rapidly at higher energies. The interference of the different contributions in the whole amplitude change the phase shift. Two classes of weak vertices reproduce the scattering phase shift from LASS[2], whereas the third one describe the behaviour of $K^- \pi^+$ phase shift from FOCUS[1] in the elastic range. This result suggests a dominant decay mechanism in the $D^+ \rightarrow K^- \pi^+ \pi^+$.
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[1] J.M. Link {\it et al.} [FOCUS Collaboration],
Phys.\ Lett.\ B {\bf 653}, (2007) 1; J.M. Link {\it et al.} [FOCUS Collaboration], Phys.\ Lett.\ B {\bf 681}, (2009) 14;
[2]D. Aston {\it et al.}, Nucl. Physc. {\bf B 296} (1988) 493.
[3] G. Ecker, J. Gasser, A. Pich and E. De Rafael,
Nucl. Phys. B{\bf 321}, 311 (1989); J.A. Oller and E. Oset, Nucl. Phys. A {\bf 620}, 438 (1997); M. Jamin, J.A. Oller, A. Pich, Nucl. Phys. {\bf B 587} (2000) 331.

### Primary author

Ms
Patricia Magalhães, C.
(University of São Paulo, Brazil)

### Co-authors

Prof.
Alberto dos Reis, C
(Centro Brasileiro de Pesquisas Físicas - Rio de Janeiro, RJ, Brazil)
Prof.
Ignacio Bediaga
(Centro Brasileiro de Pesquisas Físicas - Rio de Janeiro, RJ, Brazil)
Ms
Karin Guimarães, S.F.F.
(Instituto Tecnológico da Aeronáutica, São José dos Campos,SP, Brazil)
Prof.
Manoel Robilotta, R.
(University of São Paulo, Brazil)
Prof.
Tobias Frederico
(Instituto Tecnológico da Aeronáutica, São José dos Campos,SP, Brazil)