Towards three-body unitarity in D⁺ → K^-π⁺π⁺ decays

Patrícia C. Magalhães (São Paulo)

We study the mechanism involved in the D⁺ → K⁻π⁺π⁺ decay and discuss possible reasons for the experimental data discrepancy between K⁻π⁺ phases extracted from D⁺ → K⁻π⁺π⁺ [1] and those from scattering amplitudes [2].

We explore two gaps in the theoretical models.  The first one is the weak vertex, which we know relatively little about.  The other concerns the final-state interactions.  We focus on the low-energy part of the Kπ spectrum, making two assumptions: the contribution of π⁺π⁺ 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 Kπ amplitude based on unitarized chiral perturbation theory [3], with parameters determined by a fit to elastic LASS data [2].  Its analytic extension to the second sheet allows the determination of two poles, associated with the κ and the K^*(1430), and a representation of the amplitude based on them is constructed.  For the weak vertex, three different topologies are considered.  The perturbative solution involves the sum of diagrams with different numbers of loops.  We find that each term in this series is systematically related to the previous one and a ressummation of the whole series is performed.

The analysis shows that the proper three-body effects are important and the resummed series is relevant to final results.  One class of weak vertices describes the behaviour of the K⁻π⁺ phase shift from FOCUS [1] in the elastic range.  This result seems to indicate a dominant decay mechanism in the D⁺ → K⁻π⁺π⁺ .

[1] J.M. Link et al. [FOCUS Collaboration], Phys. Lett. B 653 (2007) 1; Phys. Lett. B 681 (2009) 14.
[2] D. Aston et al., Nucl. Phys. B 296 (1988) 493.
[3] G. Ecker, J. Gasser, A. Pich and E. De Rafael, Nucl. Phys. B321 (1989) 311; J.A. Oller and E. Oset, Nucl. Phys. A 620 (1997) 438; M. Jamin, J.A. Oller and A. Pich, Nucl. Phys. B 587 (2000) 331.

(Seminarraum II)