2011/05/31 by P. Camargo Magalhaes, P. C. Magalhães, M. R. Robilotta +7 · 1 citation
Mathematics · Physics and Astronomy · #Amplitude #Combinatorics #Graph #Hadron #High-Energy Particle Collisions Research #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Unitarity #Vertex (graph theory) #hep-ex #hep-ph
paper · pdf · doi:10.1103/physrevd.84.094001
published as Phys. Rev. D 84, 094001 (2011) · version published
openalex publication_date 2011/11/02 · arxiv created 2012/04/11 · arxiv updated 2015/03/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We assess the importance of final state interactions in D+\ensuremath→K^\ensuremath-\ensuremathπ+\ensuremathπ+, stressing the consistency between two- and three-body interactions. The basic building block in the calculation is a K\ensuremathπ amplitude based on unitarized chiral perturbation theory and with parameters determined by a fit to elastic LASS data. Its analytic extension to the second sheet allows the determination of two poles, associated with the \ensuremathκ and the K*(1430), and a representation of the amplitude based on them is constructed. The problem of unitarity in the three-body system is formulated in terms of an integral equation, inspired in the Faddeev formalism, which implements a convolution between the weak vertex and the final state hadronic interaction. Three different topologies are considered for the former and, subsequently, the decay amplitude is expressed as a perturbation series. Each term in this series is systematically related to the previous one and a resummation was performed. Remaining effects owing to single and double rescattering processes were then added and results compared to FOCUS data. We found that proper three-body effects are important at threshold and fade away rapidly at higher energies. Our model, based on a vector-weak vertex, can describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region.