Kπform factors and final state interactions inD+→K−π+π+decays

Abstract

We present a model for the decay ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorization approach. Hadronic final state interactions are taken into account through the $K\ensuremath{\pi}$ scalar and vector form factors fulfilling analyticity, unitarity, and chiral symmetry constraints. The model has only two free parameters that are fixed from experimental branching ratios. We show that the modulus and phase of the $S$ wave thus obtained agree nicely with experiments up to 1.55 GeV. We perform Monte Carlo simulations to compare the predicted Dalitz plot with experimental analyses. Allowing for a global phase difference between the $S$ and $P$ waves of $\ensuremath{-}65\ifmmode^\circ\else\textdegree\fi{}$, the Dalitz plot of the ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$ decay, the $K\ensuremath{\pi}$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.