Elastic $K\pi$ amplitude: a simple model

TL;DR

This paper introduces a simple chiral model for the elastic $K\pi$ amplitude in the $J=0, I=1/2$ channel, useful for data analysis between threshold and 1.5 GeV, and explains the pole structure analytically.

Contribution

It provides a straightforward, physics-informed model for the $K\pi$ amplitude that simplifies understanding of its pole structure using polynomial approximations.

Findings

Identifies a pole at approximately 0.75 GeV with an imaginary part of 0.24 GeV.

Shows the model's analytic structure explains the number of physical poles.

Demonstrates the model's applicability in $D^+ o K^- \pi^+ \pi^+$ data analysis.

Abstract

We present a chiral model for the $J=0, I=1/2,$ elastic $K\p$ amplitude, suited to be employed in $D^+ \rar K^- \p^+ \p^+$ data analyses and valid between threshold and $1.5 $GeV. Although not as precise as other versions available in the literature, it is rather simple and incorporates the essential physics in this energy domain. In the case of the $K$-matrix approximation, the model allows the pole structure of the $K\p$ amplitude to be understood by solving a quadratic equation in $s$. We show that the solutions to this equation can be well approximated by polynomials of masses and coupling constants. This analytic structure allows a clear understanding why, depending on the values of one of the coupling constants, one may have one or two physical poles. The model yields a pole, associated with the $\k$, at $\sqrt{s}= (0.75 - i 0.24) $GeV.