$Kπ$ $I=1/2$ $S$-wave from $η_c$ decay data at BaBar and classic Meson-Meson scattering from LASS

Abstract

A recent analysis of data on the two photon production of the $η_c$ and its decay to $K(Kπ)$ has determined the $Kπ$ $S$-wave amplitude in a "model-independent" way assuming primarily that the additional kaon is a spectator in this decay. The purpose of this paper is to fit these results, together with classic $Kπ$ production data from LASS, within a formalism that implements unitarity for the di-meson interaction. This fixes the $I=1/2$ $Kπ\to Kπ$ $S$-wave amplitude up to 2.4 GeV. This resolves the Barrelet ambiguity in the original LASS analysis, and constrains the amount of inelasticity in $Kπ$ scattering, highlighting that this becomes significant beyond 1.8 GeV. This result needs to be checked by experimental information on the many inelastic channels, in particular $Kη^\prime$ and $Kπππ$. Our analysis provides a single representation for the $Kπ$ $S$-wave from threshold, controlled by Chiral Perturbation Theory, through the broad $κ$, $K_0^*(1430)$ and $K_0^*(1950)$ resonances. There is no arbitrary sum of Breit-Wigner forms and random backgrounds for real $Kπ$ masses. Rather the form provides a representation that can be translated to other processes with $Kπ$ interactions with their own coupling functions, while automatically maintaining consistency with the chiral dynamics near threshold, with the LASS data and the new results on $η_c$ decay.

A new analysis superceding this earlier version is under way and will be submitted to the arXiv once complete. (original version 8 pages, 6 figures)