Lessons from fitting the lowest order energy independent chiral based $\bar{K}N$ potential to experimental data

Abstract

It is shown, that fitting parameters of a KN interaction model to different sets of experimental data can lead to physical conclusions which might provide a deeper insight into the physics of this multichannel system. The available experimental data are divided into three parts: the "classical" set consisting of the low-energy K − p cross sections and the threshold branching ratios, the SIDDHARTA 1s level shift in kaonic hydrogen and the CLAS photoproduction data. We have fitted the parameters of a recently introduced energy-independent chiral based potential to different combinations of these data. We found, that for lowest order potentials the two poles corresponding to the I = 0 nuclear quasi-bound state (Λ( 1405)) and to the K − p 1s atomic level seem to resist to their simultaneous reproduction at the right place, though a more or less satisfactory compromise can be achieved. Potentials with the Λ(1405) pole pinned down close to the PDG value fail to reproduce the classical two-body data with an acceptable accuracy. We think, that the proposed way of fitting potential parameters to experimental data could be useful in the case of other models, too.

Importance of chiral constraints for the pole content of the K¯N scattering amplitude

“…As a different dataset and fitting approach was used in [5] the χ 2 /dof taken from this earlier publication cannot be compared directly with the χ 2 /dof obtained for our current models. We also note that no χ 2 /dof was provided in [1] but the same author presented χ 2 /dof in more extendend fits performed later in [20]. The parameter values obtained in our fits are reasonable, in particular the meson decay constants of both BC models and of the JR 2 one are in agreement with predictions of other analyses [40], [41].…”

“…In a recent publication [1] (see also [20]), J. Révai criticized a procedure commonly used to simplify the solution of the above-mentioned integral equations, namely, the so-called on-shell factorisation which reduces the integral equation to an algebraic equation that can be solved immediately. Solving a Lippmann-Schwinger equation (LSE) without applying this approximation, the author of [1] obtained a kernel without energy dependence (an advantageous feature for few-body calculations), and found that the solution ".…”