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 $$\bar{K}N$$ K ¯ N 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 $$K^-p$$ 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 the potential to different combinations of these data. We found, that the two poles corresponding to the $$I=0$$ I = 0 nuclear quasi-bound state $$(\Lambda (1405))$$ ( Λ ( 1405 ) ) and to the $$K^-p$$ 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 $$\Lambda (1405)$$ Λ ( 1405 ) pole pinned down close to the PDG value fail to reproduce the classical two-body data with an acceptable accuracy. We also added comments on two papers criticizing the potential used in the fits.

Trace of $Λ(1405)$ resonance in low energy $K^{-}+\, ^{3}\mathrm{He}\rightarrow (π^{0}Σ^{0})+d$ reaction

“…To study the dependence of the results to the KN − πΣ model of interaction, we also used the potential given by Akaishi and Yamazaki [1] and the new potential given in Ref. [55] which the first one is an extremely deep potential. We referred to these potentials as AY and Rev-A potentials, respectively.…”

“…Five different interaction models (A-E) are presented in Ref. [55]. As the A model reproduce the lowest value of χ, the A version was chosen to be used in present calculations.…”

Application of the Uniformized Mittag-Leffler Expansion to $Λ(1405)$

“…while hardly interpreted as an excitation in the standard three-quark description. Moreover, calculations in the chiral-unitary model, such as [16][17][18][19][20][21], display a double-pole structure in the region of Λ(1405), contrary to phenomenological local potential models, such as [22][23][24][25], which predict a single-pole structure. In order to settle the debate between the single-pole or double-pole structure of Λ(1405), a model-independent analysis is strongly in need.…”