Lessons from Fitting the Lowest Order Energy Independent Chiral Based bar{K}N Potential to Experimental Data

J Révai

doi:10.1007/s00601-020-01565-1

Abstract

It is shown, that fitting parameters of a bar{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 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 nuclear quasi-bound state (Lambda (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 Lambda (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.

Highlights

In the last decade the antikaon nucleon interactions attracted considerable attention
((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
There are two main directions along which these interactions are constructed: (a) A possibly complete reproduction of multichannel two-body data in a wide energy range. These approaches use relativistic formulation and in order to obtain good agreement with experimental data, they go beyond the lowest order term in the chiral perturbation expansion

Summary

Introduction

In the last decade the antikaon nucleon interactions attracted considerable attention. (b) In view of possible existence of kaonic nuclear clusters, the main idea of the other approach is to construct a potential, which can be used for calculation of n > 2 systems In this case the simplicity of the potential is essential, the usual practice is to keep the form of the lowest order Weinberg-Tomozawa (WT) term of the chiral expansion and try to adjust it to the experimental data. The potential which we shall use to demonstrate the effects of data fitting [4,5], is an energy-independent implementation of the lowest order WT term of the chiral SU (3) meson-baryon interaction Lagrangian, designed for non-relativistic calculations in two- and few-body systems. There is some confusion in the literature how to treat the statistical and systematic errors in the fitting procedure

Lessons from Fitting the Lowest Order Energy

All values are in MeV

About the Acceptance of the Potential

Findings

Conclusions