Analysis of the low-energy $π^- p$ charge-exchange data

Details Analysis of the low-energy $π^- p$ charge-exchange data Analysis of the low-energy $π^- p$ charge-exchange data

2012-03-17

arxiv.org/abs/1203.3856v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

Submitted for reviewing

Scientific paper

We analyse the charge-exchange (CX) measurements $\pi^- p\rightarrow \pi^0 n$ below pion laboratory kinetic energy of 100 MeV. After the removal of five degrees of freedom from the initial database, we combined it with the truncated $\pi^+ p$ database of our recent PSA and fitted to the data using the ETH model. The set of model-parameter values, as well as the predictions (which are derived on their basis) for the phase shifts and for the low-energy $\pi N$ constants, are significantly different from the results we obtained in the analysis of the truncated $\pi^\pm p$ elastic-scattering databases. Concerning the phase shifts, the main difference occurs in $\tilde{\delta}_{0+}^{1/2}$; smaller differences have been found in two p-wave phase shifts. We discuss the implications of these findings in terms of the violation of the isospin invariance in the hadronic part of the $\pi N$ interaction. The effect observed is at the level of $7-8%$ in the CX scattering amplitude below about 70 MeV. The results and conclusions of this study agree very well with those obtained in the mid 1990s, when the isospin invariance was first tested by using $\pi N$ experimental data, and disagree with the predictions obtained within the framework of the heavy-baryon Chiral-Perturbation Theory.

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