Study of ambiguities in $\pi^-p\to \Lambda K^0$ scattering amplitudes

TL;DR

This study investigates ambiguities in reconstructing scattering amplitudes for the reaction p, highlighting how additional data and partial wave analysis can resolve these ambiguities and comparing different amplitude solutions.

Contribution

The paper introduces a method to resolve amplitude ambiguities in p scattering by incorporating additional data and partial wave analysis, comparing energy-dependent and independent solutions.

Findings

Ambiguities exist when reconstructing amplitudes from limited data.

Including D waves introduces multiple solutions fitting the data equally well.

Full reconstruction is possible when p data on .

Abstract

Amplitudes for the reaction $\pi^-p\to \Lambda K^0$ are reconstructed from data on the differential cross section $d\sigma/d\Omega$, the recoil polarization $P$, and on the spin rotation parameter $\beta$. At low energies, no data on $\beta$ exist, resulting in ambiguities. An approximation using $S$ and $P$ waves leads only to a fair description of the data on $d\sigma/d\Omega$ and $P$; in this case, there are two sets of amplitudes. Including $D$ waves, the data on $d\sigma/d\Omega$ and $P$ are well reproduced by the fit but now, there are several distinct solutions which describe the data with identical precision. In the range where the spin rotation parameter $\beta$ was measured, a full and unambiguous reconstruction of the partial wave amplitudes is possible. The energy-independent amplitudes are compared to the energy dependent amplitudes which resulted from a coupled channel fit (BnGa2011-02) to a large data set including both pion and photo-induced reactions. Significant deviations are observed. Consistency between energy dependent and energy independent solutions by choosing the energy independent solution which is closest to the energy dependent solution. In a second step, the {\it known} energy dependent solution for low (or high) partial waves is imposed and only the high (or low) partial waves are fitted leading to smaller uncertainties.