Spin observables of the reaction pd-3He eta and quasi-bound 3He-eta pole

TL;DR

This paper develops a formalism for analyzing spin observables in the pd to 3He eta reaction, focusing on near-threshold energies to investigate the possible quasi-bound 3He-eta state through polarization measurements.

Contribution

It introduces a model-independent formalism for spin observables with six amplitudes and explores simplified models with fewer amplitudes near threshold, aiding the search for a 3He-eta quasi-bound state.

Findings

Measurement of polarization transfer coefficients helps distinguish s- and p-wave amplitudes.

Specific observables involving products of s- and p-wave amplitudes can reveal the 3He-eta pole position.

Analysis shows that analyzing powers and spin correlations alone are insufficient for complete amplitude separation.

Abstract

A formalism for spin observables of the reaction $pd\to ~^3He\eta$ is derived in a model independent way. The general case with a full set of six independent spin amplitudes is studied. Furthermore, approximations by five and four spin amplitudes are investigated in the near threshold region. This region is of great interest to search for a quasi-bound $^3He-\eta$ state, in particular, by measurement of energy dependence of relative phases of s- and p-wave amplitudes. Complete polarization experiments, allowing determination of spin amplitudes, are analyzed. It is shown that measurement of only analyzing powers and spin correlation coefficients hardly allows one to separate the s- and p-wave amplitudes, but additional measurement of polarization transfer coefficients simplifies this problem. Specific observables, given by products of one s- and one p-wave amplitudes, are found. Measurement of these observables will provide new independent information on the $^3He-\eta$ pole position.