Search for Quasi Bound $\eta$ Mesons

TL;DR

This paper reviews the theoretical and experimental efforts to detect quasi-bound $ ext{eta}$ mesons in nuclei, discussing models, data analysis methods, and experimental evidence for such states.

Contribution

It provides a comprehensive overview of the theoretical models and experimental techniques used to search for quasi-bound $ ext{eta}$ mesons in nuclei, including new derivations of $s$ wave amplitudes.

Findings

Three experiments provide evidence for quasi-bound $ ext{eta}$ mesons.

Model calculations predict specific binding energies and widths.

Extraction of $s$ wave interaction from experimental data is detailed.

Abstract

The search for a quasi bound $\eta$ meson in atomic nuclei is reviewed. This tentative state is studied theoretically as well as experimentally. The theory starts from elastic $\eta$ nucleon scattering which is derived from production data within some models. From this interaction the $\eta$ nucleus interaction is derived. Model calculations predict binding energies and widths of the quasi bound state. Another method is to derive the $\eta$ nucleus interaction from excitation functions of $\eta$ production experiments. The $s$ wave interaction is extracted from such data via final state interaction theorem. We give the derivation of $s$ wave amplitudes in partial wave expansion and in helicity amplitudes and their relation to observables. Different experiments extracting the final state interaction are discussed as are production experiments. So far only three experiments give evidence for the existence of the quasi bound state: a pion double charge exchange experiment, an effective mass measurement, and a transfer reaction at recoil free kinematics with observation of the decay of the state.