The $\eta$- and $\eta'$-nucleus interactions and the search for $\eta$, $\eta'$- mesic states

Abstract

The isoscalar $\eta$ and $\eta'$ mesons are special in QCD, being linked both to chiral symmetry and to non-perturbative glue associated with the axial anomaly. The properties of these mesons in medium are sensitive to how these dynamics work in the nuclear environment. In contrast to pionic and kaonic atoms which are mainly bound by the Coulomb interaction with some corrections due to the strong force (Coulomb assisted binding), the $\eta$ and $\eta'$ as neutral mesons can only be bound by the strong interaction. Is this interaction strong enough? This topic has inspired a vigorous program of experiments, conducted in close contact with theory, One has to determine the complex $\eta$, $\eta'$-nucleus potential. Does the real part $V$ provide a sufficiently deep potential? Is the imaginary part $W$ small enough to allow for narrow states that can more easily be detected experimentally, i.e. $|W| \ll |V|$? The $\eta'$ effective mass is observed to be suppressed by $\approx -40$ MeV at nuclear matter density. Bound state searches are ongoing. This article gives an overview of the status of knowledge in this field together with an outlook to future experiments.