Investigation of the $nn\Lambda$ bound state in pionless effective theory

Abstract

The possibility of an $nn\Lambda$ bound state is investigated in the framework of pionless effective field theory at leading order. A system of coupled integral equations are constructed in the spin-isospin basis, of which numerical solutions are investigated. In particular, we make use of the limit cycle behavior, i.e., cyclic singularities of coupled integral equations of the system, which would be associated with the formation of a three-body bound state, so-called the Efimov state, in the unitary limit. Furthermore, we find that, when the sharp momentum cutoff introduced in the integral equations is taken significantly larger than the hard scale of the effective theory, the coupling of a three-body contact interaction becomes cyclically singular indicating the onset of Efimov-like bound state formation. However, the paucity of empirical information to determine the parameters of the theory precludes a definitive conclusion on the existence of such a bound state. As a simple test of the feasibility of the $nn\Lambda$ bound system in nature, we explore the cutoff dependence of the theory, and uncertainties of the present study are discussed as well.