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The possibility of an $nn\Lambda$ bound state is investigated in theframework of pionless effective field theory at leading order. A system ofcoupled integral equations are constructed in the spin-isospin basis, of whichnumerical solutions are investigated. In particular, we make use of the limitcycle behavior, i.e., cyclic singularities of coupled integral equations of thesystem, which would be associated with the formation of a three-body boundstate, so-called the Efimov state, in the unitary limit. Furthermore, we findthat, when the sharp momentum cutoff introduced in the integral equations istaken significantly larger than the hard scale of the effective theory, thecoupling of a three-body contact interaction becomes cyclically singularindicating the onset of Efimov-like bound state formation. However, the paucityof empirical information to determine the parameters of the theory precludes adefinitive conclusion on the existence of such a bound state. As a simple testof the feasibility of the $nn\Lambda$ bound system in nature, we explore thecutoff dependence of the theory, and uncertainties of the present study arediscussed as well.

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