Double Lambda He-6 in cluster effective field theory

The bound state of \nuclide[6][\Lambda\Lambda]{He} is studied as a three-body ($\mathrm{\Lambda }\mathrm{\Lambda }\alpha$) system in a cluster effective field theory at leading order (LO). We find that the system exhibits the limit cycle which is associated with the formation of bound states called the Efimov states. This implies that the three-body contact interaction should be promoted to LO. The relationship of the binding energy and the $\mathrm{\Lambda }\mathrm{\Lambda }$ scattering length is discussed as well as the role of the scale in this system.