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Universal properties of mass-imbalanced three-body systems in 2D are studiedusing zero-range interactions in momentum space. The dependence of thethree-particle binding energy on the parameters (masses and two-body energies)is highly non-trivial even in the simplest case of two identical particles anda distinct one. This dependence is parametrized for ground and excited statesin terms of {\itshape supercircles} functions in the most general case of threedistinguishable particles.

Universality of three-body systems in 2D: parametrization of the bound states energies