A Universal Trimer in a Three-Component Fermi Gas

We show that the recently measured magnetic field dependence of three-body loss in a three-component mixture of ultracold $^6$Li atoms [1,2] can be explained by the presence of a universal trimer state. Previous work suggested a universal trimer state as a probable explanation, yet failed to get good agreement between theory and experiment over the whole range of magnetic fields. For our description we adapt the theory of Braaten and Hammer [3] for three identical bosons to the case of three distinguishable fermions by combining the three scattering lengths $a_{12},$ $a_{23}$ and $a_{13}$ between the three components to an effective interaction parameter $a_m$. We show that taking into account a magnetic field variation of the lifetime of the trimer state is essential to obtain a complete understanding of the observed decay rates.