  We investigate the formation of three-body bound states (trimers) in
two-component Fermi gases confined in one dimensional optical lattice with
spin-dependent tunneling rates. The binding energy and the effective mass of
the trimer are obtained from the solution of the Mattis integral equation
generalized to the case of unequal Bloch masses. We show that this equation
admits multiple solutions corresponding to excited bound states, which are only
stable for large mass asymmetry.
