or more spin states [@Efimov]. Several features associated with Efimov trimers in $^6$Li atoms have been reported recently. Two three-body recombination features were observed by Ottenstein [*et al.*]{} [@Heidelberg] and Huckans [*et al.*]{} [@PennState]. These features were analyzed theoretically in Refs. [@Braaten:2008wd; @schmidt:2008fz; @Naidon:2009] and traced back to an Efimov trimer close to the three-atom threshold [@schmidt:2008fz; @Naidon:2009; @Braaten:2009ey]. Another recombination feature was discovered by Williams [*et al.*]{} [@Williams:2009zzd] and identified as a second trimer close to the threshold. Braaten [*et al.*]{}[@Braaten:2009ey] analyzed the energy spectrum of Efimov trimers and predicted the crossings of the trimers with the atom-dimer threshold. These crossings imply two resonances in atom-dimer scattering. The resonances were identified in recent experiments by Lompe [*et al.*]{}[@Lompe:2010] and Nakajima [*et al.*]{} [@Nakajima:2010]. Furthermore, two local minima in the atom-dimer relaxation rate were reported in Ref. [@Lompe:2010].

In this paper, we study Efimov physics in atom-dimer scattering of $^6$Li atoms in the three lowest hyperfine states and perform a complete zero-range calculation at zero temperature. The size of finite range corrections to our results is estimated. We identify the two resonances and the two minima in the atom-dimer relaxation rate. Quantitatively, our zero temperature results show deviations from the 