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Using the two-body interactions obtained from a chiral constituent quarkmodel we study all $\Lambda NN$ and $\Sigma NN$ states with I=0,1,2 andJ=1/2,3/2 at threshold, taking into account all three-body configurations withS and D wave components. We constrain further the limits for the $\Lambda N$spin-triplet scattering length a_{1/2,1}. Using the hypertriton binding energywe find a narrow interval for the possible values of the $\Lambda N$spin-singlet scattering length a_{1/2,0}. We found that the $\Sigma NN$ systemhas a quasibound state in the (I,J) = (1,1/2) channel very near threshold witha width of about 2.1 MeV.

$\Lambda NN$ and $\Sigma NN$ systems at threshold: II. The effect of D waves