We present a method to evaluate the $\overline{K}$ absorption width in the bound $\overline{K}NN$ system. Most calculations of this system ignore this channel and only consider the $\overline{K}N\to \pi \Sigma$ conversion. Other works make a qualitative calculation using perturbative methods. Since the $\Lambda \left(1405\right)$ resonance is playing a role in the process, the same resonance is changed by the presence of the absorption channels and we find that a full nonperturbative calculation is called for, which we present here. We employ the fixed center approximation to Faddeev equations to account for $\overline{K}$ rescattering on the $\left(NN\right)$ cluster and we find that the width of the states found previously for $S=0$ and $S=1$ increases by about 30 MeV due to the $\overline{K}NN$ absorption, to a total width of about 80 MeV.

• Received 11 July 2012

DOI:https://doi.org/10.1103/PhysRevC.88.044003