$\bar{K}NN$ Absorption within the Framework of the Fixed Center Approximation to Faddeev equations

We present a method to evaluate the $\bar{K}$ absorption width in the bound $\bar{K}NN$ system. Most calculations of this system ignore this channel and only consider the $\bar{K}N \rightarrow \pi \Sigma$ conversion. Other works make a qualitative calculation using perturbative methods. Since the $\Lambda(1405)$ 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 $\bar{K}$ rescattering on the $(NN)$ 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 $\bar{K}NN$ absorption, to a total width of about 80 MeV.