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

Abstract

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 $\bar{K}N\to \pi \Sigma$ 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.

15 pages, 9 figures

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• Few-body systems consisting of mesons
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• Search for the deeply bound $K^{-}pp$ state from the semi-inclusive forward-neutron spectrum in the in-flight $K^{-}$ reaction on helium-3
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• Prediction of possible exotic states in the $\eta \bar{K}{K}^{\ast }$ system
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• Possible bound states with hidden bottom from ${\bar{K}}^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ systems
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• In-medium antikaon interactions and bound states
• Recent results and future prospects of kaonic nuclei at J-PARC
• Three-body scattering problem in the fixed center approximation: the case of attraction
• The Peak Structure in the In-Flight ${}^3\text{He}(K^{-},\Lambda p)n$ Reaction Around the $\bar{K}NN$ Threshold
• Narrow bound states of the DNN system