Lower Bound for ppK– Quasi-Bound State Energy

Abstract

The kaonic cluster $$pp{{K}^{ - }}$$ is described as $$NN\bar {K}({{s}_{{NN}}} = 0)$$ system within the isospin formalism based on the configuration space Faddeev equations. In the model, the isospin singlet $$N\bar {K}$$ state is a deeply bound state associated with $$\Lambda (1405)$$ hyperon. The phenomenological isospin-dependent $$N\bar {K}$$ potentials are used for the calculation of $$pp{{K}^{ - }}$$ quasi-bound state energy. The existence of a lower bound for the energy is shown by theoretical and numerical analysis. In contrast to the isospin formalism based model, the isospinless model obtained by isospin averaging $$N\bar {K}$$ potential is also considered. The results of both models are compared.