Molecule model for kaonic nuclear cluster anti-KNN
Abstract
We analyse the properties of the kaonic nuclear cluster (KNC) anti-KNN with the structure Nx(anti-KN)(I = 0), having the quantum numbers I(JP) = 1/2(0-), and treated as a quasi-bound hadronic molecule state. We describe the properties of the hadronic molecule, or the KNC Nx(anti-KN)(I = 0), in terms of vibrational degrees of freedom with oscillator wave functions and chiral dynamics. These wave functions, having the meaning of trial wave functions of variational calculations, are parameterised by the frequency of oscillations of the (anti-KN)(I = 0) pair, which is fixed in terms of the binding energy of the strange baryon resonance Lambda(1405), treated as a quasi-bound (anti-KN)(I = 0) state. The binding energies BX and widths GammaX of the states X = (anti-KN)(I = 0) and X = anti-KNN, respectively, are calculated in the heavy-baryon approximation by using chiral Lagrangians with meson-baryon derivative couplings invariant under chiral SU(3)xSU(3) symmetry at the tree-level approximation. The results are B(anti-KNN) = 40.2 MeV and Gamma(anti-KNN) = Gamma(non-pionic)(anti-KNN) + Gamma(pionic)(anti-KNN) ~ (85 - 106) MeV and, where Gamma(non-pionic)(anti-KNN) ~ 21 MeV and Gamma(pionic)(anti-KNN) ~ (64 - 86) MeV are the widths of non-pionic anti-KNN -> N Lambda0, N Sigma and pionic anti-KNN -> N Sigma pi decay modes, calculated for B(anti-KN) = 29 MeV and Gamma(anti-KN) = (30 - 40) MeV, respectively.
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