Phenomenological model of the Kaonic Nuclear Cluster K^-pp in the ground state

Abstract

A phenomenological model is proposed for the analysis of the properties of the Kaonic Nuclear Cluster (KNC) Kpp in its ground state. Inside the KNC K^-pp we describe the relative motion of the protons in the pp pair and the motion of the K^- meson relative to the pp pair in terms of wave functions of 3-dimensional harmonic oscillators. The interaction strength is parameterised in our model by the frequency of the longitudinal oscillation of the K^- meson relative to the pp pair. This parameter was determined with the binding energy and width of the strange baryon Lambda(1405) by assuming that it is a bound state of the K^-p pair. In terms of this interaction strength we calculate the binding energy epsilon_(Kpp) = - 118 MeV, the partial widths of non-pionic decay channels and the total width, Gamma_(Kpp) = 58 MeV. This agrees well with the experimental data by the FINUDA Collaboration (PRL 94, 212303 (2005)): epsilon_exp = - 115(+6/-5) MeV and Gamma_exp = 67(+14/-11) MeV. The discrepancy with the results, obtained by Akaishi and Yamazaki within the potential model approach, is discussed.