Application of a coupled-channel complex scaling method with Feshbach projection to the K− pp system

sari wahyuni;

Kaonic nuclei (nuclear systems with anti-kaons) are an interesting subject in hadron and strange nuclear physics, because the strong attraction between anti-kaons and nucleons might bring exotic properties to those systems. In this article, we investigate K− pp as a prototype of kaonic nuclei. Here, K− pp is a three-body resonant state in the K¯ N N–πY N coupled channels, where Y represents hyperons  and . In order to treat resonant states in a coupled-channel system
properly, we propose a coupled-channel complex scaling method combined with the Feshbach projection, namely, the ccCSM + Feshbach method. In this method, the Feshbach projection
is realized with the help of the so-called extended closure relation held in the complex scaling method, and a complicated coupled-channel problem is reduced to a simple single-channel problem, which one can treat easily. First, we confirm that the ccCSM + Feshbach method completely reproduces the results of a full coupled-channel calculation in the case of the two-body K¯ N–πY system. We then proceed to study the three-body K¯ N N–πY N system, and successfully find solutions of the K− pp resonance by imposing self-consistency for the complex K¯ N energy. The obtained binding energy of K− pp is well converged around 27MeV, with an energydependent K¯ N(–πY ) potential based on the chiral SU(3) theory, independently of ansatzes for self-consistency. This binding energy is as small as those reported in earlier studies based on chiral models. On the other hand, the decay width of K− pp strongly depends on the ansatz. We also calculate the correlation density of N N and K¯ N pairs by using the obtained complex-scaled wave function of the K− pp resonance. The effect of the repulsive core of the NN potential is seen in the N N correlation density. In the K¯ N correlation density, we can confirm the survival
of the  ∗ resonance (I = 0 K¯ N resonance) in the three-body resonance.