On a Quasi-Bound State in the $$\pmb {{ K^- d}}$$ K - d System Caused by Strong Interactions
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N.V. Shevchenko
On a Quasi-Bound State in the K −d System Caused by Strong Interactions
Received: 17 June 2020 / Accepted: 10 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract It was found that N N potential could influence the results of the quasi-bound state search in the K − d system, where the corresponding pole is situated close to the threshold. Three-body Faddeev-type calculations of the K¯ N N − πΣ N system performed with a new model of nucleon-nucleon interaction predict the existence of the quasi-bound K − d state caused by strong interactions. Its binding energy is small (1–2 MeV), while the width is comparable with the width of the K − pp quasi-bound state (40–60 MeV).
1 Introduction Many theoretical works and several experiments were devoted to the question of a quasi-bound state in systems consisting of an antikaon(s) and nucleons, see e.g. [1]. Particular interest was attracted to the lightest possible system K¯ N N with zero spin (usually denoted as K − pp): all theoretical works predicted the quasi-bound state in it. The methods of and the inputs for the calculations are quite different, and the predicted binding energy and width of the state also variate in quite a wide range. We also predicted a quasi-bound state in the spin zero K¯ N N system [1] with binding energy and width strongly depending on the particular form of the antikaon–nucleon potential, which is used as a input. We solved three-body Faddeev-type AGS equations [2] with coupled K¯ N N and πΣ N channels and used three different models of K¯ N interaction: two phenomenological potentials and one chirally motivated model. We also studied another state of the K¯ N N system with spin one (which will be denoted as K − d). It has an atomic state, kaonic deuterium, which is mainly caused by Coulomb attraction between K − and p, while the strong interactions give corrections to the binding energy and width (see [3] and references therein). But we did not find a pole caused by purely strong interactions corresponding to the quasi-bound state in K − d [4] similar to that one in the K − pp system. We demonstrated, that the strong quasi-bound state appears in the K − d system if the attraction in the isospin-zero K¯ N − K¯ N part of the coupled-channel K¯ N − πΣ potential is increased by hands. After studying K¯ N N and K¯ K¯ N systems (the last one also has a quasi-bound state [5]) we started investigations of the four-body K¯ N N N system. We are using four-body Faddeev-type equations [6] on four-body transition amplitudes, which contain, among others, three-body transition amplitudes evaluated at every step of the four-body calculations. We constructed a new nucleon-nucleon potential for these calculations, and found out that the quasi-bound state caused by the strong interactions appeared in the K − d system. The present paper is devoted to this state. The work was supported by the Czech GACR Grant 19-19640S. N. V. Shevchenko (B) ˇ Nuclear Physics Institute, 25068 Rež, Czech Republic E-mail: [email protected]
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