Bound state formation in the DDK system

Abstract

We study the DDK system in a coupled channel approach, by including DD s η and DD s π, and find that the dynamics involved in the system forms a bound state with isospin 1=2 and mass 4140 MeV when one of the DK pair is resonating in isospin 0, forming the D Ã s0 ð2317Þ. The state can be interpreted as a DD Ã s0 ð2317Þ molecule like state with exotic quantum numbers: doubly charged, doubly charmed, and with single strangeness.

DK , DDK , and DDDK molecules–understanding the nature of the Wu1, Liu2, Geng3 et al. 2019Phys. Rev. DSelf Cite

“…We notice that the geometry of the DDK system is more or less of a proper triangle, which agrees qualitatively with the findings of Ref. [47]. From the last two columns of Table V, it is clear that the DD interaction is weakly attractive, accounting for only a few MeV of the total potential energy.…”

“…Later a more complete study appeared in Ref. [47], which uses the method developed by the Valencia group [54][55][56][57][58][59][60][61][62] to solve the Faddeev equation [63] for the DDK system, predicting a bound state at about 90 MeV below the DDK threshold.…”

“…The prediction of this trimer confirms the previous calculations of Refs. [46,47], while the prediction of the tetramer is novel to the present work.…”

“…If the DK interaction is strongly attractive, a natural question to ask is what happens when one adds one extra D meson to the system 2 . The answer seems to be that it binds [46,47]. In Ref.…”

“…[47] leads to a binding energy of about 90 MeV for the DDK three-body system. In the present manuscript we revisit the calculation of the DDK bound state and extend it to the DDDK system by using the Gaussian Expansion Method (GEM), which offers a number of advantages compared to previous studies [46,47]. First, it allows one to calculate directly the density distribution of the three (four) body system, which then gives a transparent picture for their spacial distributions.…”