Superexotic $K^{\ast +}{D}^{\ast +}{K}^{\ast +}$ bound state

Abstract

We study a system made from $K^{\ast +}{D}^{\ast +}{K}^{\ast +}$ with charge $3$, isospin $I=3/2$, spin $J=3$, and a quark content of $c\bar{d}\bar{s}u\bar{s}u$, which make it highly exotic relative to the standard $q\bar{q}$ structure of mesons. The interaction of the three body system is obtained starting from a cluster of $K^{\ast +}{D}^{\ast +}$ in $I=1$ and $J=2$, that in different works has been found bound, and adding to it an extra $K^{\ast +}$ with spin aligned with those of the vectors of the cluster. We find that the $K^{\ast }{K}^{\ast }$ interaction in $I=1$ and $J=2$ is repulsive, but its strength is small compared to that of $K^{\ast +}{D}^{\ast +}$ in $I=1$ and $J=2$, such that we find a three body state bound by about $100\mathrm{MeV}$ with respect to the mass of a $K^{\ast +}$ and the $K^{\ast +}{D}^{\ast +}$ cluster. The width of the state, of about $10\mathrm{MeV}$, is much smaller than the binding, which facilitates its observation. We suggest to find that state by measuring the invariant mass of $KD{K}^{\ast }$, something feasible in present experimental facilities.

8 pages, 4 figures; v2: discussion added, references added