Can the three new states around 2.2 GeV assign to $\ddot{I}‰(3D)$

Abstract

Recently, the BESIII Collaboration reported three resonances: $X(2232)$ with $M=2232\pm 19\pm 27$ MeV and $\hat{I}“=93\pm 53\pm 20$ MeV, $X(2200)$ whose mass $M=2200\pm 11\pm 17$ MeV and width $\hat{I}“=74\pm 20\pm 24$ MeV as well as $X(2222)$ which has mass of $2222\pm 7\pm 2$ MeV and the width of $59\pm 30\pm 6$ MeV. The mass spectrum of $\ddot{I}‰$ meson family is studied utilizing the modified Godfrey-Isgur model, and the two-body strong decays of $X(2232)$, $X(2200)$ and $X(2222)$ within two different approaches of the ${}^3{P}_0$ model. We find that the newly discovered states $X(2232)$, $X(2200)$ and $X(2222)$ may be the same and are most likely to be the $\ddot{I}‰(3D)$ state. The discovery could be useful in establishing entire $\ddot{I}‰$ mesons.

5 pages,2 figures