Prediction of a Narrow Exotic Hadronic State with Quantum Numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>
Teng Ji, Xiang-Kun Dong, Feng-Kun Guo, B. S. Zou
Abstract
Lots of charmonium-like structures have been observed in the last two decades. Most of them have quantum numbers that can be formed by a pair of charm and anticharm quarks, thus it is difficult to unambiguously identify the exotic ones among them. In this Letter, by exploiting heavy quark spin symmetry, we present a robust prediction of the hadronic molecular scenario, where the $\ensuremath{\psi}(4230)$, $\ensuremath{\psi}(4360)$ and $\ensuremath{\psi}(4415)$ are identified as $D{\overline{D}}_{1}$, ${D}^{*}{\overline{D}}_{1}$, and ${D}^{*}{\overline{D}}_{2}^{*}$ bound states, respectively. We show that a flavor-neutral charmonium-like exotic state with quantum numbers ${J}^{PC}={0}^{\ensuremath{-}\ensuremath{-}}$, denoted as ${\ensuremath{\psi}}_{0}(4360)$, should exist as a ${D}^{*}{\overline{D}}_{1}$ bound state. The mass and width of the ${\ensuremath{\psi}}_{0}(4360)$ are predicted to be $(4366\ifmmode\pm\else\textpm\fi{}18)\text{ }\text{ }\mathrm{MeV}$ and less than 10 MeV, respectively. The ${\ensuremath{\psi}}_{0}(4360)$ is significant in two folds: no ${0}^{\ensuremath{-}\ensuremath{-}}$ hadron has been observed so far, and a study of this state will enlighten the understanding of the mysterious vector mesons between 4.2 and 4.5 GeV, as well as the nature of previously observed exotic ${Z}_{c}$ and ${P}_{c}$ states. We propose that such an exotic state can be searched for in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\psi}}_{0}(4360)$ and uniquely identified by measuring the angular distribution of the outgoing $\ensuremath{\eta}$ meson.