Reaction $e^{+}{e}^{-}\to \bar{D}D$ and $\ddot{I}{ˆ}^{\prime }$ mesons

Abstract

We study the reaction $e^{+}{e}^{-}\to \bar{D}D$ near threshold in the ${}^3{P}_0$ non-relativistic quark model, including as intermediate states the $J/\ddot{I}ˆ$, $\ddot{I}ˆ(2S)$, $\ddot{I}ˆ(3770)$ and $\ddot{I}ˆ(4040)$ mesons. The work reveals that experimental data strongly favor one of the two $\ddot{I}ˆ(2S)-\ddot{I}ˆ(3770)$ mixing angles derived by fitting to the $e^{-}{e}^{+}$ partial decay widths of the $\ddot{I}ˆ(2S)$ and $\ddot{I}ˆ(3770)$ mesons. The meson $X(3940)$ as well as the resonance around 3.9 GeV observed by Belle and BaBar Collaborations in the reaction $e^{+}{e}^{-}\to \bar{D}D$ is unlikely to be a $c\bar{c}$ $I^G(J^{PC})=0^{-}(1^{--})$ state.

7 pages, 1 figure, accepted for publication in Physical Review D