Does $\ddot{I}ˆ(4660)$ exist?

Abstract

We investigate $S$-wave coupled-channel effects in $e^{+}{e}^{-}$ annihilation in the energy region $\sqrt{s}\in [4.0,5.5]\mathrm{GeV}$, including the open-charm final states $\hat{I}{›}_c^{+}\bar{\hat{I}}{›}_c^{-}$, $\hat{I}{ž}_c^{+}\bar{\hat{I}}{ž}_c^{-}$, $\hat{I}{ž}_c^0\bar{\hat{I}}{ž}_c^0$, and $\ddot{I}ˆ(2S)\ddot{I}{€}^{+}\ddot{I}{€}^{-}$. Motivated by the recent high-precision BESIII measurements of the $e^{+}{e}^{-}\to \hat{I}{›}_c^{+}\bar{\hat{I}}{›}_c^{-}$ cross section, which shows a nearly flat lineshape around $4.66\mathrm{GeV}$ and a non-zero value right at threshold, in striking contrast to earlier Belle observation, we construct an effective coupled-channel framework by using short-ranged contact potentials in the heavy-quark limit.Two charmonium states, i.e. the $\ddot{I}ˆ(4360)$ and $\ddot{I}ˆ(4660)$, assigned as the $4S$ and $5S$ excitations, respectively, are explicitly included. The scattering amplitudes are obtained by solving the Lippmann-Schwinger equation.The Belle and BESIII $e^{+}{e}^{-}\to \hat{I}{›}_c^{+}\bar{\hat{I}}{›}_c^{-}$ and $e^{+}{e}^{-}\to \ddot{I}ˆ(2S)\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ cross-sections reveal markedly different pole structures for the $\ddot{I}ˆ(4360)$. It emerges as a dynamically generated state for the Belle data, whereas it appears as a bare state in the BESIII fit. In contrast, the $\ddot{I}ˆ(4660)$ pole found on the unphysical Riemann sheet above the $\hat{I}{›}_c^{+}\bar{\hat{I}}{›}_c^{-}$ threshold is associated with a bare pole on the real axis in both fits.

16 pages, 5 figures