Does $\psi(4660)$ 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 $\Lambda_c^+\bar{\Lambda}_c^-$, $\Xi_c^+\bar{\Xi}_c^-$, $\Xi_c^0\bar{\Xi}_c^0$, and $\psi(2S)\pi^+\pi^-$. Motivated by the recent high-precision BESIII measurements of the $e^+e^-\to\Lambda_c^+\bar{\Lambda}_c^-$ 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 $\psi(4360)$ and $\psi(4660)$, 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 $e^+e^-\to\Lambda_c^+\bar{\Lambda}_c^-$ and $e^+e^-\to\psi(2S)\pi^+\pi^-$ cross-sections reveal markedly different pole structures for the $\psi(4360)$. 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 $\psi(4660)$ pole found on the unphysical Riemann sheet above the $\Lambda_c^+\bar{\Lambda}_c^-$ threshold is associated with a bare pole on the real axis in both fits.