Discussions on the Line-shape of $X(4660)$ Resonance

Abstract

A careful reanalysis is made on $e^{+}{e}^{-}\to X(4660)\to ({\Lambda }_c{\bar{\Lambda }}_c)/({\psi }^{\prime }\pi \pi )$ processes, aiming at resolving the apparent conflicts between Belle and BESIII data above ${\Lambda }_c{\bar{\Lambda }}_c$ threshold. We use a model containing a Breit-Wigner resonance and ${\Lambda }_c{\bar{\Lambda }}_c$ four-point contact interactions, with which the enhancement right above the ${\Lambda }_c{\bar{\Lambda }}_c$ threshold is well explained by a virtual pole generated by ${\Lambda }_c{\bar{\Lambda }}_c$ attractive final state interaction, located at $M_V=4.566\pm 0.007$ GeV. Meanwhile, $X(4660)$ remains to be a typical Breit-Wigner resonance, and is hence of confinement nature. Our analysis strongly suggests the existence of the virtual pole with statistical significance of $4.2$ standard deviation ($\sigma$). Nevertheless, the conclusion crucially depends on the line-shape of cross sections which are of limited statistics, hence we urge new experimental analyses from Belle II, BESIII, and LHCb to settle the issue.

Comments: 7 pages, 7 figures