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

## TL;DR

This paper reanalyzes the $X(4660)$ resonance line-shape in $e^+e^-$ processes, proposing a virtual pole explanation for threshold enhancements and confirming the resonance's confinement nature, while emphasizing the need for more experimental data.

## Contribution

The study introduces a model combining Breit-Wigner resonance and contact interactions to explain the $X(4660)$ line-shape, revealing a virtual pole near the $ ext{Lambda}_car{ ext{Lambda}}_c$ threshold.

## Key findings

- Identification of a virtual pole at 4.566 GeV with 4.2σ significance.
- Confirmation that $X(4660)$ is a typical Breit-Wigner resonance.
- Highlighting the dependence of conclusions on limited statistical data.

## Abstract

A careful reanalysis is made on $e^+e^-\to X(4660)\to (\Lambda_c\bar{\Lambda}_c)/(\psi'\pi\pi)$ 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 $M_V=4.566\pm0.007$ 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.