Abstract
In this work, we provide a simultaneous and accurate description of the $\pi^+\pi^-$ and $\pi^{\pm} J/\psi$ invariant mass distributions of the recent BESIII data on $e^+ e^- \to J/\psi \; \pi^+ \pi^-$ together with the $e^+ e^- \to J/\psi \; K^+K^-$ cross sections at $e^+e^-$ center-of-mass energies $q=4.23$ GeV and $q=4.26$ GeV. The rescattering effects between pions in the S and D-waves are taken into account through the Muskhelishvili-Omn\`es formalism. Since the physical region of the $\pi\pi$ invariant mass extends above 1 GeV, the important $K\bar{K}$ intermediate state in the S-wave is implemented through coupled-channel unitarity. For the left-hand cuts, we account for the well established charged exotic state $Z_c(3900)$ in $t$- and $u$-channels, while the other contributions are absorbed in the subtraction constants. For the $e^+ e^- \to J/\psi\, K \bar{K}$ we provide the prediction of the two-kaon invariant mass distribution. The constructed amplitudes serve as an essential framework to interpret the present and forthcoming measurements by the BESIII and Belle II Collaborations.
Highlights
The charged exotic charmoniumlike state Zcð3900Þ was discovered simultaneously by the BESIII and Belle Collaborations in 2013 both in direct production [1] and using initial-state radiation [2], in the process eþe− → J=ψπþπ− and was soon confirmed using the CLEO-c data [3]
To check on the physical importance of the latter, we will compare in the following for the S-wave contribution, the fitted subtraction constants with the sum rule result, which one would obtain from a once-subtracted dispersive formalism
We provided a quantitative and simultaneous description of the πþπ− and πÆJ=ψ invariant mass distributions of the recent BESIII data on eþe− → J=ψπþπ− together with the total cross sections σðJ=ψKþK−Þ at eþe− center-of-mass energies q 1⁄4 4.23 GeV and q 1⁄4 4.26 GeV
Summary
The charged exotic charmoniumlike state Zcð3900Þ was discovered simultaneously by the BESIII and Belle Collaborations in 2013 both in direct production [1] and using initial-state radiation [2], in the process eþe− → J=ψπþπ− and was soon confirmed using the CLEO-c data [3]. The nature of Zcð3900Þ is still a puzzle [11,12,13,14] Most likely it corresponds to a pole in the unphysical Riemann sheet, which could be a hadrocharmonium [15,16], molecular state [13,17], or a virtual state [18,19].
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