Simultaneous description of the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ processes

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-Omnès 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.