Simultaneous Dalitz-plot decomposition of the $e^{+}{e}^{-}\to J\mathrm{/}\psi \pi \pi (K\bar{K})$ processes in the 4.13-4.36 GeV region using dispersive final-state interactions

We present a joint analysis of the processes $e^{+}{e}^{-}\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}\to J\mathrm{/}\psi K^{+}{K}^{-}$ at center-of-mass energies from 4.13 to 4.36 GeV. The amplitudes are constructed using the Dalitz-plot decomposition formalism, with the $e^{+}{e}^{-}$ energy dependence encoded through the $Y(4220)$ and $Y(4320)$ resonant structures together with a non-resonant production mechanism. The scalar $\pi \pi \mathrm{/}K\bar{K}$ final-state interaction is treated dispersively using a coupled-channel Omnès representation. This allows us to describe the measured total cross sections and one-dimensional invariant-mass distributions with a single set of energy-independent parameters. We find that a purely resonant description of the BESIII data is insufficient, requiring a non-resonant term at the amplitude level which undergoes $\pi \pi \mathrm{/}K\bar{K}$ rescattering. Within the present isobar model, we extract Breit-Wigner parameters for the $Z_c(3900)$, $Y(4220)$, and $Y(4320)$ states, and determine the corresponding subprocess cross sections.