Simultaneous description of the e + e − → J / ψ π π ( K K ¯ ) processes

In this work, we provide a simultaneous and accurate description of the π+ π− and π± J / ψ invariant mass distributions of the recent BESIII data on e+ e− → J / ψ π+ π−, together with the e+ e− → J / ψ 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 π π invariant mass extends above 1 GeV, the important KK 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 Zc ( 3900 ) in t and u channels, while the other contributions are absorbed in the subtraction constants. For the e+ e− → J / ψ KK, 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.