Simultaneous description of the <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi><mi>π</mi><mo>(</mo><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover><mo>)</mo></math> processes

In this work, we provide a simultaneous and accurate description of the π+π− and π&#177;J/ψ invariant mass distributions of the recent BESIII data on e+e−→J/ψπ+π−, together with the e+e−→J/ψK+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&#232;s formalism. Since the physical region of the ππ invariant mass extends above 1 GeV, the important KK&#175; 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/ψKK&#175;, 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.