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Generalized distribution amplitudes (GDAs) of mesons can be probed by thereactions $e^- e^+ \to M_1 M_2 \gamma$, which are accessible atelectron-positron colliders such as BESIII and Belle II. After discussing theneutral meson production case in the first paper of this series, we discusshere the complementary case of the charged meson ($M^+ M^-$) production, whereone can extract the complete information on GDAs from the interference of theamplitudes of the two competing processes where the photon is emitted either inthe initial or in the final state. Considering the importance of the chargedmeson production, we present a complete expression for the interference term ofthe cross section which is experimentally accessible thanks to its chargeconjugation specific property. We adopt two types of models for leading twist$\pi \pi$ GDAs to estimate the size of the interference term in the process$e^- e^+ \to \pi^+ \pi^- \gamma$ numerically, namely a model extracted fromprevious experimental results on $\gamma^* \gamma \to \pi^0 \pi^0$ at Belle andthe asymptotic form predicted by QCD evolution equations. We include in thecalculation the kinematical higher-twist corrections up to twist 4 for thehelicity amplitudes. Both models of GDAs indicate that the kinematicalcorrections are not negligible for the interference term of the cross sectionmeasured at BESIII, thus it is necessary to include them if we try to extractthe GDAs precisely. On the other side, the kinematical corrections are verytiny for the measurements at Belle II, and the leading twist-2 formula of theinterference term will be good enough to describe the charge conjugation oddpart of the differential cross section.

Kinematical higher-twist corrections in $\gamma^* \to M_1 \bar M_2 \gamma$: II. Charged meson production