Analysis of the decays ψ′ → J/ψπ+π− and η′c → ηcπ+π− with the heavy-quark symmetry

In this article, we study the decays ψ′ → J/ψπ+π− and η′c → ηcπ+π− by taking into account the chiral symmetry breaking effects, the final-state interactions and the heavy-quark symmetry. We can confront the predictions of the η′c → ηcπ+π− decay width and differential decay width with the experimental data in the future, and obtain powerful constraints on the chiral breaking effects and the final-state interactions, and test the heavy-quark symmetry.