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By considering the contributions of intermediate charmed mesons triangle loops within an effective Lagrangian approach, it is shown that the calculated partial widths of $Z_c(3900) \\to \\gamma \\chi_{cJ}$ are about a few hundreds keVs, while the obtained partial widths $Z_c(4020) \\to \\gamma \\chi_{cJ}$ are about tens of keVs. 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By considering the contributions of intermediate charmed mesons triangle loops within an effective Lagrangian approach, it is shown that the calculated partial widths of $Z_c(3900) \\to \\gamma \\chi_{cJ}$ are about a few hundreds keVs, while the obtained partial widths $Z_c(4020) \\to \\gamma \\chi_{cJ}$ are about tens of keVs. 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