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The charmonium transitions from the $\chi_{cJ}$ states to $\eta_c$ withemission of one or two pions are considered. It is shown that the onlyprocesses of such type arising in the leading order in the QCD multipoleexpansion are the decays $\chi_{c1} \to \eta_c \pi^+ \pi^-$ and $\chi_{c0} \to\eta_c \pi^0$. The absolute rate of the latter decay, in spite of beingisotopically suppressed, is by about an order of magnitude larger than that ofthe former, so that the branching fractions for the two processes areapproximately equal, and are expected to be significantly below the recentupper bound reported by BESIII. The rates of both decays are also related tothat of another similar transition $h_c \to J/\psi \pi^0$.

Pion transitions from \chi_{cJ} to \eta_c