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Search for the isospin violating decay $Y(4260)\rightarrow J/ψηπ^{0}$

Using data samples collected at center of mass energies of $\sqrt{s}$ = 4.009, 4.226, 4.257, 4.358, 4.416 and 4.599 GeV with the BESIII detector operating at the BEPCII storage ring, we search for the isospin violating decay $Y(4260)\rightarrow J/ψηπ^{0}$. No signal is observed, and upper limits on the cross section $σ(e^{+}e^{-}\rightarrow J/ψηπ^{0})$ at the 90\% confidence level are determined to be 3.6, 1.7, 2.4, 1.4, 0.9 and 1.9 pb, respectively.