First observation of $eta(1405)$ decays into $f_{0}(980)pi^0$

The decays $J/psi rightarrow gamma pi^+pi^-pi^0$ and $J/psi rightarrow gamma pi^0pi^0pi^0$ are analyzed using a sample of 225 million $jpsi$ events collected with the BESIII detector. The decay of $eta(1405)ar f_{0}(980)pi^0$ with a large isospin violation is observed for the first time. The width of the $f_{0}(980)$ observed in the dipion mass spectra is anomalously narrower than the world average. Decay rates for three-pion decays of the $eta$ are also measured precisely.