Observation of the isospin-violating decay $J/psi to phipi^{0}f_{0}(980)$

Using a sample of 1.31 billion $J/psi$ events collected with the BESIII detector at the BEPCII collider, the decays $J/psi to phi pi^{+}pi^{-}pi^{0}$ and $J/psi to phi pi^{0}pi^{0}pi^{0}$ are investigated. The isospin violating decay $J/psi to phi pi^{0} f_{0}(980)$ with $f_{0}(980) to pipi$, is observed for the first time. The width of the $f_{0}(980)$ obtained from the dipion mass spectrum is found to be much smaller than the world average value. In the $pi^{0} f_{0}(980)$ mass spectrum, there is evidence of $f_1(1285)$ production. By studying the decay $J/psi to phieta$, the branching fractions of $eta to pi^{+}pi^{-}pi^{0}$ and $eta to pi^{0}pi^{0}pi^{0}$, as well as their ratio, are also measured.