Improved measurement of the decays $η' \to π^{+}π^{-}π^{+(0)}π^{-(0)}$ and search for the rare decay $η' \to 4π^{0}$
Using a sample of 10 billion $J/ψ$ events collected with the BESIII detector, the decays $η' \to π^{+}π^{-}π^{+}π^{-}$, $η' \to π^{+}π^{-}π^{0}π^{0}$ and $η' \to 4 π^{0}$ are studied via the process $J/ψ\toγη'$. The branching fractions of $η' \to π^{+}π^{-}π^{+}π^{-}$ and $η' \to π^{+}π^{-}π^{0}$ $π^{0}$ are measured to be $( 8.56 \pm 0.25({\rm stat.}) \pm 0.23({\rm syst.}) ) \times {10^{ - 5}}$ and $(2.12 \pm 0.12({\rm stat.}) \pm 0.10({\rm syst.})) \times {10^{ - 4}}$, respectively, which are consistent with previous measurements but with improved precision. No significant $η' \to 4 π^{0}$ signal is observed, and the upper limit on the branching fraction of this decay is determined to be less than $1.24 \times {10^{-5}}$ at the $90\%$ confidence level. In addition, an amplitude analysis of $η' \to π^{+}π^{-}π^{+}π^{-}$ is performed to extract the doubly virtual isovector form factor $α$ for the first time. The measured value of $α=1.22 \pm 0.33({\rm stat.}) \pm 0.04({\rm syst.})$, is in agreement with the prediction of the VMD model.