Improved measurement of the decays η′ →π+π-π+ (0)π- (0) and search for the rare decay η′ →4π0

Using a sample of 10 billion J/ψ events collected with the BESIII detector, the decays η′→π+π-π+π-, η′→π+π-π0π0 and η′→4π0 are studied via the process J/ψ→γη′. The branching fractions of η′→π+π-π+π- and η′→π+π-π0 π0 are measured to be (8.56±0.25(stat)±0.23(syst))×10-5 and (2.12±0.12(stat)±0.10(syst))×10-4, respectively, which are consistent with previous measurements but with improved precision. No significant η′→4π0 signal is observed, and the upper limit on the branching fraction of this decay is determined to be less than 1.24×10-5 at the 90% confidence level. In addition, an amplitude analysis of η′→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±0.33(stat)±0.04(syst), is in agreement with the prediction of the vector meson dominance model.