Study of e+e-→π+π-π0ηc and evidence for Zc(3900 )± decaying into ρ±ηc

We study the reaction e⁺e^-→π⁺π^-π⁰η_c for the first time using data samples collected with the BESIII detector at center-of-mass energies √{s }=4.226 , 4.258, 4.358, 4.416, and 4.600 GeV. Evidence of this process is found and the Born cross section σ^B(e⁺e^-→π⁺π^-π⁰η_c) , excluding e⁺e^-→ω η_c and η η_c, is measured to be (46_-11⁺¹²±10 ) pb at √{s }=4.226 GeV . Evidence for the decay Z_c(3900 )^±→ρ^±η_c is reported at √{s }=4.226 GeV with a significance of 3.9 σ , including systematic uncertainties, and the Born cross section times branching fraction σ^B(e⁺e^-→π^∓Z_c(3900 )^±)×B (Z_c(3900 )^±→ρ^±η_c) is measured to be (48 ±11 ±11 ) pb , which indicates that e⁺e^-→π^∓Z_c(3900 )^±→π^∓ρ^±η_c dominates the e⁺e^-→π⁺π^-π⁰η_c process. The Z_c(3900 )^±→ρ^±η_c signal is not significant at the other center-of-mass energies and the corresponding upper limits are determined. In addition, no significant signal is observed in a search for Z_c(4020 )^±→ρ^±η_c with the same data samples. The ratios R_Zc(3900)=B (Z_c(3900 )^±→ρ^±η_c)/B (Z_c(3900 )^±→π^±J /ψ ) and R_Zc(4020)=B (Z_c(4020 )^±→ρ^±η_c)/B (Z_c(4020 )^±→π^±h_c) are obtained and compared with different theoretical interpretations of the Z_c(3900 )^± and Z_c(4020 )^± .