We study the reaction e(+)e(-) -> pi(+)pi(-)pi(0)eta(c) for the first time using data samples collected with the BESIII detector at center-of-mass energies root s = 4.226, 4.258, 4.358, 4.416, and 4.600 GeV. Evidence of this process is found and the Born cross section sigma(B) (e(+)e(-) -> pi(+)pi(-)pi(0)eta(c)), excluding e(+)e(-) -> omega eta(c) and eta eta(c), is measured to be (46(-11)(+12) +/- 10) pb at root s = 4.226 GeV. Evidence for the decay Z(c) (3900)(+/-) -> rho(+/-)eta(c) is reported at root s = 4.226 GeV with a significance of 3.9 sigma, including systematic uncertainties, and the Born cross section times branching fraction sigma(B)(e(+)e(-) -> pi(-/+)Z(c) (3900)(+/-)) x B(Z(c)(3900)(+/-) -> rho(+/-)eta(c)) is measured to be (48 +/- 11 +/- 11) pb, which indicates that e(+) e(-)-> pi(-/+)Z(c) (3900)(+/-) -> pi(-/+)rho(+/-)eta(c) dominates the e(+) e(-) -> pi(+)pi(-)pi(0)eta(c) process. The Z(c)(3900)(+/-)->rho(+/-)eta(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)(+/-) -> rho(+/-)eta(c) with the same data samples. The ratios R-Zc(3900) = B(Z(c)(3900)(+/-) -> rho(+/-)eta(c))/B(Z(c)(3900)(+/-) -> pi(+/-)J/psi) and RZ(c)((4020)) = B(Z(c)(4020)(+/-) -> rho(+/-)eta(c))/B(Z(c)(4020)(+/-) -> pi(+/-)eta(c)) are obtained and compared with different theoretical interpretations of the Z(c)(3900)(+/-) and Z(c)(4020)(+/-).
展开▼
