Study of the Decay D-s(+) -> pi(+) pi(+) pi(-)eta and Observation of the W-annihilation Decay D-s(+) -> a(0)(980)(+)rho(0)

Abstract

The decay D-s(+) -> pi(+) pi(+) pi(-)eta is observed for the first time, using e(+)e(-) collision data corresponding to an integrated luminosity of 6.32 fb(-1), collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be B(D-s(+) -> pi(+) pi(+) pi(-)eta) = (3.12 +/- 0.13(stat) +/- 0.09(syst))% The first amplitude analysis of this decay reveals the substructures in D-s(+) -> pi(+) pi(+) pi(-)eta and determines the relative fractions and the phases among these substructures. The dominant intermediate process is D-s(+) -> a(1)(1260)(+)eta, a(1)(1260)(+) -> rho(770)(0)pi(+) with a branching fraction of (1.73 +/- 0.14(stat) +/- 0.08(syst))%. We also observe the W-annihilation process D-s(+) -> a(0)(980)(+) rho(770)(0), a(0)(980)(+) -> pi(+)eta. with a branching fraction of (0.21 +/- 0.08(stat) +/- 0.05(syst))%, which is larger than the branching fractions of other measured pure W-annihilation decays by 1 order of magnitude.