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Using data corresponding to an integrated luminosity of 651 pb−1 accumulated at 22 center-of-mass energy points between 2.0000 and 3.0800 GeV by the BESIII experiment, the process e+e−→ϕπ+π− is studied. The Born cross sections for e+e−→ϕπ+π− are consistent with previous results, but with improved precision. A fit to the cross section is performed, which reveals contributions from two structures: the first one has a mass of M = (2158+30−33 ± 4) MeV/c2 and a width of Γ = (218+81−64 ± 5) MeV, and the second one has a mass of M = (2298+60−44 ± 6) MeV/c2 and a width of Γ = (219+117−112 ± 6) MeV, where the first uncertainties are statistical and the second systematic.
Using an e+e− collision data sample with a total integrated luminosity of 3.19 fb−1 collected with the BESIII detector at a center-of-mass energy of 4.178 GeV, the branching fraction of the inclusive decay of the D+s meson to final states including at least three charged pions is measured for the first time to be B(D+s→π+π+π−X)=(32.81±0.35stat±0.63syst)%. In this measurement the charged pions from K0S meson decays are excluded. The partial branching fractions of D+s→π+π+π−X are also measured as a function of the π+π+π− invariant mass.
Using an e+e− collision data sample with a total integrated luminosity of 3.19 fb−1 collected with the BESIII detector at a center-of-mass energy of 4.178 GeV, the branching fraction of the inclusive decay of the D+s meson to final states including at least three charged pions is measured for the first time to be B(D+s→π+π+π−X)=(32.81±0.35stat±0.82syst)%. In this measurement the charged pions from K0S meson decays are excluded. The partial branching fractions of D+s→π+π+π−X are also measured as a function of the π+π+π− invariant mass.