Study of the f0 (980) and f0 (500) Scalar Mesons through the Decay Ds+ →π+π-e+νe

Using e+e- collision data corresponding to an integrated luminosity of 7.33 fb-1 recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV, we present an analysis of the decay Ds+→π+π-e+νe, where the Ds+ is produced via the process e+e-→Ds∗±D. We observe the f0(980) in the π+π- system and the branching fraction of the decay Ds+→f0(980)e+νe with f0(980)→π+π- measured to be (1.72±0.13stat±0.10syst)×10-3, where the uncertainties are statistical and systematic, respectively. The dynamics of the Ds+→f0(980)e+νe decay are studied with the simple pole parametrization of the hadronic form factor and the Flatté formula describing the f0(980) in the differential decay rate, and the product of the form factor f+f0(0) and the c→s Cabibbo-Kobayashi-Maskawa matrix element |Vcs| is determined for the first time to be f+f0(0)|Vcs|=0.504±0.017stat±0.035syst. Furthermore, the decay Ds+→f0(500)e+νe is searched for the first time but no signal is found. The upper limit on the branching fraction of Ds+→f0(500)e+νe, f0(500)→π+π- decay is set to be 3.3×10-4 at 90% confidence level.