Observation of D+ →f0 (500)e+νe and Improved Measurements of D →ρe+νe

Using a data sample corresponding to an integrated luminosity of 2.93 fb-1 recorded by the BESIII detector at a center-of-mass energy of 3.773 GeV, we present an analysis of the decays D0→π-π0e+νe and D+→π-π+e+νe. By performing a partial wave analysis, the π+π-S-wave contribution to D+→π-π+e+νe is observed to be (25.7±1.6±1.1)% with a statistical significance greater than 10σ, besides the dominant P-wave contribution. This is the first observation of the S-wave contribution. We measure the branching fractions B(D0→ρ-e+νe)=(1.445±0.058±0.039)×10-3, B(D+→ρ0e+νe)=(1.860±0.070±0.061)×10-3, and B(D+→f0(500)e+νe,f0(500)→π+π-)=(6.30±0.43±0.32)×10-4. An upper limit of B(D+→f0(980)e+νe,f0(980)→π+π-)<2.8×10-5 is set at the 90% confidence level. We also obtain the hadronic form factor ratios of D→ρe+νe at q2=0 assuming the single-pole dominance parametrization: rV={[V(0)]/[A1(0)]}=1.695±0.083±0.051, r2={[A2(0)]/[A1(0)]}=0.845±0.056±0.039.