Observation of $D^+ \to f_0(500) e^+\nu_e$ and Improved Measurements of $D \to\rho e^+\nu_e$

Abstract

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 D¯0→π+π0e−ν¯e 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 parameterization: rV=V(0)A1(0)=1.695±0.083±0.051, r2=A2(0)A1(0)=0.845±0.056±0.039.