Chiral dynamics, S-wave contributions and angular analysis in D → ππl anti ν

We present a theoretical analysis of the D^- → π⁺π^-l anti ν and anti D⁰ → π⁺π⁰l anti ν decays. We construct a general angular distribution which can include arbitrary partial waves of ππ. Retaining the S-wave and P-wave contributions we study the branching ratios, forward-backward asymmetries and a few other observables. The P-wave contribution is dominated by ρ⁰ resonance, and the S-wave contribution is analyzed using the unitarized chiral perturbation theory. The obtained branching fraction for D → ρlν, at the order 10^-3, is consistent with the available experimental data. The S-wave contribution has a branching ratio at the order of 10^-4, and this prediction can be tested by experiments like BESIII and LHCb. Future measurements can also be used to examine the π-π scattering phase shift. (orig.)