Chiral dynamics, S-wave contributions and angular analysis in $D\to ππ\ell\barν$

Abstract

We present a theoretical analysis of the $D^-\to π^+π^- \ell\barν$ and $\bar D^0\to π^+π^0 \ell\barν$ 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 $ρ^0$ resonance, and the S-wave contribution is analyzed using the unitarized chiral perturbation theory. The obtained branching fraction for $D\to ρ\ellν$, 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.