# Chiral dynamics, S-wave contributions and angular analysis in $D\rightarrow \pi \pi \ell \bar{\nu }$

The European Physical Journal C, Jul 2017

We present a theoretical analysis of the $D^-\rightarrow \pi ^+\pi ^- \ell \bar{\nu }$ and $\bar{D}^0\rightarrow \pi ^+\pi ^0 \ell \bar{\nu }$ decays. We construct a general angular distribution which can include arbitrary partial waves of $\pi \pi$. 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 $\rho ^0$ resonance, and the S-wave contribution is analyzed using the unitarized chiral perturbation theory. The obtained branching fraction for $D\rightarrow \rho \ell \nu$, 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 $\pi$–$\pi$ scattering phase shift.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-017-5016-1.pdf

Yu-Ji Shi, Wei Wang, Shuai Zhao. Chiral dynamics, S-wave contributions and angular analysis in $D\rightarrow \pi \pi \ell \bar{\nu }$, The European Physical Journal C, 2017, 452, DOI: 10.1140/epjc/s10052-017-5016-1