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

Abstract

We present a theoretical analysis of the $D^{-}\to {\pi }^{+}{\pi }^{-}\ell \bar{\nu }$ and ${\bar{D}}^0\to {\pi }^{+}{\pi }^0\ell \bar{\nu }$ 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 $D\to \rho \ell \nu$, 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.

19 pages, 9 figures, 2 tables. To match the published version

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Cited by in corpus (13)

• Parametrizations of three-body hadronic $B$- and $D$-decay amplitudes in terms of analytic and unitary meson-meson form factors
• Observation of $D^{+}\to f_0(500)e^{+}{\nu }_e$ and Improved Measurements of $D\to \rho e^{+}{\nu }_e$
• Semileptonic Decays of Charmed Mesons to Light Scalar Mesons
• S-wave contributions in ${\bar{B}}_s^0\to (D^0,{\bar{D}}^0){\pi }^{+}{\pi }^{-}$ within perturbative QCD approach
• Hadronic three-body D decays mediated by scalar resonances
• The $D\to \rho$ semileptonic and radiative decays within the light-cone sum rules
• Measurement of the Branching Fraction of the Decay ${\mathbf{B}}^{+}\to {\mathbf{\pi }}^{+}{\mathbf{\pi }}^{-}{\mathbf{\ell }}^{+}{\mathbf{\nu }}_{\mathbf{\ell }}$ in Fully Reconstructed Events at Belle
• Two-Meson Form Factors in Unitarized Chiral Perturbation Theory
• Semileptonic decays $D\to \eta \pi e^{+}{\nu }_e$ in the $a_0(980)$ region
• Four-body Semileptonic Charm Decays $D\to P_1{P}_2{\ell }^{+}{\nu }_{\ell }$ Based on SU(3) Flavor Analysis
• Chiral dynamics and S-wave contributions in ${\bar{B}}^0/D^0\to {\pi }^{\pm }\eta l^{\mp }\nu$ decays
• Studying the localized $CP$ violation and the branching fraction of the ${\bar{B}}^0\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• P wave mesons emitting weak decays of bottom mesons