Abstract
We present a theoretical analysis of the D^-rightarrow pi ^+pi ^- ell bar{nu } and bar{D}^0rightarrow 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 Drightarrow 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.
Highlights
The Cabbibo–Kobayashi–Maskawa (CKM) matrix elements are key parameters in the Standard Model (SM)
For leptons do not participate in the strong interaction, all the strong dynamics is included in the form factors; a e-mail: wei.wang@sjtu.edu.cn b e-mail: shuai.zhao@sjtu.edu.cn it provides a good platform to measure the form factors
The internal structure of light mesons is an important issue in hadron physics
Summary
The Cabbibo–Kobayashi–Maskawa (CKM) matrix elements are key parameters in the Standard Model (SM) They are essential to understand CP violation within the SM and search for new physics (NP). It is difficult to study light mesons by QCD perturbation theory due to the large strong coupling in the low-energy region. 452 Page 2 of 13 lated by using unitarized chiral perturbation theory Based on these results, we present a full analysis on the angular distribution of D → π π ν. We explore various distribution observables, including the differential decay width, the S-wave fraction, forward–backward asymmetry, and so on. These results will be collected in Sect. The details of the coefficients in angular distributions are relegated to the appendix
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