Up-down asymmetries and angular distributions in D→K1(→Kππ)ℓ+νℓ

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for cascade $D\to K_{1}(1270,1400)\ell^+\nu_{\ell}\to (K\pi\pi)\ell^+\nu_{\ell} (\ell=e,\mu)$, in which electron muon mass is explicitly included. a set of phenomenological results K_1$ form factors, calculate partial branching fractions $D^0\to K_1^-\ell^+\nu_{\ell}$ $D^+\to K_1^0\ell^+\nu_{\ell}$, but find that ${\cal B}(D\to K_1(1270)e^+\nu_{e})$ are larger than recent BESIII measurements by about factor 1.5. We further demonstrate measurement up-down asymmetry K_{1}e^+\nu_e\to (K\pi\pi)e^+\nu_{e}$ K_{1}\ell^+\nu_\ell\to (K\pi\pi)\ell^+\nu_{\ell}$ can help to determine hadronic requested $B\to K_1(\to K\pi\pi)\gamma$. Based on Monte-Carlo simulation with LHCb geometrical acceptance, MC events be well described.