Semileptonic $D_{(s)} \to A \ell^+ \nu$ and nonleptonic $D\to K_1(1270,1400) \pi$ decays in LCSR

In this work, the transition form factors are calculated for the semileptonic $D_{(s)} \to A \ell^+ \nu$ where $A=a_{1}, b_{1}, K_{1}(1270,1400)$, i.e., $D^{+} \to a^{0}_{1} (b^{0}_{1}, K^{0}_{1}) \ell^+ \nu$, $D^{0} \to a^{-}_{1} (b^{-}_{1}) \ell^+ \nu$, and $D^{+}_{s}\to K^{0}_{1} \ell^+ \nu$ in the frame work of the light-cone QCD sum rules (LCSR) approach up to the twist-3 distribution amplitudes (DAs). Since the masses of these axial vector mesons are comparable to the charm quark mass, we keep out in our calculations all terms including ${m_{A}}/{m_c}$ in expansion of two--parton DAs. Branching ratio values are estimated for the semileptonic $D_{(s)} \to A \ell \nu$ and nonleptonic $D\to K_1 (1270,1400) \pi$ decays. A comparison is also made between our results and predictions of other methods and the existing experimental values.