Sensitivity study of ${\bar{K}}_1(1270)$ decay dynamics using four $D\to {\bar{K}}_1(1270)(\to \bar{K}\pi \pi )e^{+}\nu$ decay channels

A sensitivity study for the measurement of ${\bar{K}}_1(1270)$ decay modes is performed using semileptonic $D$-meson decays. The BESIII experiment is taken as a case study, where a simultaneous analysis of ${\bar{K}}_1(1270)$ decays to the four thee-body final states $K^{-}{\pi }^{+}{\pi }^{-}$, $K^{-}{\pi }^{+}{\pi }^0$, $K_S^0{\pi }^{+}{\pi }^{-}$, and $K_S^0{\pi }^{-}{\pi }^0$ is presented and a model-independent determination of \mbox{$\mathcal{B}({\bar{K}}_1(1270)\to \bar{K}\pi \pi )$}, without requiring detailed knowledge of intermediate resonant contributions, is proposed.