Amplitude analysis of $D^0\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$

We present an amplitude analysis of the decay $D^{0} \rightarrow K^{-} \pi^{+} \pi^{+} \pi^{-}$basedonadatasampleof2.93${\mbox{,fb}^{-1}}$acquiredbytheBESIIIdetectoratthe$\psi(3770)$ resonance. With a nearly background free sample of about 16000 events, we investigate the substructure of the decay and determine the relative fractions and the phases among the different intermediate processes. Our amplitude model includes the two-body decays $D^0\to {\bar{K}}^{\ast 0}{\rho }^0$, $D^{0} \rightarrow K^{-}a_{1}^{+}(1260)$and$D^{0} \rightarrow K_{1}^{-}(1270)\pi^{+}$, the three-body decays $D^0\to {\bar{K}}^{\ast 0}{\pi }^{+}{\pi }^{-}$ and $D^{0} \rightarrow K^{-}\pi^{+}\rho^{0}$,aswellasthefour-bodydecay$D^{0} \rightarrow K^{-}\pi^{+}\pi^{+}\pi^{-}$\mathrm{.}Thedominantintermediateprocessis$D^{0} \rightarrow K^{-}a_{1}^{+}(1260)$,accountingforafitfractionof$54.6%$.