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We present an amplitude analysis of the decay $D^{0} \rightarrow K^{-}\pi^{+} \pi^{+} \pi^{-}$ based on a data sample of 2.93 ${\mbox{\,fb}^{-1}}$acquired by the BESIII detector at the $\psi(3770)$ resonance. With a nearlybackground free sample of about 16000 events, we investigate the substructureof the decay and determine the relative fractions and the phases among thedifferent intermediate processes. Our amplitude model includes the two-bodydecays $D^{0} \rightarrow \bar{K}^{*0}\rho^{0}$, $D^{0} \rightarrowK^{-}a_{1}^{+}(1260)$ and $D^{0} \rightarrow K_{1}^{-}(1270)\pi^{+}$, thethree-body decays $D^{0} \rightarrow \bar{K}^{*0}\pi^{+}\pi^{-}$ and $D^{0}\rightarrow K^{-}\pi^{+}\rho^{0}$, as well as the four-body decay $D^{0}\rightarrow K^{-}\pi^{+}\pi^{+}\pi^{-}$. The dominant intermediate process is$D^{0} \rightarrow K^{-}a_{1}^{+}(1260)$, accounting for a fit fraction of$54.6\%$.

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