Amplitude analysis and branching fraction measurement of the Cabibbo-favored decay $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^0$

An amplitude analysis of the Cabibbo-favored decay $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^0$ is performed, using 7.93 ${\mathrm{f}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector at the center-of-mass energy of 3.773 GeV. The branching fractions of the intermediate processes are measured, with the dominant contribution $D^{+}\to {\bar{K}}^{\ast }(892{)}^0\rho (770{)}^{+}$ observed to have a branching fraction of $(4.15\pm {0.07}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.17}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\mathrm{\%}$. With the detection efficiency derived from the amplitude analysis, the absolute branching fraction of $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^0$ is measured to be $(6.06\pm {0.04}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.07}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\mathrm{\%}$.