Measurements of absolute branching fractions of $D^{0(+)}\to KKK\pi$ decays

Using an $e^{+}{e}^{-}$ sample of $20.3\mathrm{f}{\mathrm{b}}^{-1}$ collected at the center-of-mass energy $\sqrt{s}=$ 3.773 GeV with the BESIII detector, we report measurements of several four-body hadronic decays of the $D$ mesons. The absolute branching fractions are determined to be $\mathcal{B}(D^0\to K_S^0{K}^{+}{K}^{-}{\pi }^0)=(18.4_{-2.5}^{+2.6}\pm 2.4)\times {10}^{-5}$, $\mathcal{B}(D^0\to K_S^0{K}_S^0{K}^{-}{\pi }^{+})=(12.9_{-1.6}^{+1.7}\pm 2.5)\times {10}^{-5}$, $\mathcal{B}(D^0\to K_S^0{K}_S^0{K}^{+}{\pi }^{-})=(5.7_{-1.1}^{+1.2}\pm 1.3)\times {10}^{-5}$, $\mathcal{B}(D^0\to K^{+}{K}^{-}{K}^{-}{\pi }^{+})=(17.4_{-1.7}^{+1.8}\pm 2.2)\times {10}^{-5}$, and $\mathcal{B}(D^{+}\to K_S^0{K}^{+}{K}^{-}{\pi }^{+})=(13.8_{-2.2}^{+2.4}\pm 2.5)\times {10}^{-5}$. Furthermore, significant $\phi$ signals are found in the decay channels involving $K^{+}{K}^{-}$ pair, and the corresponding branching fractions are measured as $\mathcal{B}(D^0\to \phi K_S^0{\pi }^0)=(22.7_{-5.1}^{+5.4}\pm 3.7)\times {10}^{-5}$, $\mathcal{B}(D^0\to \phi K^{-}{\pi }^{+})=(25.2_{-3.3}^{+3.5}\pm 4.6)\times {10}^{-5}$, $\mathcal{B}(D^{+}\to \phi K_S^0{\pi }^{+})=(16.5_{-5.3}^{+6.0}\pm 2.6)\times {10}^{-5}$. The branching fractions of $D^0\to K_S^0{K}^{+}{K}^{-}{\pi }^0$, $D^0\to \phi K_S^0{\pi }^0$, and $D^{+}\to \phi K_S^0{\pi }^{+}$ are measured for the first time, and those of $D^0\to K_S^0{K}_S^0{K}^{-}{\pi }^{+}$, $D^0\to K_S^0{K}_S^0{K}^{+}{\pi }^{-}$, $D^0\to K^{+}{K}^{-}{K}^{-}{\pi }^{+}$, $D^0\to \phi K^{-}{\pi }^{+}$, and $D^{+}\to K_S^0{K}^{+}{K}^{-}{\pi }^{+}$ are measured with improved precision. The first uncertainties are statistical and the second are systematic.