Measurements of branching fractions of $D^0\to K^- 3π^+2π^-$, $D^0\to K^- 2π^+π^-2π^0$ and $D^+\to K^- 3π^+π^-π^0$

Utilizing $7.9\,\rm fb^{-1}$ of $e^+e^-$ collision data taken with the BESIII detector at the center-of-mass energy of 3.773 GeV, we report the measurements of absolute branching fractions of the hadronic decays $D^0\to K^- 3π^+2π^-$, $D^0\to K^- 2π^+π^-2π^0$ and $D^+\to K^- 3π^+π^-π^0$. The $D^0\to K^- 3π^+2π^-$ decay is measured with improved precision, while the latter two decays are observed with statistical significance higher than $5σ$ for the first time. The absolute branching fractions of these decays are determined to be ${\mathcal B}(D^0\to K^- 3π^+2π^-)=( 1.35\pm 0.23\pm 0.08 )\times 10^{-4}$, ${\mathcal B}(D^0\to K^- 2π^+π^-2π^0)=( 19.0\pm 1.1\pm 1.5)\times 10^{-4}$, and ${\mathcal B}(D^+\to K^- 3π^+π^-π^0)=( 6.57\pm 0.69\pm 0.33)\times 10^{-4}$, where the first uncertainties are statistical and the second systematic.