Measurement of the absolute branching fraction of the inclusive decay ${D}_{s}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}X$

Using an ${e}^{+}{e}^{-}$ collision data sample with a total integrated luminosity of $3.19\text{}\text{}{\mathrm{fb}}^{-1}$ collected with the BESIII detector at a center-of-mass energy of 4.178 GeV, the branching fraction of the inclusive decay of the ${D}_{s}^{+}$ meson to final states including at least three charged pions is measured for the first time to be $B\left({D}_{s}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}X\right)=\left(32.81±0.3{5}_{\mathrm{stat}}±0.6{3}_{\mathrm{syst}}\right)%$. In this measurement the charged pions from ${K}_{S}^{0}$ meson decays are excluded. The partial branching fractions of ${D}_{s}^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}X$ are also measured as a function of the ${\pi }^{+}{\pi }^{+}{\pi }^{-}$ invariant mass.