Measurement of the absolute branching fraction of the inclusive decay Ds plus ? p plus p plus p-X

Using an e thorn e- collision data sample with a total integrated luminosity of 3.19 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 thorn s meson to final states including at least three charged pions is measured for the first time to be BoD thorn s & RARR; & pi; thorn & pi; thorn & pi;-X thorn 1/4 o32.81 ⠂0.35stat ⠂0.63syst thorn %. In this measurement the charged pions from K0S meson decays are excluded. The partial branching fractions of D thorn s & RARR;& pi; thorn & pi; thorn & pi;-X are also measured as a function of the & pi; thorn & pi; thorn & pi;- invariant mass.