Amplitude analysis and branching fraction measurement of the decay ${D}_{s}^{+}$ → K+ π + π − π 0

The singly Cabibbo-suppressed decay ${D}_{s}^{+}$ → K + π + π − π 0 is observed by using a data set corresponding to an integrated luminosity of 6.32 fb −1 recorded by the BESIII detector at the centre-of-mass energies between 4.178 and 4.226 GeV. The first amplitude analysis of ${D}_{s}^{+}$ → K + π + π − π 0 reveals the sub-structures in this decay and determines the fractions and relative phases of different intermediate processes. The dominant intermediate process is ${D}_{s}^{+}$ → K *0 ρ +, with a fit fraction of (40.5 ± 2.8stat. ± 1.5syst. )%. With the detection efficiency based on our amplitude analysis, the absolute branching fraction for ${D}_{s}^{+}$ → K + π + π − π 0 is measured to be (9.75 ± 0.54stat. ± 0.17syst. ) × 10 −3.