Amplitude analysis and branching fraction measurement of the decay $\mathrm{D}_s^+$ → $\mathrm{K}^+π^+π^-π^0$
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 ± 2.8 stat. ± 1.5 syst. )%. 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 ± 0.54 stat. ± 0.17 syst. ) x 10 -3 .