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

Using e + e − annihilation data corresponding to a total integrated luminosity of 6.32 fb −1 collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we perform an amplitude analysis of the decay ${D}_{s}^{+}$ → K − K + π + π + π − and determine the relative fractions and phases of different intermediate processes. Absolute branching fraction of ${D}_{s}^{+}$ → K − K + π + π + π − decay is measured to be (6.60 ± 0.47stat. ± 0.38syst. ) × 10 −3. The dominant intermediate process is ${D}_{s}^{+}$ → a 1(1260)+ ϕ, ϕ → K − K + , a 1(1260)+ → ρπ + , ρ → π + π − , with a branching fraction of (5.15 ± 0.41stat. ± 0.32syst. ) × 10 −3.