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Study of the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>η</mml:mi></mml:math> and observation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="…
The decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$ is observed for the first time, using ${e}^{+}{e}^{\ensuremath{-}}$ collision data corresponding to an integrated luminosity of $6.32\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta})=(3.12\ifmmode\pm\else\textpm\fi{}0.1{3}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.0{9}_{\mathrm{syst}})%$. The first amplitude …