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Dalitz plot analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>→</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:math>decay
Using $281\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data recorded by the CLEO-c detector in ${e}^{+}{e}^{\ensuremath{-}}$ collisions at the $\ensuremath{\psi}(3770)$, corresponding to $0.78\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${D}^{+}{D}^{\ensuremath{-}}$ pairs, we investigate the substructure of the decay ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$ using the Dalitz plot technique. We find that our data are consistent with the following intermediate states: $\ensuremath{\rho}(770){\ensuremath{\pi}}^{+}$, ${f}_{2}(1270){\ensuremath{\pi}}^{+}$, ${f}_{0}(1370){\ensuremath{\pi}}^{+}$, …