Measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3686</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> from 4.008 to 4.600 GeV and observation of a charged structure in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>π</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3686</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> mass spectrum

We study the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\psi}(3686)$ using $5.1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected at 16 center-of-mass energy ($\sqrt{s}$) points from 4.008 to 4.600 GeV by the BESIII detector operating at the BEPCII collider. The measured Born cross sections for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\psi}(3686)$ are consistent with previous results, but with much improved precision. A fit to the cross section shows contributions from two structures: the first has $M=4209.5\ifmmode\pm\else\textpm\fi{}7.4\ifmmode\pm\else\textpm\fi{}1.4\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and $\mathrm{\ensuremath{\Gamma}}=80.1\ifmmode\pm\else\textpm\fi{}24.6\ifmmode\pm\else\textpm\fi{}2.9\text{ }\text{ }\mathrm{MeV}$, and the second has $M=4383.8\ifmmode\pm\else\textpm\fi{}4.2\ifmmode\pm\else\textpm\fi{}0.8\text{ }\text{ }\mathrm{MeV}/{\mathrm{c}}^{2}$ and $\mathrm{\ensuremath{\Gamma}}=84.2\ifmmode\pm\else\textpm\fi{}12.5\ifmmode\pm\else\textpm\fi{}2.1\text{ }\text{ }\mathrm{MeV}$, where the first errors are statistical and the second systematic. The lower-mass resonance is observed in the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\psi}(3686)$ for the first time with a statistical significance of $5.8\ensuremath{\sigma}$. A charged charmoniumlike structure is observed in the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\psi}(3686)$ invariant mass spectrum for data at $\sqrt{s}=4.416\text{ }\text{ }\mathrm{GeV}$. A fit with an $S$-wave Breit-Wigner function yields a mass $M=4032.1\ifmmode\pm\else\textpm\fi{}2.4\text{ }\text{ }\mathrm{MeV}/{c}^{2}$, where the errors are statistical only. However, there are still unresolved discrepancies between the fit model and data. The width of the intermediate state varies in a wide range for different kinematic regions within the data set. Therefore, no simple interpretation of the data has been found, and a future data sample with larger statistics and more theoretical input will be required to better understand this issue.