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Physical Review Letters（2019）
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摘要
Using a data sample corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded by the BESIII detector at a center-of-mass energy of 3.773 GeV, we present an analysis of the decays ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{e}^{+}{\ensuremath{\nu}}_{e}$ and ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{e}^{+}{\ensuremath{\nu}}_{e}$. By performing a partial wave analysis, the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ $S$-wave contribution to ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{e}^{+}{\ensuremath{\nu}}_{e}$ is observed to be $(25.7\ifmmode\pm\else\textpm\fi{}1.6\ifmmode\pm\else\textpm\fi{}1.1)%$ with a statistical significance greater than $10\ensuremath{\sigma}$, besides the dominant $P$-wave contribution. This is the first observation of the $S$-wave contribution. We measure the branching fractions $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e})=(1.445\ifmmode\pm\else\textpm\fi{}0.058\ifmmode\pm\else\textpm\fi{}0.039)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$, $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{e}^{+}{\ensuremath{\nu}}_{e})=\phantom{\rule{0ex}{0ex}}(1.860\ifmmode\pm\else\textpm\fi{}0.070\ifmmode\pm\else\textpm\fi{}0.061)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}3}$, and $\mathcal{B}\mathbf{(}{D}^{+}\ensuremath{\rightarrow}{f}_{0}(500){e}^{+}{\ensuremath{\nu}}_{e},{f}_{0}(500)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\mathbf{)}=(6.30\ifmmode\pm\else\textpm\fi{}0.43\ifmmode\pm\else\textpm\fi{}0.32)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}4}$. An upper limit of $\mathcal{B}\mathbf{(}{D}^{+}\ensuremath{\rightarrow}{f}_{0}(980){e}^{+}{\ensuremath{\nu}}_{e},{f}_{0}(980)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\mathbf{)}<2.8\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}5}$ is set at the 90% confidence level. We also obtain the hadronic form factor ratios of $D\ensuremath{\rightarrow}\ensuremath{\rho}{e}^{+}{\ensuremath{\nu}}_{e}$ at ${q}^{2}=0$ assuming the single-pole dominance parametrization: ${r}_{V}={[V(0)]/[{A}_{1}(0)]}=1.695\ifmmode\pm\else\textpm\fi{}0.083\ifmmode\pm\else\textpm\fi{}0.051$, ${r}_{2}={[{A}_{2}(0)]/[{A}_{1}(0)]}=\phantom{\rule{0ex}{0ex}}0.845\ifmmode\pm\else\textpm\fi{}0.056\ifmmode\pm\else\textpm\fi{}0.039$.
