Observation of $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ and study of $D^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ decay dynamics

Abstract

Using $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector at the center-of-mass energy of 3.773 GeV,we investigate the semileptonic decays $D^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ ($\ell =e$ and $\mu$). The $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ decay is observed for the first time. By analyzing simultaneously the differential decay rates of $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ and $D^{+}\to f_0(500)e^{+}{\nu }_e$ in different ${\ell }^{+}{\nu }_{\ell }$ four-momentum transfer intervals, the product of the relevant hadronic form factor $f_{+}^{f_0}(0)$ and the magnitude of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ is determined to be $f_{+}^{f_0}(0)|V_{cd}|=0.143\pm 0.014_{\mathrm{stat}}\pm 0.011_{\mathrm{syst}}$ for the first time. With the input of $|V_{cd}|$ from the global fit in the standard model, we determine $f_{+}^{f_0}(0)=0.63\pm 0.06_{\mathrm{stat}}\pm 0.05_{\mathrm{syst}}$. The absolute branching fractions of $D^{+}\to f_0(500{)}_{({\pi }^{+}{\pi }^{-})}{\mu }^{+}{\nu }_{\mu }$ and $D^{+}\to {\rho }_{({\pi }^{+}{\pi }^{-})}^0{\mu }^{+}{\nu }_{\mu }$ are determined as $(0.72\pm 0.13_{\mathrm{stat}}\pm 0.08_{\mathrm{syst}})\times 10^{-3}$ and $(1.64\pm 0.13_{\mathrm{stat}}\pm 0.10_{\mathrm{syst}})\times 10^{-3}$. Combining these results with those of previous BESIII measurements on their semielectronic counterparts from the same data sample, we test lepton flavor universality by measuring the branching fraction ratios ${\mathcal{B}}_{D^{+}\to {\rho }^0{\mu }^{+}{\nu }_{\mu }}/{\mathcal{B}}_{D^{+}\to {\rho }^0{e}^{+}{\nu }_e}=0.88\pm 0.10$ and ${\mathcal{B}}_{D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }}/{\mathcal{B}}_{D^{+}\to f_0(500)e^{+}{\nu }_e}=1.14\pm 0.26$, which are compatible with the standard model expectation.

Final version accepted for publication

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