Observation of $D^{+}\to f_0(500)\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and study of $D^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ 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 $D^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ ($\ell =e$ and $\hat{I}¼$). The $D^{+}\to f_0(500)\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ decay is observed for the first time. By analyzing simultaneously the differential decay rates of $D^{+}\to f_0(500)\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D^{+}\to f_0(500)e^{+}\hat{I}{½}_e$ in different ${\ell }^{+}\hat{I}{½}_{\ell }$ 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 $D^{+}\to f_0(500{)}_{(\ddot{I}{€}^{+}\ddot{I}{€}^{-})}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D^{+}\to \ddot{I}{}_{(\ddot{I}{€}^{+}\ddot{I}{€}^{-})}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ 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 ${\mathcal{B}}_{D^{+}\to \ddot{I}{}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼}/{\mathcal{B}}_{D^{+}\to \ddot{I}{}^0{e}^{+}\hat{I}{½}_e}=0.88\pm 0.10$ and ${\mathcal{B}}_{D^{+}\to f_0(500)\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼}/{\mathcal{B}}_{D^{+}\to f_0(500)e^{+}\hat{I}{½}_e}=1.14\pm 0.26$, which are compatible with the standard model expectation.

Final version accepted for publication