Improved Measurements of $D^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D^{+}\to \hat{I}\cdot \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$

Abstract

Using 20.3 fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the branching fractions of $D^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D^{+}\to \hat{I}\cdot \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ to be $(9.75\pm 0.29\pm 0.28)\times 10^{-4}$ and $(9.08\pm 0.35\pm 0.23)\times 10^{-4}$, where the first and second uncertainties are statistical and systematic, respectively. From a simultaneous fit to their partial decay rates, we determine the product of the hadronic form factor $f^{\hat{I}}{\cdot }_{+}(0)$ and the modulus of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ to be $f^{\hat{I}}{\cdot }_{+}(0)|V_{cd}|=0.078\pm 0.002\pm 0.001$. Taking the $|V_{cd}|$ value from the Standard Model global fit as input, we obtain $f^{\hat{I}}{\cdot }_{+}(0)=0.345\pm 0.008\pm 0.003$. The ratio between the measured branching fractions of $D^{+}\to \hat{I}{\cdot }^{+}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$, is determined to be $0.93\pm 0.05_{stat.}\pm 0.02_{syst.}$, indicating no violation of lepton flavor universality.