Observation of $D_s^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, Precision Test of Lepton Flavor Universality with $D_s^{+}\to \hat{I}{\cdot }^{(\prime )}{\ell }^{+}\hat{I}{½}_{\ell }$, and First Measurements of $D_s^{+}\to \hat{I}{\cdot }^{(\prime )}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ Decay Dynamics

Abstract

By analyzing 7.33 fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector, we report the observation of the semileptonic decay $D_s^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, with a statistical significance larger than 10$\ddot{I}ƒ$, and the measurements of the $D_s^{+}\to \hat{I}\cdot \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ decay dynamics for the first time. The branching fractions of $D_s^{+}\to \hat{I}\cdot \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ are determined to be $(2.235\pm 0.051_{\mathrm{stat}}\pm 0.052_{\mathrm{syst}})\%$ and $(0.801\pm 0.055_{\mathrm{stat}}\pm 0.028_{\mathrm{syst}})\%$, respectively, with precision improved by factors of 6.0 and 6.6 compared to the previous best measurements. Combined with the results for the decays $D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$, the ratios of the decay widths are examined both inclusively and in several ${\ell }^{+}\hat{I}{½}_{\ell }$ four-momentum transfer ranges. No evidence for lepton flavor universality violation is found within the current statistics. The products of the hadronic form factors $f_{+,0}^{\hat{I}{\cdot }^{(\prime )}}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ are determined. The results based on the two-parameter series expansion are $f^{\hat{I}}{\cdot }_{+,0}(0)|V_{cs}|=0.452\pm 0.010_{\mathrm{stat}}\pm 0.007_{\mathrm{syst}}$ and $f_{+,0}^{\hat{I}{\cdot }^{\prime }}(0)|V_{cs}|=0.504\pm 0.037_{\mathrm{stat}}\pm 0.012_{\mathrm{syst}}$, which help to constrain present models on $f_{+,0}^{\hat{I}{\cdot }^{(\prime )}}(0)$. The forward-backward asymmetries are determined to be $⟨A_{\mathrm{FB}}^{\hat{I}}\cdot ⟩=-0.059\pm 0.031_{\mathrm{stat}}\pm 0.005_{\mathrm{syst}}$ and $⟨A_{\mathrm{FB}}^{\hat{I}{\cdot }^{\prime }}⟩=-0.064\pm 0.079_{\mathrm{stat}}\pm 0.006_{\mathrm{syst}}$ for the first time, which are consistent with the theoretical calculation.