First Measurement of the $D_s^{+}\to K^{\ast }(892{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ Decay, Study of Dynamics and Test of Lepton Universality with $D_s^{+}\to K^{\ast }(892{)}^0{\ell }^{+}\hat{I}{½}_{\ell }$ Decays

Abstract

We report the first measurement of the semileptonic decay $D_s^{+}\to K^{\ast }(892{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and an improved measurement of the decay $D_s^{+}\to K^{\ast }(892{)}^0{e}^{+}\hat{I}{½}_e$ using a sample of $7.33{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at center-of-mass energies between 4.128 to 4.226~GeV with the BESIII detector at the BEPCII collider. We measure the branching fractions to be $\mathcal{B}(D_s^{+}\to K^{\ast }(892{)}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=(2.07\pm 0.22_{\mathrm{stat}}\pm 0.10_{\mathrm{syst}})\times 10^{-3}$ and $\mathcal{B}(D_s^{+}\to K^{\ast }(892{)}^0{e}^{+}\hat{I}{½}_e)=(2.14\pm 0.18_{\mathrm{stat}}\pm 0.10_{\mathrm{syst}})\times 10^{-3}$. Based on a simultaneous study of the dynamics in two semileptonic decays, the hadronic form factor parameters in the $D_s^{+}\to K^{\ast }(892{)}^0$ transition are determined to be $r_V=V(0)/A_1(0)=1.63\pm 0.14_{\mathrm{stat}}\pm 0.08_{\mathrm{syst}}$, $r_2=A_2(0)/A_1(0)=0.60\pm 0.13_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}}$, and $A_1(0)=0.56\pm 0.02_{\mathrm{stat}}\pm 0.01_{\mathrm{syst}}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial-vector form factors evaluated at $q^2=0$. The precision of $r_V$ and $r_2$ is improved by twofold and $A_1(0)$ is measured for the first time. We also report the first model-independent measurements of the differential decay rates and the lepton forward-backward asymmetries for $D_s^{+}\to K^{\ast }(892{)}^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays. Based on these measurements, we perform a test of lepton flavor universality in full and separate $q^2$ intervals with $D_s^{+}\to K^{\ast }(892{)}^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays. No violation is found within uncertainties. Our results present for the first time a complete study of the dynamics in the $D_s^{+}\to K^{\ast }(892{)}^0$ transition, and provide stringent tests of various non-perturbative theoretical calculations.

12 pages, 6 figures