Precise measurements of $D^0\to K^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and $D^{+}\to {\bar{K}}^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays

Abstract

Using $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of 20.3 fb${}^{-1}$, collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we present precise measurements of $D^0\to K^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and $D^{+}\to {\bar{K}}^0{\ell }^{+}\hat{I}{½}_{\ell }$ ($\ell =e,\hat{I}¼$) decays. The branching fractions of $D^0\to K^{-}{e}^{+}\hat{I}{½}_e$, $D^0\to K^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, $D^{+}\to {\bar{K}}^0{e}^{+}\hat{I}{½}_e$, and $D^{+}\to {\bar{K}}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ are measured to be $(3.548\pm 0.006_{\mathrm{stat}}\pm 0.017_{\mathrm{syst}})\%$, $(3.445\pm 0.007_{\mathrm{stat}}\pm 0.017_{\mathrm{syst}})\%$, $(8.928\pm 0.025_{\mathrm{stat}}\pm 0.050_{\mathrm{syst}})\%$, and $(8.770\pm 0.029_{\mathrm{stat}}\pm 0.053_{\mathrm{syst}})\%$, respectively. The partial decay rates of these four decays are measured with improved precision, and their forward-backward asymmetries are determined for the first time. By performing a simultaneous fit to the measured partial decay rates and the forward-backward asymmetries of $D\to \bar{K}{\ell }^{+}\hat{I}{½}_{\ell }$, a search for a possible scalar current contribution in the $c\to s{\ell }^{+}\hat{I}{½}_{\ell }$ transition is performed. The results are $\mathrm{Re}(c_S^{\hat{I}}¼)=0.017\pm 0.008_{\mathrm{stat}}\pm 0.006_{\mathrm{syst}}$ and $\mathrm{Im}(c_S^{\hat{I}}¼)=\pm (0.077\pm 0.011_{\mathrm{stat}}\pm 0.009_{\mathrm{syst}})$, corresponding to a difference from the SM with a significance of $2.3\ddot{I}ƒ$. The product of the form factor $f_{+}(0)$ and the modulus of the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined to be $f_{+}(0)|V_{cs}|=0.7183\pm 0.0007_{\mathrm{stat}}\pm 0.0014_{\mathrm{syst}}$. With the inputs $|V_{cs}|=0.97349\pm 0.00016$ from the Standard Model global fit or $\ffK=0.7452\pm0.0031$ from the lattice quantum chromodynamics calculation, we derive $f_{+}(0)=0.7383\pm 0.0007_{\mathrm{stat}}\pm 0.0014_{\mathrm{syst}}$ and $|V_{cs}|=0.9639\pm 0.0009_{\mathrm{stat}}\pm 0.0018_{\mathrm{syst}}\pm 0.0040_{\mathrm{LQCD}}$.

44 pages, 17 figures, submitted to PRD