Updated measurement of the branching fraction of $D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„$

Abstract

Using a dataset of 7.33 fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected with the BESIII detector at center-of-mass energies from 4.128 to 4.226 GeV, we report an updated measurement of the branching fraction of $D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„$ via four $\ddot{I}{„}^{+}$ decay modes: $\ddot{I}{„}^{+}\to e^{+}\hat{I}{½}_e\bar{\hat{I}}{½}_{\ddot{I}}„$, $\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼\bar{\hat{I}}{½}_{\ddot{I}}„$, $\ddot{I}{€}^{+}\bar{\hat{I}}{½}_{\ddot{I}}„$, and $\ddot{I}{€}^{+}\ddot{I}{€}^0\bar{\hat{I}}{½}_{\ddot{I}}„$. The branching fraction is determined to be $\mathcal{B}(D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„)=(5.37\pm 0.08_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}})$ %. The product of the modulus of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ and the $D_s^{+}$ decay constant $f_{D_s^{+}}$ is measured to be $f_{D_s^{+}}|V_{cs}|=(248.2\pm 1.9_{\mathrm{stat}}\pm 1.4_{\mathrm{syst}}\pm 0.6_{\mathrm{input}}\pm 0.8_{\mathrm{EM}})$ MeV. Both the branching fraction and the product $f_{D_s^{+}}|V_{cs}|$ are the most precise results yet obtained. Then, taking $f_{D_s^{+}}$ from lattice quantum chromodynamics calculations results in $|V_{cs}|=0.993\pm 0.008_{\mathrm{stat}}\pm 0.006_{\mathrm{syst}}\pm 0.003_{\mathrm{input}}\pm 0.003_{\mathrm{EM}}$. Conversely, one finds $f_{D_s^{+}}=(255.0\pm 1.9_{\mathrm{stat}}\pm 1.4_{\mathrm{syst}}\pm 0.6_{\mathrm{input}}\pm 0.8_{\mathrm{EM}})$ MeV when taking $|V_{cs}|$ from the CKMfitter group as an input. Combining with the world average value of $D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, the ratio of the branching fractions between $D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„$ and $D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ is estimated to be $10.04\pm 0.29$, which is consistent with the Standard Model prediction of lepton flavor universality.

13 pages, 2 figures