Study of the $f_0(980)$ and $f_0(500)$ Scalar Mesons through the Decay $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{e}^{+}\hat{I}{½}_e$

Abstract

Using $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of 7.33~$\mathrm{f}{\mathrm{b}}^{-1}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226~$\mathrm{GeV}$, we present an analysis of the decay $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{e}^{+}\hat{I}{½}_e$, where the $D_s^{+}$ is produced via the process $e^{+}{e}^{-}\to D_s^{\ast \pm }{D}_s^{\mp }$. We observe the $f_0(980)$ in the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ system and the branching fraction of the decay $D_s^{+}\to f_0(980)e^{+}\hat{I}{½}_e$ with $f_0(980)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ measured to be $(1.72\pm 0.13_{\mathrm{stat}}\pm 0.10_{\mathrm{syst}})\times 10^{-3}$, where the uncertainties are statistical and systematic, respectively. The dynamics of the $D_s^{+}\to f_0(980)e^{+}\hat{I}{½}_e$ decay are studied with the simple pole parametrization of the hadronic form factor and the Flatté formula describing the $f_0(980)$ in the differential decay rate, and the product of the form factor $f_{+}^{f_0}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined for the first time to be $f_{+}^{f_0}(0)|V_{cs}|=0.504\pm 0.017_{\mathrm{stat}}\pm 0.035_{\mathrm{syst}}$. Furthermore, the decay $D_s^{+}\to f_0(500)e^{+}\hat{I}{½}_e$ is searched for the first time but no signal is found. The upper limit on the branching fraction of $D_s^{+}\to f_0(500)e^{+}\hat{I}{½}_e,f_0(500)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decay is set to be $3.3\times 10^{-4}$ at 90\% confidence level.

9 pages, 3 figures