Study of the $f_{0}(980)$ and $f_{0}(500)$ Scalar Mesons through the Decay $D_{s}^{+} \to π^{+} π^{-} e^{+} ν_{e}$

Abstract

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 7.33~${\rm fb^{-1}}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226~${\rm GeV}$, we present an analysis of the decay $D_{s}^{+} \to π^{+}π^{-} e^{+}ν_{e}$, where the $D_s^+$ is produced via the process $e^+e^- \to D_{s}^{*\pm}D_{s}^{\mp}$. We observe the $f_{0}(980)$ in the $π^+π^-$ system and the branching fraction of the decay $D_{s}^{+} \to f_{0}(980)e^{+}ν_{e}$ with $f_0(980)\toπ^+π^-$ measured to be $(1.72 \pm 0.13_{\rm stat} \pm 0.10_{\rm syst}) \times10^{-3}$, where the uncertainties are statistical and systematic, respectively. The dynamics of the $D_{s}^{+} \to f_{0}(980)e^{+}ν_{e}$ 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 $f^{f_0}_+(0)|V_{cs}|=0.504\pm0.017_{\rm stat}\pm0.035_{\rm syst}$. Furthermore, the decay $D^+_s\to f_0(500) e^+ν_e$ is searched for the first time but no signal is found. The upper limit on the branching fraction of $D^+_s\to f_0(500) e^+ν_e,~f_0(500)\toπ^+π^-$ decay is set to be $3.3 \times 10^{-4}$ at 90\% confidence level.

Figures (3)

• Figure 1: Fit to the $M_{\pi^+\pi^-}$ distribution of the accepted candidates for the decay $D_{s}^{+} \to f_0(980) e^{+}\nu_{e}$. The points with error bars are data, and the blue line is the total fit. The red dotted and violet dashed lines are the signal and background shapes, respectively.
• Figure 2: Fit to the $M^{2}_{\rm miss}$ distribution of the accepted candidates for $D_{s}^{+} \to f_{0}(500) e^{+} \nu_{e}$ decay. The black points with error bars are data, and the blue line is the total fit. The red dotted and violet dashed lines are the signal and background shapes, respectively. The green dotted-dashed line is the decay $D_s^+\to f_0(980)e^+\nu_e$.
• Figure 3: Fit to the differential decay rate as a function of $q^2$ (a) and projection to the form factor $f^{f_{0}}_{+}(q^2)$ (b). The points with error bars are data, and the red line is the fit.