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

TL;DR

This study measures the decay of $D_s^+$ to $f_0(980)$ and $f_0(500)$ mesons via semileptonic decay channels, providing new insights into the properties of these scalar mesons and their production mechanisms.

Contribution

First measurement of the branching fraction and form factor product for $D_s^+ o f_0(980) e^+ u_e$, and the first search with an upper limit for $D_s^+ o f_0(500) e^+ u_e$ decay.

Findings

Branching fraction of $D_s^+ o f_0(980) e^+ u_e$ measured as $(1.72 imes 10^{-3})$

Product of form factor and CKM element determined as $0.504$

No signal observed for $D_s^+ o f_0(500) e^+ u_e$, upper limit set at $3.3 imes 10^{-4}$

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 $D_{s}^{+} \to \pi^{+}\pi^{-} e^{+}\nu_{e}$, 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 $\pi^+\pi^-$ system and the branching fraction of the decay $D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ with $f_0(980)\to\pi^+\pi^-$ 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 $D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ decay are studied with the simple pole parametrization of the hadronic form factor and the Flatt\'e 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 $D^+_s\to f_0(500) e^+\nu_e$ is searched for the first time but no signal is found. The upper limit on the branching fraction of $D^+_s\to f_0(500) e^+\nu_e,~f_0(500)\to\pi^+\pi^-$ decay is set to be $3.3 \times 10^{-4}$ at 90\% confidence level.