Study of the $f_0(980)$ and $f_0(500)$ Scalar Mesons through the Decay $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$

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 $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$, 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 ${\pi }^{+}{\pi }^{-}$ 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 $(1.72\pm 0.13_{\mathrm{stat}}\pm 0.10_{\mathrm{syst}})\times 10^{-3}$, where the uncertainties are statistical and systematic, respectively. The dynamics of the $D_s^{+}\to f_0(980)e^{+}{\nu }_e$ 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 $D_s^{+}\to f_0(500)e^{+}{\nu }_e$ 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.

arXiv comment9 pages, 3 figures

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Cited by in corpus (3)

• Probing $|V_{cs}|$ and lepton flavor universality through $D\to K_0^{\ast }(1430)\ell {\nu }_{\ell }$ decay
• Measurements of the branching fractions of semileptonic $D_s^{+}$ decays via $e^{+}{e}^{-}\to D_s^{\ast +}{D}_s^{\ast -}$
• Study of the light scalar $a_0(980)$ through the decay $D^0\to a_0(980{)}^{-}{e}^{+}{\nu }_e$ with $a_0(980{)}^{-}\to \eta {\pi }^{-}$