We study the mechanism of production of the light scalar mesons in the $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$ decays: $D_s^{+}\to s\overline{s}{e}^{+}\nu \to [\sigma (600)+f_0(980)]e^{+}\nu \to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$, and we compare it with the mechanism of production of the light pseudoscalar mesons in the $D_s^{+}\to (\eta /{\eta }^{\prime })e^{+}\nu$ decays: $D_s^{+}\to s\overline{s}{e}^{+}\nu \to (\eta /{\eta }^{\prime })e^{+}\nu$. We show that the $s\overline{s}\to \sigma (600)$ transition is negligibly small in comparison with the $s\overline{s}\to f_0(980)$ one. As for the $f_0(980)$ meson, the intensity of the $s\overline{s}\to f_0(980)$ transition makes near thirty percent from the intensity of the $s\overline{s}\to {\eta }_s$ (${\eta }_s=s\overline{s}$) transition. So, the $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$ decay supports the previous conclusions about a dominant role of the four-quark components in the $\sigma (600)$ and $f_0(980)$ mesons.

• Received 24 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.114010