Light scalars in semi-leptonic decays of heavy quarkonia

Abstract

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

Comments: 8 pages, 3 figures, the variant matches the publication in Phys. Rev. D