Semileptonic decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ as the probe of constituent quark-antiquark pairs in the light scalar mesons

Abstract

Decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ serve as probes that check the existence of constituent $q\bar{q}$ components in the wave functions of scalar mesons decaying into ${\pi }^{+}{\pi }^{-}$. There exists a great deal of concrete evidence in favor of the exotic four-quark nature of light scalars. At the same time, the further expansion of the area of the $q^2{\bar{q}}^2$ model validity for light scalars on ever new processes seems extremely interesting and important. We analyze the BESIII and CLEO data on the decays $D^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and show that the results of these experiments together can be interpreted in favor of the four-quark nature of light scalar mesons $\sigma (500)$ and $f_0(980)$. Our approach can also be applied to the description of other similar decays involving light scalars.

Comments: 8 pages, 8 figures; v2: published version, clarifications and references added