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.