Investigating the nature of light scalar mesons with semileptonic decays of D mesons

We study the semileptonic decays of $D_{s}^{+}$, $D^{+}$, and $D^{0}$ mesons into the light scalar mesons [$f_{0} (500)$, $K_{0}^{\ast} (800)$, $f_{0} (980)$, and $a_{0}(980)$] and the light vector mesons [$\rho (770)$, $\omega (782)$, $K^{\ast} (892)$, and $\phi (1020)$]. With the help of a chiral unitarity approach in coupled channels, we compute the branching fractions for scalar meson processes of the semileptonic $D$ decays in a simple way. Using current known values of the branching fractions, we make predictions for the branching fractions of the semileptonic decay modes with other scalar and vector mesons. Furthermore, we calculate the $\pi ^{+} \pi ^{-}$, $\pi \eta$, $\pi K$, and $K^{+} K^{-}$ invariant mass distributions in the semileptonic decays of $D$ mesons, which will help us clarify the nature of the light scalar mesons.