The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$

Abstract

We study the process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$ by introducing the triangle mechanism, in which $f_0(980)$ is considered to be dynamically generated from the meson-meson interaction. For the total contribution of this process, the contribution of the triangular loop formed by $K^{\ast }\bar{K}K$ particles could generate a triangular singularity of about 1418 MeV. We calculate the differential decay width of this process and show a narrow peak of about 980 MeV in the ${\pi }^{+}{\pi }^{-}$ invariant mass distribution, which comes from $f_0$ decay. For the $M_{inv}(\pi f_0)$ invariant mass distribution, we obtain a finite peak at 1418 MeV, which is consistent with the triangle singularity.