Role of triangle singularity in the decay process D0 → π+ π- f0 (980), f0 → π+ π-

We study the process D-0 -> pi(+)-pi(-) f(0)(980), f(0 ->) 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*(K) over barK 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 M-eV 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.