Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$

Abstract

Motivated by the near-threshold enhancement and the dip structure around 1~GeV in the ${\pi }^0{\pi }^0$ invariant mass distribution of the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$ observed by the CLEO Collaboration, we have investigated this process by taking into account the contribution from the $S$-wave pseudoscalar meson-pseudoscalar meson interactions within the chiral unitary approach, and also the one from the intermediate resonance $K^{\ast }(892)$. Our results are in good agreement with the CLEO measurements, which implies that, the near-threshold enhancement near the ${\pi }^0{\pi }^0$ threshold is mainly due to the contributions from the scalar meson $f_0(500)$ and the intermediate $K^{\ast }$, and the cusp structure around 1~GeV in the ${\pi }^0{\pi }^0$ invariant mass distribution should be associated with the scalar meson $f_0(980)$.

Comments: 6 pages, 5 figures