The scalar $f_0(500)$ and $f_0(980)$ resonances and vector mesons in the single Cabibbo-suppressed decays $\Lambda_c \to p K^+K^-$ and $p\pi^+\pi^-$

Abstract

In the chiral unitary approach, we have studied the single Cabibbo-suppressed decays $\Lambda_c\to pK^+K^-$ and $\Lambda_c \to p \pi^+\pi^-$ by taking into account the $s$-wave meson-meson interaction as well as the contributions from the intermediate vectors $\phi$ and $\rho^0$. Our theoretical results for the ratios of the branching fractions of $\Lambda_c\to p \bar{K}^{*0}$ and $\Lambda_c\to p \omega$ with respect to the one of $\Lambda_c\to p \phi$ are in agreement with the experimental data. Within the picture that the scalar resonances $f_0(500)$, $f_0(980)$, and $a_0(980)$ are dynamically generated from the pseudoscalar-pseudoscalar interactions in $s$-wave, we have calculated the $K^+K^-$ and $\pi^+\pi^-$ invariant mass distributions respectively for the decays $\Lambda_c\to pK^+K^-$ and $\Lambda_c\to p\pi^+\pi^-$. One can find a broad bump structure for the $f_0(500)$ and a narrow peak for the $f_0(980)$ in the $\pi^+\pi^-$ invariant mass distribution of the decay $\Lambda_c\to p\pi^+\pi^-$. For the $K^+K^-$ invariant mass distribution, in addition to the narrow peak for the $\phi$ meson, there is an enhancement structure near the $K^+K^-$ threshold mainly due to the contribution from the $f_0(980)$. Both the $\pi^+\pi^-$ and $K^+K^-$ invariant mass distributions are compatible with the BESIII measurement. We encourage our experimental colleagues to measure these two decays, which would be helpful to understand the nature of the $f_0(500)$, $f_0(980)$, and $a_0(980)$.