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 ${\Lambda }_c\to p{K}^{+}{K}^{-}$ 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 $\varphi$ and ${\rho }^0$. Our theoretical results for the ratios of the branching fractions of ${\Lambda }_c\to p{\bar{K}}^{\ast 0}$ and ${\Lambda }_c\to p\omega$ with respect to the one of ${\Lambda }_c\to p\varphi$ 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 ${\Lambda }_c\to p{K}^{+}{K}^{-}$ 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 $\varphi$ 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 $a_0(980)$.

arXiv comment14 pages, 10 figures, the version to be published in EPJC

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