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 $a_0(980)$.

14 pages, 10 figures, the version to be published in EPJC

References in corpus (8)

• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• The low lying scalar resonances in the $D^0$ decays into $K_s^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$
• Amplitude analysis of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ decays
• $f_0(500)$, $f_0(980)$ and $a_0(980)$ production in the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ reaction
• Triangle singularity in the $J/\psi \to K^{+}{K}^{-}{f}_0(980)(a_0(980))$ decays
• $B^0$ and $B_s^0$ decays into $J/\psi$ plus a scalar or vector meson
• Search for ${\Lambda }_c^{+}\to \varphi p{\pi }^0$ and branching fraction measurement of ${\Lambda }_c^{+}\to K^{-}{\pi }^{+}p{\pi }^0$

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• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• Study of the $B^{-}\to K^{-}\eta {\eta }_c$ decay due to the $D\bar{D}$ bound state
• Hadronic decay $D^{+}\to {\pi }^{+}\eta \eta$ and the $a_0(980)$ and $f_0(1370)$ contributions
• Theoretical study in the ${\bar{B}}^0\to J/\psi {\bar{K}}^{\ast 0}{K}^0$ and ${\bar{B}}^0\to J/\psi f_1(1285)$ decays
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• Probing the isospin structure and low-lying resonances in ${\Lambda }_c^{+}\to n{\bar{K}}^0{\pi }^{+}$ decays