The scalar $$f_0(500)$$, $$f_0(980)$$, and $$a_0(980)$$ resonances and vector mesons in the single Cabibbo-suppressed decays $$\Lambda _c \rightarrow p K^+K^-$$ and $$p\pi ^+\pi ^-$$

Abstract

AbstractIn the chiral unitary approach, we have studied the single Cabibbo-suppressed decays $$\Lambda _c\rightarrow pK^+K^-$$ Λ c → p K + K - and $$\Lambda _c \rightarrow p \pi ^+\pi ^-$$ Λ c → p π + π - by taking into account the s-wave meson–meson interaction as well as the contributions from the intermediate vectors $$\phi $$ ϕ and $$\rho ^0$$ ρ 0 . Our theoretical results for the ratios of the branching fractions of $$\Lambda _c\rightarrow p {\bar{K}}^{*0}$$ Λ c → p K ¯ ∗ 0 and $$\Lambda _c\rightarrow p \omega $$ Λ c → p ω with respect to the one of $$\Lambda _c\rightarrow p \phi $$ Λ c → p ϕ are in agreement with the experimental data. Within the picture that the scalar resonances $$f_0(500)$$ f 0 ( 500 ) , $$f_0(980)$$ f 0 ( 980 ) , and $$a_0(980)$$ a 0 ( 980 ) are dynamically generated from the pseudoscalar-pseudoscalar interactions in s-wave, we have calculated the $$K^+K^-$$ K + K - and $$\pi ^+\pi ^-$$ π + π - invariant mass distributions respectively for the decays $$\Lambda _c\rightarrow pK^+K^-$$ Λ c → p K + K - and $$\Lambda _c\rightarrow p\pi ^+\pi ^-$$ Λ c → p π + π - . One can find a broad bump structure for the $$f_0(500)$$ f 0 ( 500 ) and a narrow peak for the $$f_0(980)$$ f 0 ( 980 ) in the $$\pi ^+\pi ^-$$ π + π - invariant mass distribution of the decay $$\Lambda _c\rightarrow p\pi ^+\pi ^-$$ Λ c → p π + π - . For the $$K^+K^-$$ K + K - invariant mass distribution, in addition to the narrow peak for the $$\phi $$ ϕ meson, there is an enhancement structure near the $$K^+K^-$$ K + K - threshold mainly due to the contribution from the $$f_0(980)$$ f 0 ( 980 ) . Both the $$\pi ^+\pi ^-$$ π + π - and $$K^+K^-$$ 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 ( 500 ) , $$f_0(980)$$ f 0 ( 980 ) , and $$a_0(980)$$ a 0 ( 980 ) .