Revisit the diquark of $\Lambda_c$ in the $\Lambda_c\to \Lambda K^+$ and $\Lambda_c\to \Sigma^0 K^+$ processes

The spatial distributions of $[ud]$ diquark and heavy-light diquark of the SU(3)-flavor antitriplet charmed baryons are investigated by the two singly Cabibbo-suppressed hadronic weak decays, $\Lambda_c\to \Lambda K^+$ and $\Lambda_c\to \Sigma^0 K^+$ within the nonrelativistic constituent quark model. The above two spatial distributions are reflected by the two parameters $\alpha_\rho$ and $\alpha_\lambda$, which are the harmonic oscillator strength parameters of the charmed baryons. These two parameters obtain strong constraints from the decay widths of $\Lambda_c\to \Lambda K^+$ and $\Lambda_c\to \Sigma^0 K^+$. The larger the harmonic oscillator parameter is, the more compact the spatial distribution will become. The current $\alpha_\rho$ and $\alpha_\lambda$ indicate that neither the light diquark nor the heavy-light diquark turns out to favor a compact structure. In addition, some selection rules, including the ``$\Lambda$ selection rule'', can be useful for the search of excited baryons in the heavy-flavor baryon hadronic weak decays.