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

TL;DR

This study investigates the spatial structures of diquarks within $\Lambda_c$ baryons using decay data, revealing that neither light nor heavy-light diquarks are particularly compact, and introduces selection rules for excited baryon searches.

Contribution

It provides new constraints on diquark spatial distributions in $\Lambda_c$ baryons through decay analysis within a nonrelativistic quark model, highlighting their non-compact nature.

Findings

Neither light nor heavy-light diquarks are highly compact.

Decay widths strongly constrain the harmonic oscillator parameters.

Selection rules can aid in searching for excited heavy-flavor baryons.

Abstract

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.