Probing the diquark structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </m

The spatial distributions of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">[</a:mo> <a:mi>u</a:mi> <a:mi>d</a:mi> <a:mo stretchy="false">]</a:mo> </a:math> diquark and heavy-light diquark of the SU(3)-flavor antitriplet charmed baryons are investigated by the two singly Cabibbo-suppressed hadronic weak decays, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi mathvariant="normal">Λ</e:mi> <e:mi>c</e:mi> </e:msub> <e:mo stretchy="false">→</e:mo> <e:mi mathvariant="normal">Λ</e:mi> <e:msup> <e:mi>K</e:mi> <e:mo>+</e:mo> </e:msup> </e:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi mathvariant="normal">Λ</j:mi> <j:mi>c</j:mi> </j:msub> <j:mo stretchy="false">→</j:mo> <j:msup> <j:mi mathvariant="normal">Σ</j:mi> <j:mn>0</j:mn> </j:msup> <j:msup> <j:mi>K</j:mi> <j:mo>+</j:mo> </j:msup> </j:math> within the nonrelativistic constituent quark model. The above two spatial distributions are reflected by the two parameters <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>α</o:mi> <o:mi>ρ</o:mi> </o:msub> </o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>α</q:mi> <q:mi>λ</q:mi> </q:msub> </q:math> , which are the harmonic oscillator strength parameters of the charmed baryons. These two parameters obtain strong constraints from the decay widths of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi mathvariant="normal">Λ</s:mi> <s:mi>c</s:mi> </s:msub> <s:mo stretchy="false">→</s:mo> <s:mi mathvariant="normal">Λ</s:mi> <s:msup> <s:mi>K</s:mi> <s:mo>+</s:mo> </s:msup> </s:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi mathvariant="normal">Λ</x:mi> <x:mi>c</x:mi> </x:msub> <x:mo stretchy="false">→</x:mo> <x:msup> <x:mi mathvariant="normal">Σ</x:mi> <x:mn>0</x:mn> </x:msup> <x:msup> <x:mi>K</x:mi> <x:mo>+</x:mo> </x:msup> </x:math> . The larger the harmonic oscillator parameter is, the more compact the spatial distribution will become. The current <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>α</cb:mi> <cb:mi>ρ</cb:mi> </cb:msub> </cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>α</eb:mi> <eb:mi>λ</eb:mi> </eb:msub> </eb:math> 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 “ <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi mathvariant="normal">Λ</gb:mi> </gb:math> selection rule,” can be useful for the search of excited baryons in the heavy-flavor baryon hadronic weak decays.