Nonleptonic decays of the double-charmed baryon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>c

In this work, we investigate the two-body nonleptonic decays of double-charmed baryon <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi mathvariant="normal">Ω</a:mi> <a:mrow> <a:mi>c</a:mi> <a:mi>c</a:mi> </a:mrow> <a:mo>+</a:mo> </a:msubsup> </a:math> within a nonrelativistic quark model, in which the nonfactorizable amplitudes contributed by <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>W</d:mi> </d:math> -exchange diagrams are evaluated under the pole model assumption. To reduce the sensitivity of decay amplitudes to an arbitrary choice of baryon wave functions, we adopt charmed baryon wave functions obtained by solving the Schrödinger equation with a nonrelativistic quark potential model. Our results show that the branching fractions of Cabibbo-favored decays <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:msubsup> <f:mrow> <f:mi mathvariant="normal">Ω</f:mi> </f:mrow> <f:mrow> <f:mi>c</f:mi> <f:mi>c</f:mi> </f:mrow> <f:mrow> <f:mo>+</f:mo> </f:mrow> </f:msubsup> <f:mo stretchy="false">→</f:mo> <f:msubsup> <f:mrow> <f:mi mathvariant="normal">Ω</f:mi> </f:mrow> <f:mrow> <f:mi>c</f:mi> </f:mrow> <f:mrow> <f:mn>0</f:mn> </f:mrow> </f:msubsup> <f:msup> <f:mrow> <f:mi>π</f:mi> </f:mrow> <f:mrow> <f:mo>+</f:mo> </f:mrow> </f:msup> </f:mrow> </f:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:msubsup> <k:mrow> <k:mi mathvariant="normal">Ξ</k:mi> </k:mrow> <k:mrow> <k:mi>c</k:mi> </k:mrow> <k:mrow> <k:mo stretchy="false">(</k:mo> <k:mo>′</k:mo> <k:mo stretchy="false">)</k:mo> <k:mo>+</k:mo> </k:mrow> </k:msubsup> <k:msup> <k:mrow> <k:mi>π</k:mi> </k:mrow> <k:mrow> <k:mo>+</k:mo> </k:mrow> </k:msup> </k:mrow> </k:math> , as well as the single Cabibbo-suppressed decays <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:msubsup> <p:mrow> <p:mi mathvariant="normal">Ω</p:mi> </p:mrow> <p:mrow> <p:mi>c</p:mi> <p:mi>c</p:mi> </p:mrow> <p:mrow> <p:mo>+</p:mo> </p:mrow> </p:msubsup> <p:mo stretchy="false">→</p:mo> <p:msubsup> <p:mrow> <p:mi mathvariant="normal">Ω</p:mi> </p:mrow> <p:mrow> <p:mi>c</p:mi> </p:mrow> <p:mrow> <p:mn>0</p:mn> </p:mrow> </p:msubsup> <p:msup> <p:mrow> <p:mi>K</p:mi> </p:mrow> <p:mrow> <p:mo>+</p:mo> </p:mrow> </p:msup> </p:mrow> </p:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msubsup> <u:mi mathvariant="normal">Σ</u:mi> <u:mrow> <u:mi>c</u:mi> <u:mi>c</u:mi> </u:mrow> <u:mrow> <u:mo>+</u:mo> <u:mo>+</u:mo> </u:mrow> </u:msubsup> <u:msup> <u:mi>K</u:mi> <u:mo>−</u:mo> </u:msup> </u:math> , <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msubsup> <x:mi mathvariant="normal">Ξ</x:mi> <x:mi>c</x:mi> <x:mrow> <x:mo>′</x:mo> <x:mo>+</x:mo> </x:mrow> </x:msubsup> <x:mi>η</x:mi> </x:math> , and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msubsup> <ab:mi mathvariant="normal">Λ</ab:mi> <ab:mi>c</ab:mi> <ab:mo>+</ab:mo> </ab:msubsup> <ab:msup> <ab:mover accent="true"> <ab:mi>K</ab:mi> <ab:mo stretchy="false">¯</ab:mo> </ab:mover> <ab:mn>0</ab:mn> </ab:msup> </ab:math> can reach up to a few percent. Particularly for the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msubsup> <fb:mi mathvariant="normal">Ω</fb:mi> <fb:mrow> <fb:mi>c</fb:mi> <fb:mi>c</fb:mi> </fb:mrow> <fb:mo>+</fb:mo> </fb:msubsup> <fb:mo stretchy="false">→</fb:mo> <fb:msubsup> <fb:mi mathvariant="normal">Ω</fb:mi> <fb:mi>c</fb:mi> <fb:mn>0</fb:mn> </fb:msubsup> <fb:msup> <fb:mi>K</fb:mi> <fb:mo>+</fb:mo> </fb:msup> </fb:math> mode, owing to the large factorizable amplitude and constructive pole contributions, the branching fraction is comparable to Cabibbo-favored decays. These decay modes can serve as the discovery channels for the double-charmed baryon <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msubsup> <kb:mi mathvariant="normal">Ω</kb:mi> <kb:mrow> <kb:mi>c</kb:mi> <kb:mi>c</kb:mi> </kb:mrow> <kb:mo>+</kb:mo> </kb:msubsup> </kb:math> in future experiments, like LHCb and Belle II.