Topological diagrams of doubly charmed baryon decays in the $$SU(3)_F$$ limit

Abstract The doubly charmed baryon was first observed by LHCb via the non-leptonic decay $$\Xi _{cc}^{++}\rightarrow \Lambda ^+_cK^-\pi ^+\pi ^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Ξ</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> in 2017. Subsequently, ongoing efforts have been made to identify other doubly charmed baryons. However, there is no systematic analysis of the topological decomposition for non-leptonic decays of doubly charmed baryons. In this work, we study the topological amplitudes of doubly charmed baryon decays in the $$SU(3)_F$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>F</mml:mi> </mml:msub> </mml:mrow> </mml:math> limit. Tree- and penguin-induced topological diagrams for the $$\mathcal {B}_{cc}\rightarrow \mathcal {B}_c M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> and $$\mathcal {B}_{cc}\rightarrow \mathcal {B} D$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>B</mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> decays are presented. The linear relations between the topological amplitudes and the SU (3) irreducible amplitudes are derived through tensor contraction and SU (3) decomposition. The magnitude pattern of the topological diagrams is analyzed in the rescattering dynamics and the large $$N_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> expansion. In addition, some amplitude relations are derived to test the Körner–Pati–Woo theorem in the isospin limit.