Investigations of the weak decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> molecules

The decays of exotic states discovered experimentally always proceed via the strong and electromagnetic interactions. Recently, a tetraquark state with the quark content <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi><a:mi>c</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> was predicted by lattice QCD simulations. It is below the mass threshold of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>D</g:mi><g:mover accent="true"><g:mi>B</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math>, which can only decay via the weak interaction. In this work, based on the decay mechanism of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>T</k:mi><k:mrow><k:mi>c</k:mi><k:mi>c</k:mi></k:mrow></k:msub></k:math> as a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>D</m:mi><m:msup><m:mi>D</m:mi><m:mo>*</m:mo></m:msup></m:math> molecule, we propose that the decays of the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>b</o:mi><o:mi>c</o:mi><o:mover accent="true"><o:mi>q</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mover accent="true"><o:mi>q</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> tertaquark state as a <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>D</u:mi><u:mover accent="true"><u:mi>B</u:mi><u:mo stretchy="false">¯</u:mo></u:mover></u:math> molecule proceed via the Cabibbo-favored weak decays of the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mover accent="true"><y:mi>B</y:mi><y:mo stretchy="false">¯</y:mo></y:mover></y:math> or <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>D</cb:mi></cb:math> meson, accompanied by the tree-level decay modes and the triangle decay modes. Our results indicate that the branching fraction of the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>D</eb:mi><eb:mover accent="true"><eb:mi>B</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover></eb:math> molecule decaying into <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msup><ib:mi>π</ib:mi><ib:mo>+</ib:mo></ib:msup><ib:msup><ib:mi>K</ib:mi><ib:mo>−</ib:mo></ib:msup><ib:msup><ib:mover accent="true"><ib:mi>B</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover><ib:mn>0</ib:mn></ib:msup></ib:math> is sizable, which is a good channel to observe the <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>D</mb:mi><mb:mover accent="true"><mb:mi>B</mb:mi><mb:mo stretchy="false">¯</mb:mo></mb:mover></mb:math> molecule in future experiments. Published by the American Physical Society 2024