Heavy mesons to open-charmed tetraquark decays

Motivated by the recent observations of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>s</a:mi><a:mn>0</a:mn></a:mrow><a:mo>*</a:mo></a:msubsup><a:mo stretchy="false">(</a:mo><a:mn>2870</a:mn><a:msup><a:mo stretchy="false">)</a:mo><a:mn>0</a:mn></a:msup></a:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msubsup><e:mrow><e:mi>T</e:mi></e:mrow><e:mrow><e:mi>c</e:mi><e:mrow><e:mover accent="true"><e:mrow><e:mi>s</e:mi></e:mrow><e:mrow><e:mo stretchy="false">¯</e:mo></e:mrow></e:mover><e:mn>0</e:mn></e:mrow></e:mrow><e:mrow><e:mo>*</e:mo></e:mrow></e:msubsup><e:mrow><e:mo stretchy="false">(</e:mo><e:mn>2900</e:mn><e:msup><e:mrow><e:mo stretchy="false">)</e:mo></e:mrow><e:mrow><e:mn>0</e:mn></e:mrow></e:msup></e:mrow></e:mrow></e:math>, and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>T</k:mi><k:mrow><k:mi>c</k:mi><k:mover accent="true"><k:mi>s</k:mi><k:mo stretchy="false">¯</k:mo></k:mover><k:mn>0</k:mn></k:mrow><k:mo>*</k:mo></k:msubsup><k:mo stretchy="false">(</k:mo><k:mn>2900</k:mn><k:msup><k:mo stretchy="false">)</k:mo><k:mrow><k:mo>+</k:mo><k:mo>+</k:mo></k:mrow></k:msup></k:math> open-charmed tetraquark states by LHCb, we study the decays of heavy mesons to these open-charmed tetraquark states (<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>T</q:mi></q:math>) using a topological amplitude approach. We first obtain the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>T</s:mi><s:mo stretchy="false">→</s:mo><s:mi>D</s:mi><s:mi>P</s:mi></s:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>D</v:mi><v:mi>S</v:mi></v:math> strong decay amplitudes by decomposing them into several topological amplitudes, where <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>P</x:mi></x:math> is a light pseudoscalar particle and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>S</z:mi></z:math> is a low-lying scalar particle. Subsequently, weak decay amplitudes of <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mover accent="true"><bb:mi>B</bb:mi><bb:mo stretchy="false">¯</bb:mo></bb:mover><bb:mo stretchy="false">→</bb:mo><bb:mi>D</bb:mi><bb:mover accent="true"><bb:mi>T</bb:mi><bb:mo stretchy="false">¯</bb:mo></bb:mover></bb:math>, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mover accent="true"><ib:mi>D</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover><ib:mi>T</ib:mi></ib:math>, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mover accent="true"><mb:mi>B</mb:mi><mb:mo stretchy="false">¯</mb:mo></mb:mover><mb:mo stretchy="false">→</mb:mo><mb:mi>T</mb:mi><mb:mi>P</mb:mi></mb:math>, and <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>T</rb:mi><rb:mi>S</rb:mi></rb:math> decays are decomposed topologically. In addition, <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msubsup><tb:mi>B</tb:mi><tb:mi>c</tb:mi><tb:mo>−</tb:mo></tb:msubsup><tb:mo stretchy="false">→</tb:mo><tb:mi>T</tb:mi><tb:mover accent="true"><tb:mi>T</tb:mi><tb:mo stretchy="false">¯</tb:mo></tb:mover></tb:math> decays are also discussed. Using these results, modes with an unambiguous exotic interpretation in flavor are highlighted.