<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> <mml:mi>c</mml:mi> <mml:mover accent="true"> <mml:mi>s</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </

We perform a theoretical study of the decay process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">ϒ</a:mi> <a:mo stretchy="false">→</a:mo> <a:msup> <a:mi>D</a:mi> <a:mo>−</a:mo> </a:msup> <a:msup> <a:mover accent="true"> <a:mi>B</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mn>0</a:mn> </a:msup> <a:msubsup> <a:mi>D</a:mi> <a:mi>s</a:mi> <a:mo>+</a:mo> </a:msubsup> </a:math> in search of the doubly heavy tetraquark states <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>T</g:mi> <g:mrow> <g:mi>b</g:mi> <g:mi>c</g:mi> <g:mover accent="true"> <g:mi>s</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> </g:mrow> </g:msub> </g:math> with quark content <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>b</k:mi> <k:mi>c</k:mi> <k:mover accent="true"> <k:mi>s</k:mi> <k:mo stretchy="false">¯</k:mo> </k:mover> <k:mover accent="true"> <k:mi>d</k:mi> <k:mo stretchy="false">¯</k:mo> </k:mover> </k:math> . These <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>T</q:mi> <q:mrow> <q:mi>b</q:mi> <q:mi>c</q:mi> <q:mover accent="true"> <q:mi>s</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> </q:mrow> </q:msub> </q:math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msubsup> <u:mover accent="true"> <u:mi>B</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mi>s</u:mi> <u:mrow> <u:mo stretchy="false">(</u:mo> <u:mo>*</u:mo> <u:mo stretchy="false">)</u:mo> <u:mn>0</u:mn> </u:mrow> </u:msubsup> <u:msup> <u:mi>D</u:mi> <u:mrow> <u:mo stretchy="false">(</u:mo> <u:mo>*</u:mo> <u:mo stretchy="false">)</u:mo> <u:mo>+</u:mo> </u:mrow> </u:msup> </u:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mover accent="true"> <cb:mi>B</cb:mi> <cb:mo stretchy="false">¯</cb:mo> </cb:mover> <cb:mrow> <cb:mo stretchy="false">(</cb:mo> <cb:mo>*</cb:mo> <cb:mo stretchy="false">)</cb:mo> <cb:mn>0</cb:mn> </cb:mrow> </cb:msup> <cb:msubsup> <cb:mi>D</cb:mi> <cb:mi>s</cb:mi> <cb:mrow> <cb:mo stretchy="false">(</cb:mo> <cb:mo>*</cb:mo> <cb:mo stretchy="false">)</cb:mo> <cb:mo>+</cb:mo> </cb:mrow> </cb:msubsup> </cb:math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>P</kb:mi> </kb:math> or vectors <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>V</mb:mi> </mb:math> ), they are labeled as <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msubsup> <ob:mi>T</ob:mi> <ob:mrow> <ob:mi>b</ob:mi> <ob:mi>c</ob:mi> <ob:mover accent="true"> <ob:mi>s</ob:mi> <ob:mo stretchy="false">¯</ob:mo> </ob:mover> </ob:mrow> <ob:mrow> <ob:mn>0</ob:mn> <ob:mo>,</ob:mo> <ob:mi>P</ob:mi> <ob:mi>P</ob:mi> </ob:mrow> </ob:msubsup> </ob:math> , <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:msubsup> <sb:mi>T</sb:mi> <sb:mrow> <sb:mi>b</sb:mi> <sb:mi>c</sb:mi> <sb:mover accent="true"> <sb:mi>s</sb:mi> <sb:mo stretchy="false">¯</sb:mo> </sb:mover> </sb:mrow> <sb:mrow> <sb:mn>0</sb:mn> <sb:mo>,</sb:mo> <sb:mi>V</sb:mi> <sb:mi>V</sb:mi> </sb:mrow> </sb:msubsup> </sb:math> , and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msubsup> <wb:mi>T</wb:mi> <wb:mrow> <wb:mi>b</wb:mi> <wb:mi>c</wb:mi> <wb:mover accent="true"> <wb:mi>s</wb:mi> <wb:mo stretchy="false">¯</wb:mo> </wb:mover> </wb:mrow> <wb:mrow> <wb:mn>2</wb:mn> <wb:mo>,</wb:mo> <wb:mi>V</wb:mi> <wb:mi>V</wb:mi> </wb:mrow> </wb:msubsup> </wb:math> , respectively. The <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"> <ac:msup> <ac:mover accent="true"> <ac:mi>B</ac:mi> <ac:mo stretchy="false">¯</ac:mo> </ac:mover> <ac:mn>0</ac:mn> </ac:msup> <ac:msubsup> <ac:mi>D</ac:mi> <ac:mi>s</ac:mi> <ac:mo>+</ac:mo> </ac:msubsup> </ac:math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"> <ec:msub> <ec:mi>T</ec:mi> <ec:mrow> <ec:mi>b</ec:mi> <ec:mi>c</ec:mi> <ec:mover accent="true"> <ec:mi>s</ec:mi> <ec:mo stretchy="false">¯</ec:mo> </ec:mover> </ec:mrow> </ec:msub> </ec:math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"> <ic:msubsup> <ic:mi>T</ic:mi> <ic:mrow> <ic:mi>b</ic:mi> <ic:mi>c</ic:mi> <ic:mover accent="true"> <ic:mi>s</ic:mi> <ic:mo