Production of a BB¯ bound state via ϒ(4S) radiative decays

Motivated by recent theoretical predictions about the existence of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>B</a:mi><a:mover accent="true"><a:mi>B</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> bound state [also denoted as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>X</e:mi><e:mo stretchy="false">(</e:mo><e:mn>10550</e:mn><e:mo stretchy="false">)</e:mo></e:math>], in this work we estimate the production of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>S</i:mi></i:math>-wave <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>B</k:mi><k:mo>+</k:mo></k:msup><k:msup><k:mi>B</k:mi><k:mo>−</k:mo></k:msup></k:math> molecule via <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="normal">ϒ</m:mi><m:mo stretchy="false">(</m:mo><m:mn>4</m:mn><m:mi>S</m:mi><m:mo stretchy="false">)</m:mo></m:math> radiative decays. In particular, we make use of effective Lagrangian approach and the compositeness condition to calculate the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>X</r:mi><r:mo stretchy="false">(</r:mo><r:mn>10550</r:mn><r:mo stretchy="false">)</r:mo></r:math> production rate via <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi mathvariant="normal">ϒ</v:mi><v:mo stretchy="false">(</v:mo><v:mn>4</v:mn><v:mi>S</v:mi><v:mo stretchy="false">)</v:mo><v:mo stretchy="false">→</v:mo><v:mi>γ</v:mi><v:mi>X</v:mi><v:mo stretchy="false">(</v:mo><v:mn>10550</v:mn><v:mo stretchy="false">)</v:mo></v:math> decays employing triangle diagrams. Our results show that the partial decay width of this reaction is of the order of 0.5–192 keV for a respective binding energy of 1–100 MeV, corresponding to a branching fraction of <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mrow><db:msup><db:mrow><db:mn>10</db:mn></db:mrow><db:mrow><db:mo>−</db:mo><db:mn>5</db:mn></db:mrow></db:msup><db:mi>–</db:mi><db:mrow><db:msup><db:mrow><db:mn>10</db:mn></db:mrow><db:mrow><db:mo>−</db:mo><db:mn>3</db:mn></db:mrow></db:msup></db:mrow></db:mrow></db:math>. These findings suggest that the existence of the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>X</fb:mi><fb:mo stretchy="false">(</fb:mo><fb:mn>10550</fb:mn><fb:mo stretchy="false">)</fb:mo></fb:math> might be checked via the analysis of the mentioned decay in present and future experiments. Published by the American Physical Society 2024