Decay property of the X(3842) as the ψ3(1D</…

In this paper, the new particle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>X</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3842</a:mn><a:mo stretchy="false">)</a:mo></a:math> discovered by the LHCb Collaboration is identified to be the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>ψ</e:mi><e:mn>3</e:mn></e:msub><e:mo stretchy="false">(</e:mo><e:msup><e:mn>1</e:mn><e:mn>3</e:mn></e:msup><e:msub><e:mi>D</e:mi><e:mn>3</e:mn></e:msub><e:mo stretchy="false">)</e:mo></e:math> state. We study its strong decays with the combination of the Bethe-Salpeter method and the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msub><i:mrow><i:mmultiscripts><i:mrow><i:mi>P</i:mi></i:mrow><i:mprescripts/><i:none/><i:mn>3</i:mn></i:mmultiscripts></i:mrow><i:mn>0</i:mn></i:msub></i:mrow></i:math> model. Its electromagnetic (EM) decay is also calculated by the Bethe-Salpeter method within the Mandelstam formalism. The strong decay widths are <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi mathvariant="normal">Γ</k:mi><k:mo stretchy="false">[</k:mo><k:mi>X</k:mi><k:mo stretchy="false">(</k:mo><k:mn>3842</k:mn><k:mo stretchy="false">)</k:mo><k:mo stretchy="false">→</k:mo><k:msup><k:mrow><k:mi>D</k:mi></k:mrow><k:mrow><k:mn>0</k:mn></k:mrow></k:msup><k:msup><k:mrow><k:mover accent="true"><k:mrow><k:mi>D</k:mi></k:mrow><k:mrow><k:mo stretchy="false">¯</k:mo></k:mrow></k:mover></k:mrow><k:mrow><k:mn>0</k:mn></k:mrow></k:msup><k:mo stretchy="false">]</k:mo><k:mo>=</k:mo><k:mn>1.27</k:mn><k:mtext> </k:mtext><k:mi>MeV</k:mi></k:mrow></k:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi mathvariant="normal">Γ</u:mi><u:mo stretchy="false">[</u:mo><u:mi>X</u:mi><u:mo stretchy="false">(</u:mo><u:mn>3823</u:mn><u:mo stretchy="false">)</u:mo><u:mo stretchy="false">→</u:mo><u:mspace linebreak="goodbreak"/><u:msup><u:mi>D</u:mi><u:mo>+</u:mo></u:msup><u:msup><u:mi>D</u:mi><u:mo>−</u:mo></u:msup><u:mo stretchy="false">]</u:mo><u:mo>=</u:mo><u:mn>1.08</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>MeV</u:mi></u:math>, and the ratio is <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi mathvariant="script">B</db:mi><db:mo stretchy="false">[</db:mo><db:mi>X</db:mi><db:mo stretchy="false">(</db:mo><db:mn>3842</db:mn><db:mo stretchy="false">)</db:mo><db:mo stretchy="false">→</db:mo><db:msup><db:mi>D</db:mi><db:mo>+</db:mo></db:msup><db:msup><db:mi>D</db:mi><db:mo>−</db:mo></db:msup><db:mo stretchy="false">]</db:mo><db:mo>/</db:mo><db:mi mathvariant="script">B</db:mi><db:mo stretchy="false">[</db:mo><db:mi>X</db:mi><db:mo stretchy="false">(</db:mo><db:mn>3823</db:mn><db:mo stretchy="false">)</db:mo><db:mo stretchy="false">→</db:mo><db:msup><db:mi>D</db:mi><db:mn>0</db:mn></db:msup><db:msup><db:mover accent="true"><db:mi>D</db:mi><db:mo stretchy="false">¯</db:mo></db:mover><db:mn>0</db:mn></db:msup><db:mo stretchy="false">]</db:mo><db:mo>=</db:mo><db:mn>0.84</db:mn></db:math>. The EM decay width is <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi mathvariant="normal">Γ</tb:mi><tb:mo stretchy="false">[</tb:mo><tb:mi>X</tb:mi><tb:mo stretchy="false">(</tb:mo><tb:mn>3842</tb:mn><tb:mo stretchy="false">)</tb:mo><tb:mo stretchy="false">→</tb:mo><tb:msub><tb:mi>χ</tb:mi><tb:mrow><tb:mi>c</tb:mi><tb:mn>2</tb:mn></tb:mrow></tb:msub><tb:mi>γ</tb:mi><tb:mo stretchy="false">]</tb:mo><tb:mo>=</tb:mo><tb:mn>0.29</tb:mn><tb:mtext> </tb:mtext><tb:mtext> </tb:mtext><tb:mi>MeV</tb:mi></tb:math>. We also estimate the total width to be 2.87 MeV, which is in good agreement with the experimental data <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:msubsup><bc:mn>2.79</bc:mn><bc:mrow><bc:mo>−</bc:mo><bc:mn>0.86</bc:mn></bc:mrow><bc:mrow><bc:mo>+</bc:mo><bc:mn>0.86</bc:mn></bc:mrow></bc:msubsup><bc:mtext> </bc:mtext><bc:mtext> </bc:mtext><bc:mi>MeV</bc:mi></bc:math>. Since the used relativistic wave functions include different partial waves, we also study the contributions of different partial waves in electromagnetic decay. Published by the American Physical Society 2024