Decipher the width of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> via the QCD sum rules

Abstract

In this work, we take the <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>3872</a:mn><a:mo stretchy="false">)</a:mo></a:math> as the hidden-charm tetraquark state with both isospin <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>I</e:mi><e:mo>=</e:mo><e:mn>0</e:mn></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>I</g:mi><g:mo>=</g:mo><g:mn>1</g:mn></g:math> components, then investigate the strong decays <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>X</i:mi><i:mo stretchy="false">(</i:mo><i:mn>3872</i:mn><i:mo stretchy="false">)</i:mo><i:mo stretchy="false">→</i:mo><i:mi>J</i:mi><i:mo>/</i:mo><i:mi>ψ</i:mi><i:msup><i:mi>π</i:mi><i:mo>+</i:mo></i:msup><i:msup><i:mi>π</i:mi><i:mo>−</i:mo></i:msup></i:math>, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>J</n:mi><n:mo>/</n:mo><n:mi>ψ</n:mi><n:mi>ω</n:mi></n:math>, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>χ</p:mi><p:mrow><p:mi>c</p:mi><p:mn>1</p:mn></p:mrow></p:msub><p:msup><p:mi>π</p:mi><p:mn>0</p:mn></p:msup></p:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mi>D</r:mi><r:mrow><r:mo>*</r:mo><r:mn>0</r:mn></r:mrow></r:msup><r:msup><r:mover accent="true"><r:mi>D</r:mi><r:mo stretchy="false">¯</r:mo></r:mover><r:mn>0</r:mn></r:msup></r:math>, and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>D</v:mi><v:mn>0</v:mn></v:msup><v:msup><v:mover accent="true"><v:mi>D</v:mi><v:mo stretchy="false">¯</v:mo></v:mover><v:mn>0</v:mn></v:msup><v:msup><v:mi>π</v:mi><v:mn>0</v:mn></v:msup></v:math> with the QCD sum rules. We take account of all the Feynman diagrams, and acquire four QCD sum rules based on rigorous quark-hadron duality. We obtain the total decay width about 1 MeV, which is in excellent agreement with the experiment data <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi mathvariant="normal">Γ</z:mi><z:mi>X</z:mi></z:msub><z:mo>=</z:mo><z:mn>1.19</z:mn><z:mo>±</z:mo><z:mn>0.21</z:mn><z:mtext> </z:mtext><z:mtext> </z:mtext><z:mi>MeV</z:mi></z:math> from the PDG, it is the first time to reproduce the tiny width of the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>X</cb:mi><cb:mo stretchy="false">(</cb:mo><cb:mn>3872</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math> via the QCD sum rules, which supports assigning the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>X</gb:mi><gb:mo stretchy="false">(</gb:mo><gb:mn>3872</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:math> as the hidden-charm tetraquark state with the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msup><kb:mi>J</kb:mi><kb:mrow><kb:mi>P</kb:mi><kb:mi>C</kb:mi></kb:mrow></kb:msup><kb:mo>=</kb:mo><kb:msup><kb:mn>1</kb:mn><kb:mrow><kb:mo>+</kb:mo><kb:mo>+</kb:mo></kb:mrow></kb:msup></kb:math>. Published by the American Physical Society 2024

Topics & Concepts