Zb states as the mixture of the molecular and diquark-anti-diquark components within the effective field theory

In this study, we reconsider the states <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>Z</a:mi><a:mi>b</a:mi></a:msub><a:mo stretchy="false">(</a:mo><a:mn>10610</a:mn><a:mo stretchy="false">)</a:mo></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>Z</e:mi><e:mi>b</e:mi></e:msub><e:mo stretchy="false">(</e:mo><e:mn>10650</e:mn><e:mo stretchy="false">)</e:mo></e:math> by investigating the presence of diquark-anti-diquark components as well as the hadronic molecule components in the framework of effective field theory. The different masses of pseudoscalar mesons such as <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>π</i:mi><i:mn>0</i:mn></i:msup></i:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>η</k:mi><k:mn>8</k:mn></k:msub></k:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>η</m:mi><m:mn>0</m:mn></m:msub></m:math>, as well as vector mesons like <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>ρ</o:mi><o:mn>0</o:mn></o:msup></o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ω</q:mi></q:math> violate the Okubo-Zweig-Iizuka (OZI) rule that is well depicted under the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo stretchy="false">[</s:mo><s:mi>U</s:mi><s:mo stretchy="false">(</s:mo><s:mn>3</s:mn><s:msub><s:mo stretchy="false">)</s:mo><s:mi>L</s:mi></s:msub><s:mo stretchy="false">⊗</s:mo><s:mi>U</s:mi><s:mo stretchy="false">(</s:mo><s:mn>3</s:mn><s:msub><s:mo stretchy="false">)</s:mo><s:mi>R</s:mi></s:msub><s:msub><s:mo stretchy="false">]</s:mo><s:mtext>global</s:mtext></s:msub><s:mo stretchy="false">⊗</s:mo><s:mo stretchy="false">[</s:mo><s:mi>U</s:mi><s:mo stretchy="false">(</s:mo><s:mn>3</s:mn><s:msub><s:mo stretchy="false">)</s:mo><s:mi>V</s:mi></s:msub><s:msub><s:mo stretchy="false">]</s:mo><s:mtext>local</s:mtext></s:msub></s:math> symmetry. To account for the contribution of intermediate bosons of heavy masses within the one-boson-exchange model, we introduce an exponential form factor instead of the commonly used monopole form factor in the past. By solving the coupled-channel Schrödinger equation with the Gaussian expansion method, our numerical results indicate that the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>Z</gb:mi><gb:mi>b</gb:mi></gb:msub><gb:mo stretchy="false">(</gb:mo><gb:mn>10610</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msub><kb:mi>Z</kb:mi><kb:mi>b</kb:mi></kb:msub><kb:mo stretchy="false">(</kb:mo><kb:mn>10650</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math> states can be explained as hadronic molecules slightly mixing with diquark-anti-diquark states. Published by the American Physical Society 2024