Predicting hidden bottom molecular tetraquarks with a complex scaling method
Аннотация
In the present work, we perform a coupled-channel analysis of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>B</a:mi><a:mrow><a:mo stretchy="false">(</a:mo><a:mi>s</a:mi><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:mo stretchy="false">(</a:mo><a:mo>*</a:mo><a:mo stretchy="false">)</a:mo></a:mrow></a:msubsup><a:msubsup><a:mover accent="true"><a:mi>B</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mrow><a:mo stretchy="false">(</a:mo><a:mi>s</a:mi><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:mo stretchy="false">(</a:mo><a:mo>*</a:mo><a:mo stretchy="false">)</a:mo></a:mrow></a:msubsup></a:math> systems with the one-boson-exchange potentials. We first study the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>I</m:mi><m:mo stretchy="false">(</m:mo><m:msup><m:mi>J</m:mi><m:mrow><m:mi>P</m:mi><m:mi>C</m:mi></m:mrow></m:msup><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>1</m:mn><m:mo stretchy="false">(</m:mo><m:msup><m:mn>1</m:mn><m:mrow><m:mo>+</m:mo><m:mo>−</m:mo></m:mrow></m:msup><m:mo stretchy="false">)</m:mo></m:math> <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>B</s:mi><s:msup><s:mover accent="true"><s:mi>B</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mo>*</s:mo></s:msup><s:mo>/</s:mo><s:msup><s:mi>B</s:mi><s:mo>*</s:mo></s:msup><s:msup><s:mover accent="true"><s:mi>B</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mo>*</s:mo></s:msup></s:math> system to describe the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>Z</y:mi><y:mi>b</y:mi></y:msub><y:mo stretchy="false">(</y:mo><y:mn>10610</y:mn><y:mo stretchy="false">)</y:mo></y:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>Z</cb:mi><cb:mi>b</cb:mi></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>10650</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math> particles as molecular states and determine the reasonable range of cutoff parameter <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi mathvariant="normal">Λ</gb:mi></gb:math>. Then, other <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msubsup><jb:mi>B</jb:mi><jb:mrow><jb:mo stretchy="false">(</jb:mo><jb:mi>s</jb:mi><jb:mo stretchy="false">)</jb:mo></jb:mrow><jb:mrow><jb:mo stretchy="false">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy="false">)</jb:mo></jb:mrow></jb:msubsup><jb:msubsup><jb:mover accent="true"><jb:mi>B</jb:mi><jb:mo stretchy="false">¯</jb:mo></jb:mover><jb:mrow><jb:mo stretchy="false">(</jb:mo><jb:mi>s</jb:mi><jb:mo stretchy="false">)</jb:mo></jb:mrow><jb:mrow><jb:mo stretchy="false">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy="false">)</jb:mo></jb:mrow></jb:msubsup></jb:math> combinations with different quantum numbers are systematically investigated. Some bound states and resonances appear in the isoscalar systems, while only several shallow bound states exist for isovector systems. Far away from the excited conventional <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:mi>P</vb:mi></vb:math>-wave bottomium, these predicted states can be easily identified as exotic particles both theoretically and experimentally. Moreover, the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msub><xb:mi>η</xb:mi><xb:mi>b</xb:mi></xb:msub><xb:mo stretchy="false">(</xb:mo><xb:mi>n</xb:mi><xb:mi>S</xb:mi><xb:mo stretchy="false">)</xb:mo><xb:mo>/</xb:mo><xb:mi mathvariant="normal">ϒ</xb:mi><xb:mo stretchy="false">(</xb:mo><xb:mi>n</xb:mi><xb:mi>S</xb:mi><xb:mo stretchy="false">)</xb:mo></xb:math> plus light mesons are the excellent final states to search for the bound states, while the <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mi>B</ec:mi><ec:msup><ec:mover accent="true"><ec:mi>B</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo>*</ec:mo></ec:msup><ec:mo>+</ec:mo><ec:mi mathvariant="normal">H</ec:mi><ec:mo>.</ec:mo><ec:mi mathvariant="normal">c</ec:mi><ec:mo>.</ec:mo></ec:math> and <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"><kc:msup><kc:mi>B</kc:mi><kc:mo>*</kc:mo></kc:msup><kc:msup><kc:mover accent="true"><kc:mi>B</kc:mi><kc:mo stretchy="false">¯</kc:mo></kc:mover><kc:mo>*</kc:mo></kc:msup></kc:math> channels are suitable for the resonances. We highly recommend that the LHCb and Belle II Collaborations hunt for these bottomoniumlike states in the future. Published by the American Physical Society 2024