Decays of 1−+ charmoniumlike hybrid using lattice QCD

By extracting the transition amplitudes, we give the first lattice QCD prediction of the two-body decay partial widths of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>1</a:mn><a:mrow><a:mo>−</a:mo><a:mo>+</a:mo></a:mrow></a:msup></a:math> charmoniumlike hybrid <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>η</c:mi><c:mrow><c:mi>c</c:mi><c:mn>1</c:mn></c:mrow></c:msub></c:math>. Given the calculated mass value <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>m</e:mi><e:msub><e:mi>η</e:mi><e:mrow><e:mi>c</e:mi><e:mn>1</e:mn></e:mrow></e:msub></e:msub><e:mo>=</e:mo><e:mn>4.329</e:mn><e:mo stretchy="false">(</e:mo><e:mn>36</e:mn><e:mo stretchy="false">)</e:mo><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi></e:math>, the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>η</i:mi><i:mrow><i:mi>c</i:mi><i:mn>1</i:mn></i:mrow></i:msub></i:math> decay is dominated by the open charm modes <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>D</k:mi><k:mn>1</k:mn></k:msub><k:mover accent="true"><k:mi>D</k:mi><k:mo stretchy="false">¯</k:mo></k:mover></k:math>, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>D</o:mi><o:mo>*</o:mo></o:msup><o:mover accent="true"><o:mrow><o:mi>D</o:mi><o:mo>,</o:mo></o:mrow><o:mo stretchy="true">¯</o:mo></o:mover></o:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>D</s:mi><s:mo>*</s:mo></s:msup><s:msup><s:mover accent="true"><s:mi>D</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mo>*</s:mo></s:msup></s:math> with partial widths of 258(133), 88(18), and 150(118) MeV, respectively. The coupling of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>η</w:mi><w:mrow><w:mi>c</w:mi><w:mn>1</w:mn></w:mrow></w:msub></w:math> to <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>χ</y:mi><y:mrow><y:mi>c</y:mi><y:mn>1</y:mn></y:mrow></y:msub></y:math> plus a flavor singlet pseudoscalar is not small, but <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>χ</ab:mi><ab:mrow><ab:mi>c</ab:mi><ab:mn>1</ab:mn></ab:mrow></ab:msub><ab:mi>η</ab:mi></ab:math> decay is suppressed by the small <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>η</cb:mi><cb:mo>−</cb:mo><cb:msup><cb:mi>η</cb:mi><cb:mo>′</cb:mo></cb:msup></cb:math> mixing angle. The partial width of <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>η</eb:mi><eb:mrow><eb:mi>c</eb:mi><eb:mn>1</eb:mn></eb:mrow></eb:msub><eb:mo stretchy="false">→</eb:mo><eb:msub><eb:mi>η</eb:mi><eb:mi>c</eb:mi></eb:msub><eb:msup><eb:mi>η</eb:mi><eb:mo>′</eb:mo></eb:msup></eb:math> is estimated to be around 1 MeV. We suggest experiments to search for <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>η</hb:mi><hb:mrow><hb:mi>c</hb:mi><hb:mn>1</hb:mn></hb:mrow></hb:msub></hb:math> in the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi>P</jb:mi></jb:math>-wave <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msup><lb:mi>D</lb:mi><lb:mo>*</lb:mo></lb:msup><lb:mover accent="true"><lb:mi>D</lb:mi><lb:mo stretchy="false">¯</lb:mo></lb:mover></lb:math> and <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msup><pb:mi>D</pb:mi><pb:mo>*</pb:mo></pb:msup><pb:msup><pb:mover accent="true"><pb:mi>D</pb:mi><pb:mo stretchy="false">¯</pb:mo></pb:mover><pb:mo>*</pb:mo></pb:msup></pb:math> systems. Especially, the polarization of <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msup><tb:mi>D</tb:mi><tb:mo>*</tb:mo></tb:msup><tb:msup><tb:mover accent="true"><tb:mi>D</tb:mi><tb:mo stretchy="false">¯</tb:mo></tb:mover><tb:mo>*</tb:mo></tb:msup></tb:math> can be used to distinguish the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msup><xb:mn>1</xb:mn><xb:mrow><xb:mo>−</xb:mo><xb:mo>+</xb:mo></xb:mrow></xb:msup></xb:math> product (total spin <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mi>S</zb:mi><zb:mo>=</zb:mo><zb:mn>1</zb:mn></zb:math>) from <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:msup><bc:mn>1</bc:mn><bc:mrow><bc:mo>−</bc:mo><bc:mo>−</bc:mo></bc:mrow></bc:msup></bc:math> products (<dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"><dc:mi>S</dc:mi><dc:mo>=</dc:mo><dc:mn>0</dc:mn></dc:math>). Published by the American Physical Society 2024