Measurements of the branching fractions of the P -wave charmonium spin-singlet state hc(P<mml:…

Based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:mn>2712.4</a:mn><a:mo>±</a:mo><a:mn>14.3</a:mn><a:mo stretchy="false">)</a:mo><a:mo>×</a:mo><a:msup><a:mn>10</a:mn><a:mn>6</a:mn></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>ψ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3686</a:mn><a:mo stretchy="false">)</a:mo></a:math> events, we investigate four hadronic decay modes of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>P</g:mi></g:math>-wave charmonium spin-singlet state <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>h</i:mi><i:mi>c</i:mi></i:msub><i:msup><i:mo stretchy="false">(</i:mo><i:mn>1</i:mn></i:msup><i:msub><i:mi>P</i:mi><i:mn>1</i:mn></i:msub><i:mo stretchy="false">)</i:mo><i:mo stretchy="false">→</i:mo><i:msup><i:mi>h</i:mi><i:mo>+</i:mo></i:msup><i:msup><i:mi>h</i:mi><i:mo>−</i:mo></i:msup><i:msup><i:mi>π</i:mi><i:mn>0</i:mn></i:msup><i:mo>/</i:mo><i:mi>η</i:mi></i:math> (<n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>h</n:mi><n:mo>=</n:mo><n:mi>π</n:mi></n:math> or <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>K</p:mi></p:math>) via the process <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>ψ</r:mi><r:mo stretchy="false">(</r:mo><r:mn>3686</r:mn><r:mo stretchy="false">)</r:mo><r:mo stretchy="false">→</r:mo><r:msup><r:mi>π</r:mi><r:mn>0</r:mn></r:msup><r:msub><r:mi>h</r:mi><r:mi>c</r:mi></r:msub></r:math> at BESIII. The <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>h</w:mi><w:mi>c</w:mi></w:msub><w:mo stretchy="false">→</w:mo><w:msup><w:mi>π</w:mi><w:mo>+</w:mo></w:msup><w:msup><w:mi>π</w:mi><w:mo>−</w:mo></w:msup><w:msup><w:mi>π</w:mi><w:mn>0</w:mn></w:msup></w:math> decay is observed with a significance of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mrow><z:mn>9.6</z:mn><z:mi>σ</z:mi></z:mrow></z:math> after taking into account systematic uncertainties. Evidences for <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>h</bb:mi><bb:mi>c</bb:mi></bb:msub><bb:mo stretchy="false">→</bb:mo><bb:msup><bb:mi>K</bb:mi><bb:mo>+</bb:mo></bb:msup><bb:msup><bb:mi>K</bb:mi><bb:mo>−</bb:mo></bb:msup><bb:msup><bb:mi>π</bb:mi><bb:mn>0</bb:mn></bb:msup></bb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>h</eb:mi><eb:mi>c</eb:mi></eb:msub><eb:mo stretchy="false">→</eb:mo><eb:msup><eb:mi>K</eb:mi><eb:mo>+</eb:mo></eb:msup><eb:msup><eb:mi>K</eb:mi><eb:mo>−</eb:mo></eb:msup><eb:mi>η</eb:mi></eb:math> are found with significances of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mn>3.5</hb:mn><hb:mi>σ</hb:mi></hb:math> and <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mn>3.3</jb:mn><jb:mi>σ</jb:mi></jb:math>, respectively, after considering the systematic uncertainties. The branching fractions of these decays are measured to be <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mi mathvariant="script">B</lb:mi><lb:mo stretchy="false">(</lb:mo><lb:msub><lb:mi>h</lb:mi><lb:mi>c</lb:mi></lb:msub><lb:mo stretchy="false">→</lb:mo><lb:msup><lb:mi>π</lb:mi><lb:mo>+</lb:mo></lb:msup><lb:msup><lb:mi>π</lb:mi><lb:mo>−</lb:mo></lb:msup><lb:msup><lb:mi>π</lb:mi><lb:mn>0</lb:mn></lb:msup><lb:mo stretchy="false">)</lb:mo><lb:mo>=</lb:mo><lb:mo stretchy="false">(</lb:mo><lb:mn>1.36</lb:mn><lb:mo>±</lb:mo><lb:mn>0.16</lb:mn><lb:mo>±</lb:mo><lb:mn>0.14</lb:mn><lb:mo stretchy="false">)</lb:mo><lb:mo>×</lb:mo><lb:msup><lb:mn>10</lb:mn><lb:mrow><lb:mo>−</lb:mo><lb:mn>3</lb:mn></lb:mrow></lb:msup></lb:math>, <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi mathvariant="script">B</tb:mi><tb:mo stretchy="false">(</tb:mo><tb:msub><tb:mi>h</tb:mi><tb:mi>c</tb:mi></tb:msub><tb:mo stretchy="false">→</tb:mo><tb:msup><tb:mi>K</tb:mi><tb:mo>+</tb:mo></tb:msup><tb:msup><tb:mi>K</tb:mi><tb:mo>−</tb:mo></tb:msup><tb:msup><tb:mi>π</tb:mi><tb:mn>0</tb:mn></tb:msup><tb:mo stretchy="false">)</tb:mo><tb:mo>=</tb:mo><tb:mo stretchy="false">(</tb:mo><tb:mn>3.26</tb:mn><tb:mo>±</tb:mo><tb:mn>0.84</tb:mn><tb:mo>±</tb:mo><tb:mn>0.36</tb:mn><tb:mo stretchy="false">)</tb:mo><tb:mo>×</tb:mo><tb:msup><tb:mn>10</tb:mn><tb:mrow><tb:mo>−</tb:mo><tb:mn>4</tb:mn></tb:mrow></tb:msup></tb:math>, and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mi mathvariant="script">B</bc:mi><bc:mo stretchy="false">(</bc:mo><bc:msub><bc:mi>h</bc:mi><bc:mi>c</bc:mi></bc:msub><bc:mo stretchy="false">→</bc:mo><bc:msup><bc:mi>K</bc:mi><bc:mo>+</bc:mo></bc:msup><bc:msup><bc:mi>K</bc:mi><bc:mo>−</bc:mo></bc:msup><bc:mi>η</bc:mi><bc:mo stretchy="false">)</bc:mo><bc:mo>=</bc:mo><bc:mo stretchy="false">(</bc:mo><bc:mn>3.13</bc:mn><bc:mo>±</bc:mo><bc:mn>1.08</bc:mn><bc:mo>±</bc:mo><bc:mn>0.38</bc:mn><bc:mo stretchy="false">)</bc:mo><bc:mo>×</bc:mo><bc:msup><bc:mn>10</bc:mn><bc:mrow><bc:mo>−</bc:mo><bc:mn>4</bc:mn></bc:mrow></bc:msup></bc:math>, where the first uncertainties are statistical and the second are systematic. No significant signal of <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:msub><jc:mi>h</jc:mi><jc:mi>c</jc:mi></jc:msub><jc:mo stretchy="false">→</jc:mo><jc:msup><jc:mi>π</jc:mi><jc:mo>+</jc:mo></jc:msup><jc:msup><jc:mi>π</jc:mi><jc:mo>−</jc:mo></jc:msup><jc:mi>η</jc:mi></jc:math> is found, and the upper limit of its decay branching fraction is determined to be <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:mi mathvariant="script">B</mc:mi><mc:mo stretchy="false">(</mc:mo><mc:msub><mc:mi>h</mc:mi><mc:mi>c</mc:mi></mc:msub><mc:mo stretchy="false">→</mc:mo><mc:msup><mc:mi>π</mc:mi><mc:mo>+</mc:mo></mc:msup><mc:msup><mc:mi>π</mc:mi><mc:mo>−</mc:mo></mc:msup><mc:mi>η</mc:mi><mc:mo stretchy="false">)</mc:mo><mc:mo><</mc:mo><mc:mn>4.0</mc:mn><mc:mo>×</mc:mo><mc:msup><mc:mn>10</mc:mn><mc:mrow><mc:mo>−</mc:mo><mc:mn>4</mc:mn></mc:mrow></mc:msup></mc:math> at the 90% confidence level. Published by the American Physical Society 2024