Magnetic moments and axial charges of the octet hidden-charm molecular pentaquark family

In this work, we calculate the magnetic moment and axial charge of the octet hidden-charm molecular pentaquark family in quark model. The Coleman-Glashow sum rule for the magnetic moments of pentaquark family is always fulfilled independently of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3</a:mn><a:mo stretchy="false">)</a:mo></a:math> symmetry breaking. In the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mn>8</e:mn><e:mrow><e:mn>2</e:mn><e:mi>f</e:mi></e:mrow></e:msub></e:math> flavor representation, the magnetic moments of hidden-charm molecular pentaquark states with spin configuration <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>J</g:mi><g:mi>P</g:mi></g:msup><g:mo>=</g:mo><g:msup><g:mfrac><g:mn>1</g:mn><g:mn>2</g:mn></g:mfrac><g:mo>−</g:mo></g:msup><g:mo stretchy="false">(</g:mo><g:msup><g:mfrac><g:mn>1</g:mn><g:mn>2</g:mn></g:mfrac><g:mo>+</g:mo></g:msup><g:mo stretchy="false">⊗</g:mo><g:msup><g:mn>0</g:mn><g:mo>−</g:mo></g:msup><g:mo stretchy="false">)</g:mo></g:math> are all equal to <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>μ</l:mi><l:mi>c</l:mi></l:msub><l:mo>=</l:mo><l:mn>0.38</l:mn><l:msub><l:mi>μ</l:mi><l:mi>N</l:mi></l:msub></l:math>. The axial charges of octet hidden-charm molecular pentaquark states are quite small compared to the axial charge of nucleon. The axial charges of the pentaquark states with the spin configuration <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mi>J</n:mi><n:mi>P</n:mi></n:msup><n:mo>=</n:mo><n:msup><n:mfrac><n:mn>1</n:mn><n:mn>2</n:mn></n:mfrac><n:mo>−</n:mo></n:msup><n:mo stretchy="false">(</n:mo><n:msup><n:mfrac><n:mn>1</n:mn><n:mn>2</n:mn></n:mfrac><n:mo>+</n:mo></n:msup><n:mo stretchy="false">⊗</n:mo><n:msup><n:mn>0</n:mn><n:mo>−</n:mo></n:msup><n:mo stretchy="false">)</n:mo></n:math> in <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mn>8</s:mn><s:mrow><s:mn>2</s:mn><s:mi>f</s:mi></s:mrow></s:msub></s:math> flavor representation are all zero.