Role of electromagnetic interactions in the X(3872) and its analogs

We investigate the role of the electromagnetic interaction in the formation and decay of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>X</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3872</a:mn><a:mo stretchy="false">)</a:mo></a:math>. The binding properties of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>X</e:mi><e:mo stretchy="false">(</e:mo><e:mn>3872</e:mn><e:mo stretchy="false">)</e:mo></e:math> are studied by assuming the molecular nature and considering the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>S</i:mi><i:mtext>−</i:mtext><i:mi>D</i:mi></i:mrow></i:math> wave mixing, isospin breaking, and coupled channel effects, and in particular the correction from the electromagnetic interaction. The radiative decays can better reflect the difference between the charged and neutral <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>D</k:mi><k:msup><k:mover accent="true"><k:mi>D</k:mi><k:mo stretchy="false">¯</k:mo></k:mover><k:mo>*</k:mo></k:msup></k:math> components, since the electromagnetic interaction explicitly breaks the isospin symmetry. We further study the radiative decay widths with the obtained wave functions for different <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>D</o:mi><o:msup><o:mover accent="true"><o:mi>D</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo>*</o:mo></o:msup></o:math> channels. We also explore other similar hidden-charm molecular states. The electromagnetic interaction can make the molecule tighter. Our result of the radiative decay width for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>X</s:mi><s:mo stretchy="false">(</s:mo><s:mn>3872</s:mn><s:mo stretchy="false">)</s:mo><s:mo stretchy="false">→</s:mo><s:mi>γ</s:mi><s:mi>J</s:mi><s:mo>/</s:mo><s:mi>ψ</s:mi></s:math> is in agreement with the experiment. The branching ratio <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msub><x:mi>R</x:mi><x:mrow><x:mi>γ</x:mi><x:mi>ψ</x:mi></x:mrow></x:msub></x:math> is less than 1 in our framework, which supports the Belle and BESIII measurements. Published by the American Physical Society 2024