Hidden charmed decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> within the <mml:math xmlns:mml

The dipionic transition 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> to the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>η</e:mi><e:mi>c</e:mi></e:msub></e:math> was investigated using an effective Lagrangian approach. In this study, the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>X</g:mi><g:mo stretchy="false">(</g:mo><g:mn>3872</g:mn><g:mo stretchy="false">)</g:mo></g:math> was assumed to be a <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:mo>+</k:mo><k:mi mathvariant="normal">c</k:mi><k:mo>.</k:mo><k:mi mathvariant="normal">c</k:mi><k:mo>.</k:mo></k:math> bound state with the quantum numbers <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>J</q:mi><q:mrow><q:mi>P</q:mi><q:mi>C</q:mi></q:mrow></q:msup><q:mo>=</q:mo><q:msup><q:mn>1</q:mn><q:mrow><q:mo>+</q:mo><q:mo>+</q:mo></q:mrow></q:msup></q:math> and to decay via triangle and box loops. It is found that the partial decay widths arising from the box loops are one order of magnitude greater than those from the triangle ones. The decay widths are model-dependent, as characterized by the cutoff parameter introduced in the form factor. Moreover, the charged and neutral <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>D</s:mi><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> configurations of the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>X</w:mi><w:mo stretchy="false">(</w:mo><w:mn>3872</w:mn><w:mo stretchy="false">)</w:mo></w:math> and its mass also influence the decay widths. With our model parameters, the decay widths for the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>X</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mn>3872</ab:mn><ab:mo stretchy="false">)</ab:mo><ab:mo stretchy="false">→</ab:mo><ab:msup><ab:mi>π</ab:mi><ab:mo>+</ab:mo></ab:msup><ab:msup><ab:mi>π</ab:mi><ab:mo>−</ab:mo></ab:msup><ab:msub><ab:mi>η</ab:mi><ab:mi>c</ab:mi></ab:msub></ab:math> can reach up to several tens of keV. We hope that the current calculations within the molecular interpretation will be helpful for the future experiments.