Searching for femtoscopic signatures of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> (<mml:math x

The femtoscopic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:mover accent="true"><a:mi>D</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> correlation functions are investigated to predict the signature of the not-yet-established <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>3700</e:mn><e:mo stretchy="false">)</e:mo></e:math> state. Here it is interpreted as a bound state generated by solving the coupled-channel Bethe-Salpeter equations with the local hidden-gauge formalism. We prospect how the relevant properties and observables characterizing this state—like the pole position, scattering lengths and compositeness—might be affected by the variation of the parameters of the model. The amplitudes are then used as input into the momentum correlation functions of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>D</i:mi><i:mn>0</i:mn></i:msup><i:msup><i:mover accent="true"><i:mi>D</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:mn>0</i:mn></i:msup></i:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>D</m:mi><m:mo>+</m:mo></m:msup><m:msup><m:mi>D</m:mi><m:mo>−</m:mo></m:msup></m:math> pairs. We discuss how their behaviors encode the features of the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>X</o:mi><o:mo stretchy="false">(</o:mo><o:mn>3700</o:mn><o:mo stretchy="false">)</o:mo></o:math> state.