Femtoscopy correlation functions and mass distributions from production experiments

We discuss the relation between the Koonin-Pratt femtoscopic correlation function (CF) and invariant mass distributions from production experiments. We show that the equivalence is total for a zero source-size and that a Gaussian finite-size source provides a form-factor for the virtual production of the particles. Motivated by this remarkable relationship, we study an alternative method to the Koonin-Pratt formula, which connects the evaluation of the CF directly with the production mechanisms. The differences arise mostly from the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi></a:math>–matrix quadratic terms and increase with the source size. We study the case of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>D</c:mi><c:mn>0</c:mn></c:msup><c:msup><c:mi>D</c:mi><c:mrow><c:mo>*</c:mo><c:mo>+</c:mo></c:mrow></c:msup></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>D</e:mi><e:mo>+</e:mo></e:msup><e:msup><e:mi>D</e:mi><e:mrow><e:mo>*</e:mo><e:mn>0</e:mn></e:mrow></e:msup></e:math> correlation functions of interest to unravel the dynamics of the exotic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>T</g:mi><g:mrow><g:mi>c</g:mi><g:mi>c</g:mi></g:mrow></g:msub><g:mo stretchy="false">(</g:mo><g:mn>3875</g:mn><g:msup><g:mo stretchy="false">)</g:mo><g:mo>+</g:mo></g:msup></g:math>, and find that these differences become quite sizable already for 1 fm sources. We nevertheless conclude that the lack of coherence in high-multiplicity-event reactions and in the creation of the fire-ball source that emits the hadrons certainly make much more realistic the formalism based on the Koonin-Pratt equation. We finally derive an improved Lednicky-Lyuboshits (LL) approach, which implements a Lorentz ultraviolet regulator that corrects the pathological behavior of the LL CF in the punctual source-size limit. Published by the American Physical Society 2024