Femtoscopy correlation functions and mass distributions from production experiments

Abstract

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

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