Abstract
A brief pedagogical introduction to correlation femtoscopy is given. We then focus on the shape of the correlation function and discuss the possible reasons for its departure from the Gaussian form and better reproduction with a Lévy stable distribution. With the help of Monte Carlo simulations based on asymmetric extension of the Blast-Wave model with resonances we demonstrate possible influence of averaging over many events and integrating over wide momentum bins on the shape of the correlation function. We also show that the shape is strongly influenced by the use of the one-dimensional parametrisation in the q i n v variable.
Highlights
Correlation femtoscopy is widely used in heavy-ion collisions for the determination of space–time characteristics of hadron-emitting sources
To keep the source simple, no resonance decays are included at this point
We explained in the introductory section of this paper that in addition to the generalisation of the concept of Central Limit Theorem [9], an especially important motivation for the use of Lévy stable parametrisation is the search for critical behaviour [10]
Summary
Correlation femtoscopy is widely used in heavy-ion collisions for the determination of space–time characteristics of hadron-emitting sources. The two-particle correlation functions are fitted by a Gaussian parametrisation augmented with correction terms due to final-state interactions. Lévy stable distributions possess the property that the shape remains unchanged when one more elementary random process is added to the ones which are already accounted for. The excitement about this particular parametrisation is supported by the argument that with the help of such a fit one could access the critical exponents of the strongly interacting matter [10]. We look at the Lévy stable parametrisations and scrutinise various effects that can lead to such a shape of the correlation function
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