Femtoscopy measurements of two-kaon combinations in Au+Au collisions at the STAR experiment

. Relativistic heavy-ion collisions can study the properties of nuclear matter in high-energy experiments like the STAR experiment. One of the meth-ods to learn about the properties of the bulk matter is the femtoscopy technique, which relies on information carried by the particles produced during the collisions. The emission source parameters, like space-time characteristics, can be extracted using the technique. High statistics data from RHIC make it possible to study the correlations between strange particles, like charged and neutral kaons. The pair-wise interactions between the identical kaons that form the basis for femtoscopy are quantum statistics and the Coulomb interaction for K ± K ± , and quantum statistics and the final-state interaction (FSI) through the f 0 (980) / a 0 (980) threshold resonances for K 0 S K 0 S . The interactions between non-identical kaons pairs of K 0 S K ± are essential, as the strong FSI is described only by the a 0 (980) resonance, which could be a four-quark state. These proceedings will present the femtoscopic measurements of strange particles with charged and neutral kaons correlations in Au + Au collisions at the RHIC energy.


Introduction
The main motivation to carry out the kaon femtoscopy study is that kaons are less affected by the feed-down from resonance decays.Kaons have a smaller cross-section on reaction with the hadronic matter and, what is also very important, they contain strange quarks.As it is known, one of the signatures of the Quark-Gluon Plasma (QGP) is the enhancement of the production of strange particles [1].Comparison of femtoscopic results for all possible kaon combinations K ± K ± , K 0 S K 0 S , and K 0 S K ± allows us to examine the a 0 resonance, which is suspected to be a four-quark state, e.g. a tetraquark [2].All the systems should give the same emission source parameters of the homogeneity region and only final state interactions would cause the difference observed in correlations.Agreement between all kaon systems will shed light on the preceding assumption about the a 0 resonance.

Analysis methods
Experimentally, it is impossible to measure properties of the source directly with a size of about 1 fm and a lifetime of about 10 −23 s.The relative momentum of particles produced during the heavy-ion collisions is used to learn about the source's characteristics.The equation (1) describes the correlation function: where S (⃗ q,⃗ r) is the emission function describing space-time properties of the source, Ψ(⃗ q,⃗ r) is the pair wave function which contains information about all effects and interactions, and | is relative distance between two particles.By measuring of pair relative momentum, space-time characteristics of the source like its size can be studied.Theoretically, the K 0 S K 0 S correlation function can be described analytically with a model derived by Lednicky-Lyuboshitz [3], which contains strong final state interaction (FSI): where scattering amplitude, which depends on masses and decay couplings of near-threshold resonances f 0 (980) and a 0 (980) (Table 1), 2 is pair relative momentum (k * is a first particle momentum in pair rest frame), R inv is the size of the particleemitting source and λ is the correlation strength.
In the case of K 0 S K ± analysis, the parametrization was also performed using the Lednicky-Lyuboshitz model, where the strong FSI is due to one resonance, a 0 (980), and all quantities have the same description as in the formula for K 0 S K 0 S :

Description of experiment and data selection
The femtoscopy method is successfully used in the case of the STAR experiment.Particle identification (PID) of charged particles is based on information from two detectors: the Time Projection Chamber (TPC) and Time of Flight (TOF) detector in the pseudorapidity range |η| < 0.9.TPC was used to measure the ionization energy loss of charged particles with a specific mass and momentum.For PID with TOF, the estimated time of flight was used to calculate the particle's mass and described as a function of the track length and momentum.On the other hand, neutral particles like K 0 S were reconstructed using their decay products.Neutral kaons decay via the weak interaction into positive and negative daughters (π + and π − ).After reconstructing the secondary particles, neutral particles are identified based on the invariant mass applying cuts on their decay topology.

Non-identical kaon femtoscopy
Correlation functions for K 0 S K + system for central (0-10%) and noncentral (10-70%) Au+Au collisions at √ s NN = 200 GeV are presented in the Figure 2. The correlation functions are  characterized by dip structure due to near-threshold resonance a 0 (980), and the depth of this dip changes with the collision centrality.Three parametrizations Antonelli, Achasov2001, and Achasov2003 reflect this shape very well.Martin parametrization describes data worse for noncentral events.

Comparison of all kaon combinations
The comparison of the results from K ± K ± , K 0 S K 0 S , and K 0 S K ± analyses for the top RHIC energy as a function of centrality is shown in Figure 3.The Antonelli parametrization gives the 3 EPJ Web of Conferences 276, 01016 (2023) https://doi.org/10.1051/epjconf/202327601016SQM 2022 best agreement in the size of the particle emitting source among all combinations.Achasov's parametrizations lead to much larger source sizes for K 0 S K ± system, while the results with Martin are smaller for K 0 S K ± .Antonelli parametrization favors the assumption that a 0 resonance could be the tetraquark.GeV.For K 0 S K ± only statistical uncertainties are shown.

Summary
In summary, femtoscopic correlations with K ± K ± , K 0 S K 0 S , and K 0 S K ± in Au+Au collisions at √ s NN = 39 and 200 GeV were presented.The extracted radii are compared among the three combinations for the first time.From the K 0 S K 0 S analysis, one can conclude that final state SI significantly affects these correlations due to two near-threshold resonances a 0 (980) and f 0 (980), and it is necessary to include this interaction in parametrization.Two-particle correlation in the K 0 S K ± system is reproduced by FSI due to the a 0 (980) resonance.Parametrization with a 0 (980) perfectly represents the signal region in the correlation function.The obtained source sizes are the biggest in the case of parametrization with the larger resonance mass (Achasov).For top RHIC energy, obtained source sizes for Antonelli parametrization are consistent among all the kaon combinations, which favors the assumption that a 0 (980) resonance could be a tetraquark.

Figure 1 Figure 1 .
Figure 1 presents correlation functions for K 0 S K 0 S combination for 0-10% most central Au+Au collisions at√ s NN = 39 GeV and 200 GeV.These correlations are dominated by the QS effects and strong FSI which gives a characteristic dip structure around q inv = 0.1 GeV/c.The parameterization, including only QS effects (Gaussian), does not describe this shape well, so it is crucial to take into account the strong interaction in the fitting procedure as well.

Figure 3 .
Figure 3. Centrality dependence of sizes of the K ± K ± [8], K 0 S K 0 S , and K 0 S K ± source at √ s NN = 200