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Description
This work presents the first measurement of the $\Lambda\Lambda$ balance functions (BFs) in OO and Ne-Ne collisions at $\sqrt{s_{\rm NN}} = 5.36$ TeV and pp collisions at $\sqrt{s} = 5.36$ TeV and $\sqrt{s} = 13.6$ TeV as a function of charged-particle multiplicity. The BF ($B^{\alpha\beta}$) is defined as the conditional probability of finding a particle $\alpha$ whose quantum numbers are partially or fully balanced by particle $\beta$. The $B^{\alpha\beta}$ is constructed from two-particle number correlation function ($R_{2}$) of $\alpha\bar{\beta}$, $\alpha\beta$, $\bar{\alpha}\beta$ and $\bar{\alpha}\bar{\beta}$ pairs.
The root-mean-square width of the BF is sensitive to the production and transport of quantum numbers in the context of the two--wave quark production in nuclear collisions. Furthermore, it is also sensitive to the kinetic freeze-out temperature and radial flow, whereas the integral of the BF is sensitive to the relative abundances of the correlated particle pairs and the temperature at which these hadrons are produced. The $B^{\Lambda\Lambda}$ measurement in pp, OO and Ne-Ne collisions thus provides crucial insights into the correlated production of $\Lambda(\bar{\Lambda})$ as a function of collision multiplicity. The $B^{\Lambda\Lambda}$ is measured as a function of relative rapidity ($\Delta y$) and relative azimuth ($\Delta\varphi$). The integral of the BF increases with the collision multiplicity. This rise in the integral can possibly be driven by radial flow and strangeness enhancement in nuclear collisions as well as finite acceptance. The experimental results are also compared with the predictions of Pythia~8 and EPOS~4 Monte Carlo event generators.