Lambda-Lambda interaction from two-particle intensity correlation in relativistic heavy-ion collisions

We investigate $\Lambda\Lambda$ interaction dependence of the $\Lambda\Lambda$ intensity correlation in high-energy heavy-ion collisions. By analyzing the correlation data recently obtained by the STAR collaboration based on theoretically proposed $\Lambda\Lambda$ interactions, we give a constraint on the $\Lambda\Lambda$ scattering length, $-1.25~\text{fm} < a_0 < 0$, suggesting that $\Lambda\Lambda$ interaction is weakly attractive and there is no loosely bound state. In addition to the fermionic quantum statistics and the $\Lambda\Lambda$ interaction, effects of collective flow, feed-down from $\Sigma^0$, and the residual source are also found to be important to understand the data. We demonstrate that the correlation data favor negative $\Lambda\Lambda$ scattering length with the pair purity parameter $\lambda=(0.67)^2$ evaluated by using experimental data on the $\Sigma^0/\Lambda$ ratio, while the positive scattering length could be favored when we regard $\lambda$ as a free fitting parameter.