Lambda-Lambda interaction from relativistic heavy-ion collisions

Abstract: We investigate the two-particle intensity correlation function of $\Lambda$ in relativistic heavy-ion collisions. We find that the behavior of the $\Lambda\Lambda$ correlation function at small relative momenta is fairly sensitive to the interaction potential and collective flows. By comparing the results of different source functions and potentials, we explore the effect of intrinsic collective motions on the correlation function. We find that the recent STAR data gives a strong constraint on the scattering length and effective range of $\Lambda\Lambda$ interaction as, $-1.8 \mathrm{fm}^{-1} < 1/a_0 < -0.8 \mathrm{fm}^{-1}$ and $3.5 \mathrm{fm} < r_\mathrm{eff} < 7 \mathrm{fm}$, respectively,if $\Lambda$ samples do not include feed-down contribution from long-lived particles. We find that feed-down correction for $\Sigma^0$ decay reduces the sensitivity of the correlation function to the detail of the $\Lambda\Lambda$ interaction. As a result, we obtain a weaker constraint $1/a_0 <-0.8$ fm$^{-1}$. Implication for the signal of existence of $H$-dibaryon is discussed. Comparison with the scattering parameters obtained from the double $\Lambda$ hypernucleus may reveal in-medium effects in the $\Lambda\Lambda$ interaction.