ΛΛ interactions in finite-density QCD sum rules

The properties of $\Lambda$-hyperons in pure $\Lambda$ matter are studied with the finite-density QCD sum rule approach. The first order quark and gluon condensates in $\Lambda$ nuclear matter are deduced from the chiral perturbation theory. The sum rule predictions are sensitive to the four-quark condensates, $<\bar{q}q>^2_{\rho}$ and $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$, and the $\pi N$ sigma term. When $<\bar{q}q>^2_{\rho}$ is nearly independent of density and $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$ depends strongly on density, we can obtain weakly attractive $\Lambda$$\Lambda$ potentials (about several MeV) in low $\Lambda$ density region, which agree with the information from the latest double $\Lambda$ hyper-nucleus experiments. The nearly no density dependence of $<\bar{q}q>^2_{\rho}$ and strong density dependence of $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$ can be explained naturally if the properties of $<\bar{q}q>^2_{\rho}$ and $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$ are assumed to be similar to those of $\pi\pi$ and $\bar{K} K$ in nuclear medium, respectively.