$Λ$$Λ$ interactions in finite-density QCD sum rules

Abstract

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