$\Lambda$$\Lambda$ interactions in finite-density QCD sum rules

Abstract

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, $<\bar{q}q{>}_{\rho }^2$ and $<\bar{q}q{>}_{\rho }<\bar{s}s{>}_{\rho }$, and the $\pi N$ sigma term. When $<\bar{q}q{>}_{\rho }^2$ 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 $<\bar{q}q{>}_{\rho }^2$ and strong density dependence of $<\bar{q}q{>}_{\rho }<\bar{s}s{>}_{\rho }$ can be explained naturally if the properties of $<\bar{q}q{>}_{\rho }^2$ 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.

10 pages and 7 figures

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Cited by in corpus (2)

• QCD sum rules for the baryon octet in nuclear matter
• The $\Sigma \Sigma$ interactions in finite-density QCD sum rules