ΛΛinteractions in finite-density QCD sum rules

Abstract

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