ΛΛinteractions 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, qq 2 ρ and qq ρ ss ρ, and the πN sigma term. When qq 2 ρ is nearly independent of density and qq ρ ss ρ depends strongly on density, we can obtain weakly attractive ΛΛ potentials (about several MeV) in low Λ density region, which agree with the information from the latest double Λ hypernucleus experiments. The nearly no density dependence of qq 2 ρ and strong density dependence of qq ρ ss ρ can be explained naturally if the properties of qq 2 ρ and qq ρ ss ρ are assumed to be similar to those of ππ and KK in nuclear medium, respectively.

ΣΣinteractions in finite-density QCD sum rules

“…[22], the other dimension-three and -four quark and gluon condensates are easily obtained. The results are…”

“…where b D , b F , and B 0 are real parameters in the chiral Lagrangian, which can be seen in many references, for example [22]. Then, from Eq.…”

“…As done in [22], we can easily extend the sum rules in nuclear matter [13] to describe the interactions in the pure matter by changing the quark and gluon condensates in nuclear matter to those in pure matter (the sum rules are listed in the Appendix). Using the obtained sum rules, the baryon scalar self-energy s , the vector self-energy v , and the effective mass M * can be related to the in-medium quark and gluon condensates at finite-density.…”

“…Thus, the contributions of the higher order term δE are neglected in the calculations. In the chiral perturbation theory (see Appendix B of [22]), the mass is given by…”

“…Based on the sum rules for N interactions [17], the interactions can be described by substituting the in-medium condensates in nucleonic nuclear matter with pure matter. This approach has been adopted in our previous work, in which the interactions were discussed [22].…”