${}_{\Lambda \Lambda }^{6}He$ in cluster effective field theory

Abstract

The hypernucleus $\nuclide[6][ΛΛ]{He}$ is studied as a three-body ($\Lambda \Lambda \alpha$) cluster system in cluster effective field theory at leading order. We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit, and thus it should be promoted to leading order. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double $\Lambda$ separation energy $B_{\Lambda \Lambda }^{}$ of $\nuclide[6][ΛΛ]{He}$ and the scattering length $a_{\Lambda \Lambda }^{}$ of the $S$-wave $\Lambda \Lambda$ scattering. The role of the scale in this approach is also discussed.

5 pages, 3 figures, REVTeX, to be published in Phys. Rev. C

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• The onset of $\Lambda \Lambda$ hypernuclear binding
• Hypernuclei in Halo/Cluster Effective Field Theory
• Universal physics of the few-body system of two neutrons and one flavored meson
• Recent progress on hypernuclei
• A renormalization method for three-boson system with a triboson field
• Investigation of ${\Xi }^{-}nn$ ($S=-2$) Hypernucleus in Low-energy Pionless Halo Effective Theory
• ${}_{\Lambda \Lambda }^5$H and ${}_{\Lambda \Lambda }^5$He Hypernuclei reexamined in Halo/Cluster Effective Theory
• Double Lambda He-6 in cluster effective field theory