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

Understand

The hypernucleus $\nuclide[6][\Lambda\Lambda]{He}$ 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 $\nuclide[6][\Lambda\Lambda]{He}$ and the scattering length $a_{\Lambda\Lambda}^{}$ of the $S$-wave $\Lambda\Lambda$ scattering.