HΛΛ5 and HeΛΛ5 hypernuclei reexamined in halo/cluster effective theory

The J=1/2 iso-doublet double-$\Lambda$-hypernuclei, namely, ${}_{\Lambda\Lambda}^{5}$H and ${}_{\Lambda\Lambda}^{5}$He, are examined as the three-body cluster states, $\Lambda\Lambda t$ ($t\equiv {}^3$H or triton) h$ ($h\equiv {}^3$He helion), respectively, in a model independent framework utilizing pionless halo effective theory. Both singlet triplet states of constituent $\Lambda T$ ($T\equiv t,h$) sub-system used elastic channel for study $_\Lambda^4$H$-\Lambda$ $_\Lambda^4$He$-\Lambda$ scattering processes. A prototypical leading order investigation using sharp momentum cut-off regulator, irrespective type chosen, yields almost identical dependence binding energy double-$\Lambda$-separation ($B_{\Lambda\Lambda}$) is obtained mirror partners, evidently suggesting good isospin symmetry these systems. Subsequently, upon normalization our solutions to integral equation with respect single pair input data from an {\it ab initio} potential analysis each hypernuclei, $B_{\Lambda\Lambda}$ which agrees fairly well various erstwhile regulator models choice $\sim 200$ MeV. This either consistent theory its slightly augmented version hard scale around $2m_\pi$, where low-energy $\Lambda$-$\Lambda$ interactions dominated by $\pi\pi$ $\sigma$-meson exchange. Finally, demonstrate predictability theory, we present preliminary estimates S-wave lengths $\Lambda$-separation energies.