Hypernuclei in Halo/Cluster Effective Field Theory

TL;DR

This paper investigates light double hypernuclei as three-body cluster systems using effective field theory, identifying conditions for Efimov states and estimating scattering lengths, thus advancing understanding of hypernuclear structures.

Contribution

It applies halo/cluster effective field theory at leading order to hypernuclei, revealing the presence or absence of Efimov states in specific systems and estimating scattering lengths.

Findings

The $ extLambda extLambda d$ system in spin-0 does not exhibit a limit cycle.

The $ extLambda extLambda d$ in spin-1 and $ extLambda extLambda extalpha$ in spin-0 do show limit cycles.

The scattering length $a_0$ for $ extLambda$-hypertriton in the spin-0 channel is estimated as 16.0±3.0 fm.

Abstract

The light double $\Lambda$ hypernuclei, ${}_{\Lambda\Lambda}^{\ \ 4}$H and ${}_{\Lambda\Lambda}^{\ \ 6}$He, are studied as three-body $\Lambda\Lambda d$ and $\Lambda\Lambda\alpha$ cluster systems in halo/cluster effective field theory at leading order. We find that the $\Lambda\Lambda d$ system in spin-0 channel does not exhibit a limit cycle whereas the $\Lambda\Lambda d$ system in spin-1 channel and the $\Lambda\Lambda\alpha$ system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the $\Lambda\Lambda d$ system in the spin-0 channel we estimate the scattering length $a_0$ for $S$-wave $\Lambda$ hyperon-hypertriton scattering as $a_0=16.0\pm 3.0$ fm. We also discuss that studying the cutoff dependences in the $\Lambda\Lambda d$ and $\Lambda\Lambda\alpha$ systems, the bound state of ${}_{\Lambda\Lambda}^{\ \ 4}$H is not an Efimov state but formed due to a high energy mechanism whereas that of ${}_{\Lambda\Lambda}^{\ \ 6}$He may be regarded as an Efimov state.