${}_{\Lambda \Lambda }^4$H in halo effective field theory

Abstract

The ${}_{\Lambda \Lambda }^4$H bound state and the $S$-wave hypertriton(${}_{\Lambda }^3$H)-$\Lambda$ scattering in spin singlet and triplet channels below the hypertriton breakup momentum scale are studied in halo/cluster effective field theory at leading order by treating the ${}_{\Lambda \Lambda }^4$H system as a three-cluster ($\Lambda$-$\Lambda$-deuteron) system. In the spin singlet channel, the amplitude is insensitive to the cutoff parameter ${\Lambda }_c$ introduced in the integral equation, and we find that there is no bound state. In this case, the scattering length of the hypertriton-$\Lambda$ scattering is found to be $a_0^{}=16.0\pm 3.0$ fm. In the spin triplet channel, however, the amplitude obtained by the coupled integral equations is sensitive to ${\Lambda }_c$, and we introduce the three-body contact interaction $g_1^{}({\Lambda }_c)$. After phenomenologically fixing $g_1^{}({\Lambda }_c)$, we find that the correlation between the two-$\Lambda$ separation energy $B_{\Lambda \Lambda }$ from the ${}_{\Lambda \Lambda }^4$H bound state and the scattering length $a_{\Lambda \Lambda }^{}$ of the $S$-wave $\Lambda$-$\Lambda$ scattering is significantly sensitive to the value of ${\Lambda }_c$.

11 pages, 10 figures, REVTeX, to appear in Phys. Rev. C

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