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Consequences of increased hypertriton binding for $s$-shell $Λ$-hypernuclear systems

Consequences of increasing the binding energy of the hypertriton ground state ${_Λ^3}{\rm H}(J^P={\frac{1}{2}}^+)$ from the emulsion value $B^{\rm EMUL}_Λ({_Λ^3}{\rm H}_{\rm g.s.})$=0.13$\pm$0.05 MeV to the STAR value $B^{\rm STAR}_Λ(^{3}_Λ{\rm H}) = (0.41\pm 0.12 \pm 0.11)$ MeV are studied for $s$-shell hypernuclei within a pionless EFT approach at leading order, constrained by the binding energies of the $0^+$ and $1^+$ ${_Λ^4} {\rm H}$ states. The stochastic variational method is used in bound-state calculations, whereas the inverse analytic continuation in the coupling constant method is used to locate $S$-matrix poles of continuum states. It is found that the $Λnn({\frac{1}{2}}^+)$ resonance becomes broader and less likely to be observed experimentally, whereas the ${_Λ^3}{\rm H}({\frac{3}{2}}^+)$ spin-flip virtual state moves closer to the $Λd$ threshold to become a shallow bound state for specific $ΛN$ interaction strengths. The effect of such a near-threshold ${_Λ^3}{\rm H}({\frac{3}{2}}^+)$ state on femtoscopic studies of $Λ$-deuteron correlations, and its lifetime if bound, are discussed. Increasing $B_Λ({_Λ^3} {\rm H}_{\rm g.s.})$ moderately, up to $\sim$0.5 MeV, hardly affects calculated values of $B_Λ({_Λ^5}{\rm He})$.