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

Abstract

Consequences of increasing the binding energy of the hypertriton ground state ${}_{\Lambda }^3\mathrm{H}(J^P={\frac{1}{2}}^{+})$ from the emulsion value $B_{\Lambda }^{\mathrm{EMUL}}({}_{\Lambda }^3{\mathrm{H}}_{g.s.})$=0.13$\pm$0.05 MeV to the STAR value $B_{\Lambda }^{\mathrm{STAR}}{(}_{\Lambda }^3\mathrm{H})=(0.41\pm 0.12\pm 0.11)$ MeV are studied for $s$-shell hypernuclei within a pionless EFT approach at leading order, constrained by the binding energies of the $0^{+}$ and $1^{+}$ ${}_{\Lambda }^4\mathrm{H}$ 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 $\Lambda nn({\frac{1}{2}}^{+})$ resonance becomes broader and less likely to be observed experimentally, whereas the ${}_{\Lambda }^3\mathrm{H}({\frac{3}{2}}^{+})$ spin-flip virtual state moves closer to the $\Lambda d$ threshold to become a shallow bound state for specific $\Lambda N$ interaction strengths. The effect of such a near-threshold ${}_{\Lambda }^3\mathrm{H}({\frac{3}{2}}^{+})$ state on femtoscopic studies of $\Lambda$-deuteron correlations, and its lifetime if bound, are discussed. Increasing $B_{\Lambda }({}_{\Lambda }^3{\mathrm{H}}_{g.s.})$ moderately, up to $\sim$0.5 MeV, hardly affects calculated values of $B_{\Lambda }({}_{\Lambda }^5\mathrm{He})$.