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

• Received 31 August 2021
• Revised 7 November 2021
• Accepted 10 January 2022

DOI:https://doi.org/10.1103/PhysRevC.105.015202