$N\mathrm{\Lambda }$ interaction from a quark model: $p\mathrm{\Lambda }$ femtoscopy and the hypertriton

Understanding the low-energy nucleon–$\mathrm{\Lambda }$ interaction is essential for describing hypernuclear structures, while its spin dependence remains insufficiently constrained by experimental data. In this work, we investigate the $N\mathrm{\Lambda }$ interaction using the quark delocalization color screening model and explore its implications for $p\mathrm{\Lambda }$ femtoscopy and the hypertriton. The energy and scattering phase shifts of the $N\mathrm{\Lambda }$ system are calculated, revealing weak attraction in both the $J^P=0^{+}$ and $1^{+}$ channels, but no bound states. The corresponding scattering lengths and effective ranges are found to be $-2.36$ fm and $1.61$ fm for $J^P=0^{+}$, and $-0.95$ fm and $1.46$ fm for $J^P=1^{+}$, respectively. Using the Gel’fand–Levitan–Marchenko inverse-scattering method, effective $N\mathrm{\Lambda }$ potentials are reconstructed from the coupled-channel scattering phase shifts and applied to calculate the $p\mathrm{\Lambda }$ femtoscopic correlation function. Comparison with experimental data suggests that the spin-triplet attraction may be underestimated in the present model. Furthermore, employing the Gaussian Expansion Method, we investigate the $NN\mathrm{\Lambda }$ three-body system and obtain a weakly bound hypertriton with a $\mathrm{\Lambda }$ separation energy of $1.06$–$1.16$ MeV. These results demonstrate that $p\mathrm{\Lambda }$ femtoscopic correlations and hypertriton binding provide complementary probes of the spin-dependent $N\mathrm{\Lambda }$ interaction, offering valuable constraints on its low-energy behavior.