Pole trajectories of the $\Lambda(1405)$ towards the SU(3) limit

We determine for the first time the quark mass dependence of the $\Lambda(1405)$ from an analysis of a recent LQCD simulation on the $\pi\Sigma-\bar{K}N$ scattering in $I=0$ and the trajectories of these poles towards the symmetric point over the $m_u+m_d+m_s=constant$ trajectory accurately. At $m_\pi\simeq 200$ MeV, our results are consistent with both, the lattice simulation and experimental data. We predict qualitatively similar trajectories at LO and up to NLO, consistent with the LO interaction's dominance. At the SU(3) symmetric point of this trajectory, both poles are on the physical sheet, and the lower pole is located at $E^{(1)}=1573(6)(6)$ MeV, becoming a SU(3) singlet, while the higher pole at $E^{(8a)}=1589(7)(5)$ MeV couples to the octet representation. The results presented here are crucial to shed light on the molecular nature of this exotic baryon and can be tested in future LQCD simulations.