Pole trajectories of the $\Lambda(1405)$ helps establish its dynamical nature

Chiral trajectories of dynamically generated resonances are intimately connected to the SU(3) breaking pattern and their nature. From an analysis of a recent LQCD simulation on the $\pi\Sigma-\bar{K}N$ scattering for $I=0$ and the study of the quark mass dependence of the octet baryon masses, we determine for the first time unambiguously the trajectories of the two poles associated to the $\Lambda(1405)$ towards the symmetric point over the $\mathrm{Tr}[M]=C$ trajectory accurately. At $m_\pi\simeq 200$ MeV, our results are consistent with the lattice simulations, and the extrapolations to the physical point, based on the NLO chiral Lagrangians, agree well with existing experimental analyses. We predict qualitatively similar trajectories at LO and up to NLO, consistent with the LO interaction's dominance. At the SU(3) symmetric point up to NLO in this trajectory, the lower pole is located at $E^{(1)}=1583(5)(1)$ MeV, being dominantly a SU(3) singlet, while the higher pole belongs to the octet representation with a mass of $E^{(8)}=1585(8)(2)$ MeV. We also make predictions on the evolution of the two poles over the $m_s=m_{s,\mathrm{phy}}$ trajectory. This can be tested in future LQCD simulations and experimental measurements.
Comment: Updating in this version: prediction of the trajectories of the three poles with $m_s=m_{s,\mathrm{phy}}$. No results are changed. Comments are welcome