Light-quark mass dependence of the $\Lambda(1405)$ resonance

Abstract

We present the light-quark mass dependence of the $\Lambda(1405)$ resonance at leading order in a renormalizable framework of covariant chiral effective field theory. The meson-baryon scattering amplitudes, which are obtained by solving the scattering equation within time-ordered perturbation theory, follow the quark mass trajectory of the Coordinated Lattice Simulations consortium. At $M_\pi\approx 200$ MeV and $M_K\approx 487$ MeV, our parameter-free prediction of $\Lambda(1405)$ poles is consistent with the recent lattice results of BaSc Collaboration [Phys. Rev. Lett. 132, 051901 (2024)]. Varying the pion mass from $135$ MeV to $400$ MeV, we present the evolution of double-pole positions of $\Lambda(1405)$: the higher pole remains a resonance around the $\bar{K}N$ threshold; whereas the lower pole undergoes a transition from resonance to a virtual state, and ultimately to a bound state of the $\pi\Sigma$ system, which could be verified by the forthcoming lattice QCD simulations.