Two-pole structure of the $\Lambda(1405)$
In plain words
The $\Lambda(1405)$ is a strange baryon that lies just below the energy needed to make an antikaon and a nucleon, and is often described as a bound state of the two. Theory based on chiral symmetry (an approximate symmetry of QCD with nearly massless light quarks) predicts that it is really two nearby states, and whether the second, broader one exists is debated.
Precise statement
In coupled-channel chiral unitary approaches to $S=-1, I=0$ meson-baryon scattering (K-bar N, pi Sigma), the $\Lambda(1405)$ region contains a narrow pole near 1425 MeV coupled mainly to K-bar N and a broad lower pole coupled mainly to $\pi\Sigma$. Determine whether the lower pole exists at physical quark masses and its position, from $\pi\Sigma$ line shapes in photoproduction and K- p reactions, kaonic-hydrogen data and lattice QCD. Answer: both pole positions with uncertainty below 20 MeV in real and imaginary parts, or exclusion of the lower pole.
What would settle it
Lattice QCD coupled-channel K-bar N and $\pi \Sigma$ scattering at the physical pion mass, combined with high-statistics $\pi \Sigma$ line shapes in several production reactions.
Status in the literature
Unverified note
Lattice QCD at $m_{\pi}$ about $200\ \mathrm{MeV}$ found two poles, a virtual state below the $\pi\ \Sigma$ threshold and a resonance just below K-bar N (Bulava et al., PRL 132, 051901, 2024); the lower pole at physical masses remained model dependent as of 2026.