Remarks on the pion-nucleon σ-term

The pion-nucleon σ-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about 3σ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.