High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations.

We present a determination of the pion-nucleon (πN) σ term σ_{πN} based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent high-precision data from pionic atoms to pin down the πN scattering lengths as well as of constraints from analyticity, unitarity, and crossing symmetry in the form of Roy-Steiner equations to perform the extrapolation to the Cheng-Dashen point in a reliable manner. With isospin-violating corrections included both in the scattering lengths and the LET, we obtain σ_{πN}=(59.1±1.9±3.0)  MeV=(59.1±3.5)  MeV, where the first error refers to uncertainties in the πN amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.