High-precision determination of the pion-nucleon $\sigma$-term from
  Roy-Steiner equations
  We present a determination of the pion-nucleon ($\pi N$) $\sigma$-term
$\sigma_{\pi N}$ based on the Cheng-Dashen low-energy theorem (LET), taking
advantage of the recent high-precision data from pionic atoms to pin down the
$\pi N$ 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 $\sigma_{\pi N}=(59.1\pm 1.9\pm 3.0)$ MeV $=(59.1\pm 3.5)$ MeV,
where the first error refers to uncertainties in the $\pi N$ amplitude and the
second to the LET. Consequences for the scalar nucleon couplings relevant for
the direct detection of dark matter are discussed.
