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

摘要

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 +/- 1.9 +/- 3.0) MeV = (59.1 +/- 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.