High-precision determination of the pion-nucleon $σ$-term from Roy-Steiner equations

Abstract

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 $σ_{πN}=(59.1\pm 1.9\pm 3.0)$ MeV $=(59.1\pm 3.5)$ 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.

6 pages, 1 figure; title changed by journal, version to be published in PRL