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

TL;DR

This paper accurately determines the pion-nucleon sigma term using Roy-Steiner equations and recent high-precision data, providing important insights for dark matter detection and nucleon structure.

Contribution

It introduces a novel combined approach using Roy-Steiner equations and high-precision pionic atom data to determine the sigma term with improved accuracy.

Findings

Sigma term value: 59.1 ± 3.5 MeV

Inclusion of isospin-violating corrections

Implications for dark matter detection

Abstract

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.