# The pion-nucleon $\sigma$ term from pionic atoms

## TL;DR

This paper determines the pion-nucleon sigma term from pionic atom data, finding a value of 57±7 MeV, which aligns with phenomenological studies but conflicts with recent lattice QCD results.

## Contribution

The study provides a robust extraction of the sigma term from pionic atom data, highlighting its consistency with phenomenology and discrepancy with lattice QCD.

## Key findings

- Sigma term value: 57±7 MeV
- Agreement with phenomenological studies
- Disagreement with lattice QCD results

## Abstract

Earlier work suggested that the in-medium $\pi N$ threshold isovector amplitude $b_1(\rho)$ gets renormalized in pionic atoms by about 30% away from its $\rho=0$ free-space value, relating such renormalization to the leading low-density decrease of the in-medium quark condensate $<\bar q q>$ and the pion decay constant $f_{\pi}$ in terms of the pion-nucleon $\sigma$ term $\sigma_{\pi N}$. Accepting the validity of this approach, we extracted $\sigma_{\pi N}$ from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value $\sigma_{\pi N}=57\pm 7$ MeV is robust with respect to variation of $\pi N$ interaction terms other than the isovector $s$-wave term with which $\sigma_{\pi N}$ was associated. Higher order corrections to the leading order in density involve some cancellations, suggesting thereby only a few percent overall systematic uncertainty. The value of $\sigma_{\pi N}$ derived here agrees with values obtained in several recent studies based on near-threshold $\pi N$ phenomenology, but sharply disagrees with values obtained in recent direct lattice QCD calculations.