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

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.

16 pages, 3 figures, some discussion and references added in v2; matches published version

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• Contribution of the Weinberg-type Operator to atomic and nuclear electric dipole moments