The pion-nucleon $σ$ term from pionic atoms

Abstract

Earlier work suggested that the in-medium $πN$ threshold isovector amplitude $b_1(ρ)$ gets renormalized in pionic atoms by about 30% away from its $ρ=0$ 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 $f_π$ in terms of the pion-nucleon $σ$ term $σ_{πN}$. Accepting the validity of this approach, we extracted $σ_{πN}$ from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value $σ_{πN}=57\pm 7$ MeV is robust with respect to variation of $πN$ interaction terms other than the isovector $s$-wave term with which $σ_{πN}$ 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 $σ_{πN}$ derived here agrees with values obtained in several recent studies based on near-threshold $πN$ 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