Abstract
Earlier work suggested that the in-medium πN threshold isovector amplitude b1(ρ) gets renormalized in pionic atoms by ∼30% away from its ρ=0 free-space value, relating such renormalization to the leading low-density decrease of the in-medium quark condensate <q¯q> and the pion decay constant fπ in terms of the pion-nucleon σ term σπN. Accepting the validity of this approach, we extracted σπN from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value σπN=57±7 MeV is robust with respect to variation of πN interaction terms other than the isovector s-wave term with which σπN 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 σπN 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.
Highlights
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Recent evaluations roughly fall into two classes: (i) pion-nucleon low-energy phenomenology, using πN s-wave scattering lengths derived precisely from pionic hydrogen and deuterium, results in calculated values of σπN ∼ (50 − 60) MeV [2, 3, 4, 5, 6], the most recent of which is 58±5 MeV, whereas (ii) recent lattice QCD calculations reach values of σπN ∼ (30 − 50) MeV [7, 8, 9, 10, 11, 12], the most recent of which is 26±7 MeV
We show that the wealth of data on pionic atoms across the periodic table provides a precise determination of σπN
Summary
Recent evaluations roughly fall into two classes: (i) pion-nucleon low-energy phenomenology, using πN s-wave scattering lengths derived precisely from pionic hydrogen and deuterium, results in calculated values of σπN ∼ (50 − 60) MeV [2, 3, 4, 5, 6], the most recent of which is 58±5 MeV, whereas (ii) recent lattice QCD calculations reach values of σπN ∼ (30 − 50) MeV [7, 8, 9, 10, 11, 12], the most recent of which is 26±7 MeV. We show that the wealth of data on pionic atoms across the periodic table provides a precise determination of σπN. Our recent analysis of pionic atoms [19] demonstrated robustness in the quality of fitting the data against details of the applied analysis methodology
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