Hidden strangeness in the proton? Determination of the real part of the isospin-even forward-scattering amplitude of pion-nucleon scattering at 54.3 MeV

The contradiction of the $\sigma$ term of pion-nucleon scattering as deduced from the Karlsruhe-Helsinki phase shifts with the smaller value calculated by the chiral perturbation theory of QCD is well known. In an effort to clarify the discrepancy we have determined the real part of the isospin-even forward-scattering amplitude of pion-nucleon scattering at a pion energy $T_{\pi }=54.3\mathrm{}$ MeV by measurement of the elastic scattering of positive and negative pions on protons in the Coulomb-nuclear interference region. The deduced value is in agreement with the prediction of the Karlsruhe-Helsinki phase-shift analysis for that energy. The resulting large value of the $\sigma$ term may be interpreted as being due to the influence of $\overline{s}s$ sea pairs even at large distances (small $Q^2$) as previously suggested by the European Muon Collaboration measurement of deep-inelastic scattering of polarized muons on polarized protons.