Hadron masses and the sigma commutator in light of chiral perturbation theory

Abstract

We analyze carefully the impact of non-analytic chiral corrections to the mass spectrum of the pseudoscalar meson octet J P = 0 − and the baryon octet J P = 1 2 + . We find that the quark mass ratios must lie in the range 21 ≤ m s m ̂ ≤ 32 and 1.6 ≤ m d m u ≤ 2.2 . We also calculate the analogous corrections to the pion-nucleon sigma commutator σ πN . It turns out that the value σ πN = 60 MeV is not compatible with the structure of the meson and baryon spectrum, unless the nucleon mass is smaller than 600 MeV in the chiral limit m u = m d = m s = 0.