We report on a lattice QCD calculation of the πN σ term, the scalar form factor, and N |ss|N . The disconnected insertion part of σ πN is found to be 1.8 ± 0.1 times larger than the connected insertion contribution. The q 2 dependence of σ πN (q 2 ) is about the same as G E (q 2 ) of the proton so that σ πN (2m 2 π )−σ πN (0) = 6.6±0.6 MeV. The ratio y = N |ss|N / N |ūu+dd|N = 0.36 ± 0.03. Both results favor a σ πN ∼ 53 MeV, slightly larger than our direct calculation of σ πN = 49.7 ± 2.6 MeV. We also compute F s and D s and find that the agreement with those from the octect baryon mass splittings crucially depends on the inclusion of the large disconnected insertion. Finally, we give our result for the KN σ term.

The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at m 0 a = 0.006. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The π and ρ masses at a fixed m π /m ρ ratio indicate small O(a 2 ) corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks.Typeset using REVT E X 1