pi N sigma term, (ss)over-bar in the nucleon, and the scalar form factor: A lattice study

We report on a lattice QCD calculation of the pi N sigma term, the scalar form factor, and [N\<(ss)over bar>\N]. The disconnected insertion part of sigma(pi N) is found to be 1.8+/-0.1 times larger than the connected insertion contribution. The q(2) dependence of sigma(pi N)(q(2)) is about the same as G(E)(q(2)) of the proton so that sigma(pi N)(2m(pi)(2)) - sigma(pi N)[0] = 6.6 +/- 0.6 MeV. The ratio gamma = [N\<(ss)over bar>\N]/[N\<(u)over bar u> + <(d)over bar d>\N] = 0.36 +/- 0.03. Both results favor a sigma(pi N)similar to 53 MeV, slightly larger than our direct calculation of sigma(pi N)=49.7+/-2.6 MeV. We also compute F-s and D-s and find that the agreement with those from the octet baryon mass splittings crucially depends on the inclusion of the large disconnected insertion. Finally, we give our result for the KN sigma term.