Pion-nucleon sigma term revisited in covariant baryon chiral perturbation theory

We study the latest Nf=2+1+1 and Nf=2 ETMC lattice QCD simulations of the nucleon masses and extract the pion-nucleon sigma term utilizing the Feynman-Hellmann theorem in SU(2) baryon chiral perturbation theory with the extended-on-mass-shell scheme. We find that the lattice QCD data can be described quite well already at the next-to-next-to-leading order. The overall picture remains essentially the same at the next-to-next-to-next-to-leading order. Our final result is σπN=50.2(1.2)(2.0) MeV, or equivalently, fu/dN=0.0535(13)(21), where the first uncertainty is statistical and second is theoretical originated from chiral truncations, which is in agreement with that determined previously from the Nf=2+1 and Nf=2 lattice QCD data and that determined by the Cheng-Dashen theorem. In addition, we show that the inclusion of the virtual Δ(1232) does not change qualitatively our results.