Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point

We present a QCD calculation of the u, d, and s scalar quark contents of nucleons based on 47 lattice ensembles with N-f = 2 + 1 dynamical sea quarks, 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and pion masses down to 120 MeV. Using the Feynman-Hellmann theorem, we obtain f(ud)(N) = 0.0405(40)(35) and f(s)(N) = 0.113(45)(40), which translates into sigma(pi N) = 38(3)(3) MeV, sigma(sN) = 105(41)(37) MeV, and y(N) = 0.20(8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second errors are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).