Direct determinations of the nucleon and pion σ terms at nearly physical quark masses

We present a high statistics study of the pion and nucleon light and strange quark sigma terms using N-f = 2 dynamical nonperturbatively improved clover fermions with a range of pion masses down to m(pi) similar to 150 MeV and several volumes, Lm(pi) = 3.4 up to 6.7, and lattice spacings, a =0.06-0.08 fm, enabling a study of finite volume and discretization effects for m(pi) greater than or similar to 260 MeV. Systematics are found to be reasonably under control. For the nucleon we obtain sigma(pi N) = 35(6) MeV and sigma(s) = 35(12) MeV, or equivalently in terms of the quark fractions, f(Tu) = 0.021(4), f(Td) = 0.016(4) and f(Ts) = 0.037(13), where the errors include estimates of both the systematic and statistical uncertainties. These values, together with perturbative matching in the heavy quark limit, lead to f(Tc) = 0.075(4), f(Tb) = 0.072(2) and f(Tt) = 0.070(1). In addition, through the use of the (inverse) Feynman-Hellmann theorem our results for sigma(pi N) are shown to be consistent with the nucleon masses determined in the analysis. For the pion we implement a method which greatly reduces excited state contamination to the scalar matrix elements from states traveling across the temporal boundary. This enables us to demonstrate the Gell-Mann-Oakes-Renner expectation sigma(pi) = m(pi)/2 over our range of pion masses.