Direct determinations of the nucleon and pionσterms at nearly physical quark masses

Abstract

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 ${m}_{\ensuremath{\pi}}\ensuremath{\sim}150\text{ }\text{ }\mathrm{MeV}$ and several volumes, $L{m}_{\ensuremath{\pi}}=3.4$ up to 6.7, and lattice spacings, $a=0.06--0.08\text{ }\text{ }\mathrm{fm}$, enabling a study of finite volume and discretization effects for ${m}_{\ensuremath{\pi}}\ensuremath{\gtrsim}260\text{ }\text{ }\mathrm{MeV}$. Systematics are found to be reasonably under control. For the nucleon we obtain ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=35(6)\text{ }\text{ }\text{MeV}$ and ${\ensuremath{\sigma}}_{s}=35(12)\text{ }\text{ }\mathrm{MeV}$, or equivalently in terms of the quark fractions, ${f}_{{T}_{u}}=0.021(4)$, ${f}_{{T}_{d}}=0.016(4)$ and ${f}_{{T}_{s}}=0.037(13)$, 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 ${f}_{{T}_{c}}=0.075(4)$, ${f}_{{T}_{b}}=0.072(2)$ and ${f}_{{T}_{t}}=0.070(1)$. In addition, through the use of the (inverse) Feynman-Hellmann theorem our results for ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}$ 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 ${\ensuremath{\sigma}}_{\ensuremath{\pi}}={m}_{\ensuremath{\pi}}/2$ over our range of pion masses.