title: Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point.
abstract: 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 σ_{πN}=38(3)(3)  MeV, σ_{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).
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.|Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Durr
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.|Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany.
authors.forename: Z
authors.initials: Z
authors.lastname: Fodor
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.
authors.forename: C
authors.initials: C
authors.lastname: Hoelbling
authors.affiliation: Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary.|MTA-ELTE Lendület Lattice Gauge Theory Research Group, H-1117 Budapest, Hungary.
authors.forename: S D
authors.initials: SD
authors.lastname: Katz
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.|Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Krieg
authors.affiliation: CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.
authors.forename: L
authors.initials: L
authors.lastname: Lellouch
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.|Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Lippert
authors.affiliation: CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.|CEA-Saclay, IRFU/SPhN, 91191 Gif-sur-Yvette, France.
authors.forename: T
authors.initials: T
authors.lastname: Metivet
authors.affiliation: CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.|Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom.
authors.forename: A
authors.initials: A
authors.lastname: Portelli
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.|Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany.
authors.forename: K K
authors.initials: KK
authors.lastname: Szabo
authors.affiliation: CNRS, Aix-Marseille U., Université de Toulon, Centre de Physique Théorique, UMR 7332, F-13288 Marseille, France.
authors.forename: C
authors.initials: C
authors.lastname: Torrero
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.
authors.forename: B C
authors.initials: BC
authors.lastname: Toth
authors.affiliation: Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany.
authors.forename: L
authors.initials: L
authors.lastname: Varnhorst