The binding energies of a range of nuclei and hypernuclei with atomic number A ≤ 4 and strangeness |s| ≤ 2, including the deuteron, di-neutron, H-dibaryon, 3 He, ΛΛ He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange-quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n f = 3 dynamical light quarks using an isotropic clover discretization of the quark action in three lattice volumes of spatial extent L ∼ 3.4 fm, 4.5 fm and 6.7 fm, and with a single lattice spacing b ∼ 0.145 fm.2

We calculate the light hadron spectrum in full QCD using two plus one flavor Asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size L ≈ 2.5 fm, and a lattice spacing of a ≈ 0.124 fm, for pion masses as light as mπ ≈ 300 MeV, and compared with the results by the MILC collaboration with Asqtad valence quarks at the same lattice spacing. Two-and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed-action heavy baryon chiral perturbation theory. Both the threeflavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order SU (3) fits are inconsistent with their phenomenological values. Nextto-next-to-leading order SU (2) continuum formulae provide a good fit to the data and yield and extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially lineaer in mπ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior.

The axial coupling of the nucleon, g, is the strength of its coupling to the weak axial current of the standard model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the standard model in nuclear environments require a quantitative understanding of nuclear physics that is rooted in quantum chromodynamics, a pillar of the standard model. The importance of g makes it a benchmark quantity to determine theoretically-a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice quantum chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two per cent would be possible by 2020 if two challenges are overcome: contamination of g from excited states must be controlled in the calculations and statistical precision must be improved markedly. Here we use an unconventional method inspired by the Feynman-Hellmann theorem that overcomes these challenges. We calculate a g value of 1.271 ± 0.013, which has a precision of about one per cent.