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We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.
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Lattice QCD at finite density suffers from a severe sign problem, which has so far prohibited simulations of the cold and dense regime. Here we study the onset of nuclear matter employing a three-dimensional effective theory derived by combined strong coupling and hopping expansions, which is valid for heavy but dynamical quarks and has a mild sign problem only. Its numerical evaluations agree between a standard Metropolis and complex Langevin algorithm, where the latter is free of the sign problem. Our continuum extrapolated data clearly show a first order phase transition building up at $mu_B approx m_B$ as the temperature approaches zero. An excellent description of the data is achieved by an analytic solution in the strong coupling limit.
We review recent lattice QCD activities with emphasis on the impact on nuclear physics. In particular, the progress toward the determination of nuclear and baryonic forces (potentials) using Nambu-Bethe-Salpeter (NBS) wave functions is presented. We discuss major challenges for multi-baryon systems on the lattice: (i) signal to noise issue and (ii) computational cost issue. We argue that the former issue can be avoided by extracting energy-independent (non-local) potentials from time-dependent NBS wave functions without relying on the ground state saturation, and the latter cost is drastically reduced by developing a novel unified contraction algorithm. The lattice QCD results for nuclear forces, hyperon forces and three-nucleon forces are presented, and physical insights are discussed. Comparison to results from the traditional Lueschers method is given, and open issues to be resolved are addressed as well.
The first lattice QCD result on the nuclear force (the NN potential) is presented in the quenched level. The standard Wilson gauge action and the standard Wilson quark action are employed on the lattice of the size 16^3times 24 with the gauge coupling beta=5.7 and the hopping parameter kappa=0.1665. To obtain the NN potential, we adopt a method recently proposed by CP-PACS collaboration to study the pi pi scattering phase shift. It turns out that this method provides the NN potentials which are faithful to those obtained in the analysis of NN scattering data. By identifying the equal-time Bethe-Salpeter wave function with the Schroedinger wave function for the two nucleon system, the NN potential is reconstructed so that the wave function satisfies the time-independent Schroedinger equation. In this report, we restrict ourselves to the J^P=0^+ and I=1 channel, which enables us to pick up unambiguously the ``central NN potential V_{central}(r). The resulting potential is seen to posses a clear repulsive core of about 500 MeV at short distance (r < 0.5 fm). Although the attraction in the intermediate and long distance regions is still missing in the present lattice set-up, our method is appeared to be quite promising in reconstructing the NN potential with lattice QCD.
We present a first attempt to determine nucleon-nucleon potentials in the parity-odd sector, which appear in 1P1, 3P0, 3P1, 3P2-3F2 channels, in Nf=2 lattice QCD simulations. These potentials are constructed from the Nambu-Bethe-Salpeter wave functions for J^P=0^-, 1^- and 2^-, which correspond to A1^-, T1^- and T2^- + E^- representation of the cubic group, respectively. We have found a large and attractive spin-orbit potential VLS(r) in the isospin-triplet channel, which is qualitatively consistent with the phenomenological determination from the experimental scattering phase shifts. The potentials obtained from lattice QCD are used to calculate the scattering phase shifts in 1P1, 3P0, 3P1 and 3P2-3F2 channels. The strong attractive spin-orbit force and a weak repulsive central force in spin-triplet P-wave channels lead to an attraction in the 3P2 channel, which is related to the P-wave neutron paring in neutron stars.
We present state-of-the-art results from a lattice QCD calculation of the nucleon axial coupling, $g_A$, using Mobius Domain-Wall fermions solved on the dynamical $N_f = 2 + 1 + 1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. Relevant three-point correlation functions are calculated using a method inspired by the Feynman-Hellmann theorem, and demonstrate significant improvement in signal for fixed stochastic samples. The calculation is performed at five pion masses of $m_pisim {400, 350, 310, 220, 130}$~MeV, three lattice spacings of $asim{0.15, 0.12, 0.09}$~fm, and we do a dedicated volume study with $m_pi Lsim{3.22, 4.29, 5.36}$. Control over all relevant sources of systematic uncertainty are demonstrated and quantified. We achieve a preliminary value of $g_A = 1.285(17)$, with a relative uncertainty of 1.33%.
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