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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.
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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 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.
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%.
Progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Large sets of spatially-extended hadron operators are used. The need for multi-hadron operators in addition to single-hadron operators is emphasized, necessitating the use of a new stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing. A new glueball operator is tested, and computing the mixing of this glueball operator with a quark-antiquark operator and multiple two-pion operators is shown to be feasible.
Including the meson-baryon (5 quark) intermediate states in a lattice simulation is challenging. However, it is important in order to obtain the correct energy eigenstates and to relate them to scattering phase shifts. Recent results for the negative parity nucleon channel and the problem of baryonic resonances in lattice calculations are discussed.
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