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We calculate potentials between a proton and a $Xi^0$ (hyperon with strangeness -2) through the equal-time Bethe-Salpeter wave function, employing quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on (4.5 fm)^4 lattice at the lattice spacing $a simeq 0.14$ fm. The ud quark mass in our study corresponds to $m_{pi}simeq 0.37$ and 0.51 GeV, while the s quark mass corresponds to the physical value of $m_K$. The central $p Xi^0$ potential has a strong (weak) repulsive core in the $^1S_0$ ($^3S_1$) channel for $r lsim 0.6$ fm, while the potential has attractive well at the medium and long distances (0.6 fm $lsim r lsim 1.2$ fm) in both channels. The sign of the $p Xi^0$ scattering length and its quark mass dependence indicate a net attraction in both channels at low energies.
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Nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32^4 (simeq (4.4 fm)^4) lattice. A NN potential V_{NN}(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the ^1S_0 and ^3S_1 channels, we show that the central part of V_{NN}(r) has a strong repulsive core of a few hundred MeV at short distances (r alt 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.
Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the computation of the nucleon form factors and moments of parton distribution functions, before proceeding to describe lattice studies of the Generalized Parton Distributions (GPDs). In particular, I show how lattice studies of GPDs contribute to building a three-dimensional picture of the proton. I conclude by describing the prospects for studying the structure of resonances from lattice QCD.
The charmonium-nucleon interaction is studied by the time-dependent HAL QCD method. We use a larger lattice volume and the relativistic heavy quark action for charm quark to obtain less systematic errors than those in our previous study. As a result, the sizable J/$psi$N hyperfine splitting is observed, indicating that the spin-spin interaction is important to understand this system quantitatively. No J/$psi$N or $eta_c$N bound state is observed below the thresholds as in the previous results.
We calculate $pXi^0$ potentials from the equal-time Bethe-Salpeter amplitude measured in the quenched QCD simulation with the spatial lattice volume, (4.4 fm)$^3$. The standard Wilson gauge action with the gauge coupling $beta=5.7$ on $32^4$ lattice together with the standard Wilson quark action are used. The hopping parameter $kappa_{ud}=0.1678$ is chosen for $u$ and $d$ quarks, which corresponds to $m_{pi}simeq 0.37$ GeV. The physical strange quark mass is used by taking the parameter $kappa_s=0.1643$ which is deduced from the physical $K$ meson mass. The lattice spacing $a=0.1420$ fm is determined by the physical $rho$ meson mass. We find that the $pXi^0$ potential has strong spin dependence. Strong repulsive core is found in $^1S_0$ channel while the effective central potential in the $^3S_1$ channel has relatively weak repulsive core. The potentials also have weak attractive parts in the medium to long distance region (0.6 fm $lsim r lsim 1.2$ fm) in both of the $^1S_0$ and $^3S_1$ channels.
An approach for relating the nucleon excited states extracted from lattice QCD and the nucleon resonances of experimental data has been developed using the Hamiltonian effective field theory (HEFT) method. By formulating HEFT in the finite volume of the lattice, the eigenstates of the Hamiltonian model can be related to the energy eigenstates observed in Lattice simulations. By taking the infinite-volume limit of HEFT, information from the lattice is linked to experiment. The approach opens a new window for the study of experimentally-observed resonances from the first principles of lattice QCD calculations. With the Hamiltonian approach, one not only describes the spectra of lattice-QCD eigenstates through the eigenvalues of the finite-volume Hamiltonian matrix, but one also learns the composition of the lattice-QCD eigenstates via the eigenvectors of the Hamiltonian matrix. One learns the composition of the states in terms of the meson-baryon basis states considered in formulating the effective field theory. One also learns the composition of the resonances observed in Nature. In this paper, we will focus on recent breakthroughs in our understanding of the structure of the $N^*(1535)$, $N^*(1440)$ and $Lambda^*(1405)$ resonances using this method.
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