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Register a new userEnergy dependence of nucleon-nucleon potentials in lattice QCD
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K. Murano
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Recently a new approach to calculate the nuclear potential from lattice QCD has been proposed. In the approach the nuclear potential is constructed from Bethe-Salpeter (BS) wave functons through the Schroedinger equation. The procedure leads to non-local but energy independent potential, which can be expanded in terms of local functions. In several recent applications of this method, local potentials, which correspond to the leading order (LO) terms of the expansion, are calculated from the BS wave function at E~0 MeV, where E is the center of mass energy. It is therefore important to check the validity of the LO approximation obtained at E~0. In this report, in order to check how well the LO approximation for the NN potentials works, we compare the LO potentials determined from the BS wave function at E~45 MeV with those at E~0 MeV in quenched QCD. We find that the difference of the LO potentials between two energies are not found wihin the statistical errors. This shows that the LO approximation for the potential is valid at low energies to describe the NN interactions.
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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.
On the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon forces obtained from lattice QCD simulations, the properties of the medium-heavy doubly-magic nuclei such as 16^O and 40^Ca are investigated. We found that those nuclei are bound for the pseudo-scalar meson mass M_PS ~ 470 MeV. The mass number dependence of the binding energies, single-particle spectra and density distributions are qualitatively consistent with those expected from empirical data at the physical point, although these hypothetical nuclei at heavy quark mass have smaller binding energies than the real nuclei.
The scale-dependence of the nucleon-nucleon interaction, which in recent years has been extensively analysed within the context of chiral effective field theory, is, in fact, inherent in any potential models constrained by a fit to scattering data. A comparison between a purely phenomenological potential and local interactions derived from chiral effective field theory suggests that--thanks to the ability to describe nucleon-nucleon scattering at higher energies, as well as the deuteron momentum distribution extracted from electro-disintegration data--phenomenological potentials are best suited for the description of nuclear dynamics at the scale relevant to neutron star matter.
Three-nucleon forces (3NF) are investigated from two-flavor lattice QCD simulations. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to determine two-nucleon forces (2NF) and 3NF in the same framework. As a first exploratory study, we extract 3NF in which three nucleons are aligned linearly with an equal spacing. This is the simplest geometrical configuration which reduces the huge computational cost of calculating the NBS wave function. Quantum numbers of the three-nucleon system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel). Lattice QCD simulations are performed using N_f=2 dynamical clover fermion configurations at the lattice spacing of a = 0.156 fm on a 16^3 x 32 lattice with a large quark mass corresponding to m_pi= 1.13 GeV. We find repulsive 3NF at short distance in the triton channel. Several sources of systematic errors are also discussed.
We study the KN interactions in the I(J^{pi})=0(1/2^-) and 1(1/2^-) channels and associated exotic state Theta^+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to m_{pi}=871 MeV. The s-wave KN potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I=1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I=0 potential is found to have attractive well at mid range. From these potentials, the $KN$ scattering phase shifts are calculated and compared with the experimental data.
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