Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics

The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of the strong interaction, the quantum chromodynamics defined on the hypercubic space-time lattice. After a brief summary of the empirical nucleon-nucleon (NN) potentials which can fit the NN scattering experiments in high precision, we outline the basic formulation to derive the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe-Salpeter amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a $32^4$ lattice with the lattice spacing $a \simeq 0.137$fm (lattice volume (4.4 fm)$^4$) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at KEK. We found that the calculated NN potential at low energy has basic features expected from the empirical NN potentials; attraction at long and medium distances and the repulsive core at short distance. Various future directions along this line of research are also summarized.Comment: 13 pages, 4 figures, version accepted for publication in "Computational Science & Discovery" (IOP

Self-Consistent Perturbation Theory for Thermodynamics of Magnetic Impurity Systems

Integral equations for thermodynamic quantities are derived in the framework of the non-crossing approximation (NCA). Entropy and specific heat of 4f contribution are calculated without numerical differentiations of thermodynamic potential. The formulation is applied to systems such as PrFe4P12 with singlet-triplet crystalline electric field (CEF) levels.Comment: 3 pages, 2 figures, proc. ASR-WYP-2005 (JAERI

Application of the operator product expansion to the short distance behavior of nuclear potentials

We investigate the short distance behavior of nucleon-nucleon (NN) potentials defined through Bethe-Salpeter wave functions, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, 1-loop computations give certain exact results for the potentials in the zero distance limit. In particular the functional form of the S-state central NN potential at short distance $r$ is predicted to be a little weaker than $r^{-2}$. On the other hand, due to the intriguing character of the anomalous dimension spectrum, perturbative considerations alone can not determine whether this potential is repulsive or attractive at short distances. A crude estimation suggests that the force at short distance is repulsive, as found numerically in lattice QCD. A similar behavior is found for the tensor potential.Comment: 40 pages, no figure

Proton decay matrix elements with domain-wall fermions

Hadronic matrix elements of operators relevant to nucleon decay in grand unified theories are calculated numerically using lattice QCD. In this context, the domain-wall fermion formulation, combined with non-perturbative renormalization, is used for the first time. These techniques bring reduction of a large fraction of the systematic error from the finite lattice spacing. Our main effort is devoted to a calculation performed in the quenched approximation, where the direct calculation of the nucleon to pseudoscalar matrix elements, as well as the indirect estimate of them from the nucleon to vacuum matrix elements, are performed. First results, using two flavors of dynamical domain-wall quarks for the nucleon to vacuum matrix elements are also presented to address the systematic error of quenching, which appears to be small compared to the other errors. Our results suggest that the representative value for the low energy constants from the nucleon to vacuum matrix elements are given as |alpha| simeq |beta| simeq 0.01 GeV^3. For a more reliable estimate of the physical low energy matrix elements, it is better to use the relevant form factors calculated in the direct method. The direct method tends to give smaller value of the form factors, compared to the indirect one, thus enhancing the proton life-time; indeed for the pi^0 final state the difference between the two methods is quite appreciable.Comment: 56 pages, 17 figures, a comment and two references added in the introduction, typo corrected in Eq.1

The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur

Dominance of a single topological sector in gauge theory on non-commutative geometry

We demonstrate a striking effect of non-commutative (NC) geometry on topological properties of gauge theory by Monte Carlo simulations. We study 2d U(1) NC gauge theory for various boundary conditions using a new finite-matrix formulation proposed recently. We find that a single topological sector dictated by the boundary condition dominates in the continuum limit. This is in sharp contrast to the results in commutative space-time based on lattice gauge theory, where all topological sectors appear with certain weights in the continuum limit. We discuss possible implications of this effect in the context of string theory compactifications and in field theory contexts.Comment: 16 pages, 27 figures, typos correcte

On two dimensional coupled bosons and fermions

We study complex bosons and fermions coupled through a generalized Yukawa type coupling in the large-N_c limit following ideas of Rajeev [Int. Jour. Mod. Phys. A 9 (1994) 5583]. We study a linear approximation to this model. We show that in this approximation we do not have boson-antiboson and fermion-antifermion bound states occuring together. There is a possibility of having only fermion-antifermion bound states. We support this claim by finding distributional solutions with energies lower than the two mass treshold in the fermion sector. This also has implications from the point of view of scattering theory to this model. We discuss some aspects of the scattering above the two mass treshold of boson pairs and fermion pairs. We also briefly present a gauged version of the same model and write down the linearized equations of motion.Comment: 25 pages, no figure

Magnetic Excitations in NpCoGa5

We report the results of inelastic neutron scattering experiments on NpCoGa$_{5}$, an isostructural analogue of the PuCoGa$_{5}$ superconductor. Two energy scales characterize the magnetic response in the antiferromagnetic phase. One is related to a non-dispersive excitation between two crystal field levels. The other at lower energies corresponds to dispersive fluctuations emanating from the magnetic zone center. The fluctuations persist in the paramagnetic phase also, although weaker in intensity. This supports the possibility that magnetic fluctuations are present in PuCoGa$_{5}$, where unconventional d-wave superconductivity is achieved in the absence of magnetic order.Comment: 4 pages, 5 figure

Green's Function for Nonlocal Potentials

The single-particle nuclear potential is intrinsically nonlocal. In this paper, we consider nonlocalities which arise from the many-body and fermionic nature of the nucleus. We investigate the effects of nonlocality in the nuclear potential by developing the Green's function for nonlocal potentials. The formal Green's function integral is solved analytically in two different limits of the wavelength as compared to the scale of nonlocality. Both results are studied in a quasi-free limit. The results illuminate some of the basic effects of nonlocality in the nuclear medium.Comment: Accepted for publication in J. Phys.

Dynamical Wilson fermions and the problem of the chiral limit in compact lattice QED

We compare the approach to the chiral transition line ~\kappa_c(\bt)~ in quenched and full compact lattice QED with Wilson fermions within the confinement phase, especially in the pseudoscalar sector of the theory. We show that in the strong coupling limit ($\beta =0$) the quenched theory is a good approximation to the full one, in contrast to the case of $\beta =0.8$. At the larger $\beta$-value the transition in the full theory is inconsistent with the zero--mass limit of the pseudoscalar particle, thus prohibiting the definition of a chiral limit.Comment: 13 pages LaTeX (epsf), all figures include