Stochastic Variational Search for ΛΛ4^{4}_{\Lambda\Lambda}H

A four-body calculation of the $pn\Lambda\Lambda$ bound state, $^{\ 4}_{\Lambda\Lambda}$H, is performed using the stochastic variational method and phenomenological potentials. The$NN$,$\Lambda N$, and$\Lambda\Lambda$potentials are taken from a recent Letter by Filikhin and Gal, PRL{\bf 89}, 172502 (2002). Although their Faddeev-Yakubovsky calculation found no bound-state solution over a wide range of$\Lambda\Lambda$interaction strengths, the present variational calculation gives a bound-state energy, which is clearly lower than the$_\Lambda^3{H}+\Lambda$threshold, even for a weak$\Lambda\Lambda$interaction strength deduced from a recent experimental$B_{\Lambda\Lambda}(^{6}_{\Lambda\Lambda}{He})$value. The binding energies obtained are close to, and slightly larger than, the values obtained from the three-body$d\Lambda\Lambda$ model in the Letter.Comment: Corrected typos, added addtional calculations regarding a truncated to l=0 interaction model, 4 pages, 3 figure

Ab initio approach to s-shell hypernuclei 3H_Lambda, 4H_Lambda, 4He_Lambda and 5He_Lambda with a Lambda N-Sigma N interaction

Variational calculations for s-shell hypernuclei are performed by explicitly including $\Sigma$ degrees of freedom. Four sets of YN interactions (SC97d(S), SC97e(S), SC97f(S) and SC89(S)) are used. The bound-state solution of $_\Lambda^5$He is obtained and a large energy expectation value of the tensor $\Lambda N-\Sigma N$ transition part is found. The internal energy of the $^4$He subsystem is strongly affected by the presence of a $\Lambda$ particle with the strong tensor $\Lambda N-\Sigma N$ transition potential.Comment: Phys. Rev. Lett. 89, 142504 (2002

Three-Cluster Equation Using Two-Cluster RGM Kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed to the Faddeev equation which uses a modified singularity-free T-matrix constructed from the two-cluster RGM kernel. The approximation of the present three-cluster formalism can be examined with more complete calculation using the three-cluster RGM. As a simple example, we discuss three di-neutron (3d') and 3 alpha systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also presented for the 3' system.Comment: 12 pages, no figur

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

Full-Coupled Channel Approach to Doubly Strange ss-Shell Hypernuclei

We describe {\it ab initio} calculations of doubly strange, $S=-2$, $s$-shell hypernuclei ($^4_{\Lambda\Lambda}$H, $^5_{\Lambda\Lambda}$H, $^5_{\Lambda\Lambda}$He and $^6_{\Lambda\Lambda}$He) as a first attempt to explore the few-body problem of the {\it full}-coupled channel scheme for these systems. The wave function includes $\Lambda\Lambda$, $\Lambda\Sigma$, $N\Xi$ and $\Sigma\Sigma$ channels. Minnesota $NN$, D2$^\prime$ $YN$, and simulated $YY$ potentials based on the Nijmegen hard-core model, are used. Bound state solutions of these systems are obtained. We find that a set of phenomenological $B_8B_8$ interactions among the octet baryons in $S=0, -1$ and -2 sectors, which is consistent with all of the available experimental binding energies of $S=0, -1$ and -2 $s$-shell (hyper-)nuclei, can predict a particle stable bound state of $^4_{\Lambda\Lambda}$H. For $^5_{\Lambda\Lambda}$H and $^5_{\Lambda\Lambda}$He, $\Lambda N-\Sigma N$ and $\Xi N-\Lambda\Sigma$ potentials enhance the net $\Lambda\Lambda-N\Xi$ coupling, and a large $\Xi$ probability is obtained even for a weaker $\Lambda\Lambda-N\Xi$ potential.Comment: 4 pages, 1 figur

Spin-Orbit Force from 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.Comment: 14 pages, 5 figures, Physics Letters B published versio

Kaon-Nucleon potential from lattice QCD

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.Comment: Talk given at 19th International IUPAP Conference on Few-Body Problems in Physics (fb19), Bonn, Germany, 30 Aug - 5 Sep 200

Baryon-Baryon Interactions from Lattice QCD

We report on new attempt to investigate baryon-baryon interactions in lattice QCD. From the Bethe-Salpeter (BS) wave function, we have successfully extracted the nucleon-nucleon ($NN$) potentials in quenched QCD simulations, which reproduce qualitative features of modern $NN$ potentials. The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperon-nucleon ($YN$) interactions, in both quenched and full QCD.Comment: 6 pages, 10 figures, A plenary talk given at the 5-th International Conference on Quark and Nuclear Physics, Beijing, September 21-26, 200