We present a lattice QCD study for the cutoff effects on nuclear forces. Two-nucleon forces are determined from Nambu-Bethe-Salpeter (NBS) wave functions using the HAL QCD method. Lattice QCD simulations are performed employing N_f = 2 clover fermion
configurations at three lattice spacings of a = 0.108, 0.156, 0.215 fm on a fixed physical volume of L^3 x T = (2.5 fm)^3 x 5 fm with a large quark mass corresponding to m_pi = 1.1 GeV. We observe that while the discretization artifact appears at the short range part of potentials, it is suppressed at the long distance region. The cutoff dependence of the phase shifts and scattering length is also presented.
We report the recent progress on the determination of three-nucleon forces (3NF) in lattice QCD. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to define the potential in quantum field theory, and extract two-nucleon forces (2NF) and 3NF on
equal footing. The enormous computational cost for calculating multi-baryon correlators on the lattice is drastically reduced by developing a novel contraction algorithm (the unified contraction algorithm). Quantum numbers of the three-nucleon (3N) system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel), and we extract 3NF in which three nucleons are aligned linearly with an equal spacing. 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. Repulsive 3NF is found at short distance.
We review recent lattice QCD activities with emphasis on the impact on nuclear physics. In particular, the progress toward the determination of nuclear and baryonic forces (potentials) using Nambu-Bethe-Salpeter (NBS) wave functions is presented. We
discuss major challenges for multi-baryon systems on the lattice: (i) signal to noise issue and (ii) computational cost issue. We argue that the former issue can be avoided by extracting energy-independent (non-local) potentials from time-dependent NBS wave functions without relying on the ground state saturation, and the latter cost is drastically reduced by developing a novel unified contraction algorithm. The lattice QCD results for nuclear forces, hyperon forces and three-nucleon forces are presented, and physical insights are discussed. Comparison to results from the traditional Lueschers method is given, and open issues to be resolved are addressed as well.
Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave-function are utilized to
extract non-local hadron-hadron potential. The ground state saturation, which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the 1S_0 channel.
We explore three-nucleon forces (3NF) from lattice QCD simulations. Utilizing the Nambu-Bethe-Salpeter (NBS) wave function, two-nucleon forces (2NF) and 3NF are determined on the same footing. Quantum numbers of the three-nucleon (3N) system are chos
en to be (I, J^P)=(1/2,1/2^+) (the triton channel). The enormous computational cost is reduced by employing the simplest geometrical configuration, where 3N are aligned linearly with an equal spacing. We perform lattice QCD simulations using Nf=2 dynamical clover fermion configurations generated by CP-PACS Collaboration, 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. Repulsive 3NF is found at short distance.
We investigate three-nucleon forces (3NF) from lattice QCD simulations, utilizing the Nambu-Bethe-Salpeter (NBS) wave function to determine two-nucleon forces (2NF) and 3NF on the same footing. Quantum numbers of the three-nucleon (3N) system are cho
sen to be (I, J^P)=(1/2, 1/2^+) (the triton channel). We consider the simplest geometrical configuration where 3N are aligned linearly with an equal spacing, to reduce the enormous computational cost. Lattice QCD simulations are performed using Nf=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.
An extension of the Luschers finite volume method above inelastic thresholds is proposed. It is fulfilled by extendind the procedure recently proposed by HAL-QCD Collaboration for a single channel system. Focusing on the asymptotic behaviors of the N
ambu-Bethe-Salpeter (NBS) wave functions (equal-time) near spatial infinity, a coupled channel extension of effective Schrodinger equation is constructed by introducing an energy-independent interaction kernel. Because the NBS wave functions contain the information of T-matrix at long distance, S-matrix can be obtained by solving the coupled channel effective Schrodinger equation in the infinite volume.
We investigate baryon-baryon interactions with strangeness $S=-2$ and isospin I=0 system from Lattice QCD. In order to solve this system, we prepare three types of baryon-baryon operators ($Lambda-Lambda$, $N-Xi$ and $Sigma-Sigma$) for the sink and c
onstruct three source operators diagonalizing the $3times3$ correlation matrix. Combining of the prepared sink operators with the diagonalized source operators, we obtain nine effective Nambu-Bethe-Salpeter (NBS) wave functions. The $3times3$ potential matrix is calculated by solving the coupled-channel Schrodinger equation. The flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with the results of the SU(3) limit calculation. Our numerical results are obtained from three sets of 2+1 flavor QCD gauge configurations provided by the CP-PACS/JLQCD Collaborations.
We investigate baryon-baryon interactions with strangeness $S=-2$ and isospin I=0 system from Lattice QCD. In order to solve this system, we prepare three types of baryon-baryon operators ($LambdaLambda$, $NXi$ and $SigmaSigma$) for the sink and cons
truct three source operators diagonalizing the $3times3$ correlation matrix. Combining of the prepared sink operators with the diagonalized source operators, we obtain nine effective Nambu-Bethe-Salpeter (NBS) wave functions. The $3times3$ potential matrix is calculated by solving the coupled-channel Schrodinger equation. The flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with the results of the SU(3) limit calculation. Our numerical results are obtained from three sets of 2+1 flavor QCD gauge configurations provided by the CP-PACS/JLQCD Collaborations.
We study the three nucleon force in the triton channel using dynamical clover fermion lattice QCD. The Nambu-Bethe-Salpeter wave function is utilized to obtain the potentials among three nucleons. Since the straightforward calculation is prohibitivel
y expensive, two different frameworks are developed to meet the challenge. In the first method, we study the effective two nucleon potentials in the three nucleon system, where the differences between the effective two nucleon potentials and the genuine two nucleon potentials correspond to the three nucleon system effect, part of which is originated from the three nucleon force. The calculation is performed using Nf=2 clover fermion at m(pi)= 1.13GeV generated by CP-PACS Collaboration, and Nf=2+1 clover fermion at m(pi)= 0.70, 0.57GeV generated by PACS-CS Collaboration. In the second method, we study the three nucleon system with 3D-configuration of nucleons fixed. This enables us to extract the three nucleon force directly, if both of parity-even and parity-odd two nucleon potentials are provided. Since parity-odd two nucleon potentials are not available in lattice QCD at this moment, we propose a new general procedure to identify the three nucleon force using only parity-even two nucleon potentials. The calculation are performed with Nf=2 clover fermion at m(pi)= 1.13GeV generated by CP-PACS Collaboration, employing the linear setup for the 3D-configuration. Preliminary results for the scalar/isoscalar three nucleon force are presented.
