Keiko Murano

Bound H dibaryon in flavor SU(3) limit of lattice QCD.

The flavor-singlet H dibaryon, which has strangeness -2 and baryon number 2, is studied by the approach recently developed for the baryon-baryon interactions in lattice QCD. The flavor-singlet central potential is derived from the spatial and imaginary-time dependence of the Nambu-Bethe-Salpeter wave function measured in N(f)=3 full QCD simulations with the lattice size of L≃2,3,4  fm. The potential is found to be insensitive to the volume, and it leads to a bound H dibaryon with the binding energy of 30-40 MeV for the pseudoscalar meson mass of 673-1015 MeV.

Hadron–hadron interactions from imaginary-time Nambu–Bethe–Salpeter wave function on the lattice

Abstract 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 S 0 1 channel.

Two-baryon potentials and H-dibaryon from 3-flavor lattice QCD simulations

Abstract Baryon–baryon potentials are obtained from 3-flavor QCD simulations with the lattice volume L ≃ 4 fm , the lattice spacing a ≃ 0.12 fm , and the pseudo-scalar-meson mass M ps = 469 – 1171 MeV . The NN scattering phase-shifts and the mass of H-dibaryon in the flavor SU ( 3 ) limit are extracted from the resultant potentials by solving the Schrodinger equation. The NN phase-shifts in the SU ( 3 ) limit is shown to have qualitatively similar behavior as the experimental data. A bound H-dibaryon in the SU ( 3 ) limit is found to exist in the flavor-singlet J P = 0 + channel with the binding energy of about 26 MeV for the lightest quark mass M ps = 469 MeV . Effect of flavor SU ( 3 ) symmetry breaking on the H-dibaryon is estimated by solving the coupled-channel Schrodinger equation for Λ Λ – N Ξ – Σ Σ with the physical baryon masses and the potential matrix obtained in the SU ( 3 ) limit: a resonant H-dibaryon is found between ΛΛ and NΞ thresholds in this treatment.

Baryon-Baryon Interactions in the Flavor SU(3) Limit from Full QCD Simulations on the Lattice

We investigate baryon-baryon (BB) interactions in the 3-flavor full QCD simulations with degenerate quark masses for all flavors. The BB potentials in the orbital S-wave are extracted from the Nambu-Bethe-Salpeter wave functions measured on the lattice. We observe strong flavor-spin dependences of the BB potentials at short distances. In particular, a strong repulsive core exists in the flavor-octet and spin-singlet channel (the 8s representation), while an attractive core appears in the flavor singlet channel (the 1 representation). We discuss the relation of such flavor-spin dependence with the Pauli exclusion principle at the quark level. The possible existence of an H-dibaryon resonance above the ΛΛ threshold is also discussed. Subject Index: 164, 234

Exploring Three-Nucleon Forces in Lattice QCD

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.

Precise determination of the strong coupling constant in Nf = 2+1 lattice QCD with the Schrödinger functional scheme

We present an evaluation of the running coupling constant for Nf = 2+1 QCD. The Schrodinger functional scheme is used as the intermediate scheme to carry out non-perturbative running from the low energy region, where physical scale is introduced, to deep in the high energy perturbative region, where conversion to the scheme is safely performed. Possible systematic errors due to the use of perturbation theory occur only in the conversion from three-flavor to four-flavor running coupling constant near the charm mass threshold, where higher order terms beyond 5th order in the β function may not be negligible. For numerical simulations we adopted Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy region and three lattice spacings to take the continuum limit at each scale. A physical scale is introduced from the previous Nf = 2+1 simulation of the CP-PACS/JL-QCD collaboration [1], which covered the up-down quark mass range heavier than mπ ~ 500 MeV. Our final result is = 0.12047(81)(48)(+0−173) and = 239(10)(6)(+0−22) MeV .

Extraction of Hadron Interactions above Inelastic Threshold in Lattice QCD

We propose a new method to extract hadron interactions above inelastic threshold from the Nambu–Bethe–Salpeter amplitude in lattice QCD. We consider the scattering such as A + B → C + D, where A, B, C, D are names of different 1-particle states. An extension to cases where particle productions occur during scatterings is also discussed.

Spin-2 NΩ dibaryon from lattice QCD

Abstract We investigate properties of the N (nucleon) – Ω (Omega) interaction in lattice QCD to seek for possible dibaryon states in the strangeness −3 channel. We calculate the NΩ potential through the equal-time Nambu–Bethe–Salpeter wave function in 2 + 1 flavor lattice QCD with the renormalization group improved Iwasaki gauge action and the nonperturbatively O ( a ) improved Wilson quark action at the lattice spacing a ≃ 0.12 fm on a ( 1.9 fm ) 3 × 3.8 fm lattice. The ud and s quark masses in our study correspond to m π = 875 ( 1 ) MeV and m K = 916 ( 1 ) MeV . At these parameter values, the central potential in the S-wave with the spin 2 shows attractions at all distances. By solving the Schrodinger equation with this potential, we find one bound state whose binding energy is 18.9 ( 5.0 ) ( − 1.8 + 12.1 ) MeV , where the first error is the statistical one, while the second represents the systematic error.

Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

A bstractSingle state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for a system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons (ΞΞ and N N ), and three and four baryons (3He and 4He) as well, employing (2+1)-flavor lattice QCD at mπ = 0.51GeV on four lattice volumes with L = 2.9, 3.6, 4.3 and 5.8 fm. Caution is required when drawing conclusions about the bound N N , 3N and 4N systems based only on the standard plateau fitting of the temporal correlation functions.

Spin–orbit force from lattice QCD

Abstract We present a first attempt to determine nucleon–nucleon potentials in the parity-odd sector, which appear in the P 1 1 , P 0 3 , P 1 3 , P 2 3 – F 2 3 channels, in N f = 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 the A 1 − , T 1 − and T 2 − ⊕ E − representation of the cubic group, respectively. We have found a large and attractive spin–orbit potential V LS ( 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 the P 1 1 , P 0 3 , P 1 3 and P 2 3 – F 2 3 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 P 2 3 channel, which is related to the P -wave neutron paring in neutron stars.