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Register a new userLambda(1405) and Negative-Parity Baryons in Lattice QCD
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We review briefly recent studies of the Lambda(1405) spectrum in Lattice QCD. Ordinary three-quark pictures of the Lambda(1405) in quenched Lattice QCD fail to reproduce the mass of the experimental value, which seems to support the penta-quark picture for the Lambda(1405) such as a Kbar-N molecule-like state. It is also noted that the present results suffer from relatively large systematic uncertainties coming from the finite volume effect, the chiral extrapolation and the quenching effect.
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We study negative-parity baryon spectra in quenched anisotropic lattice QCD. The negative-parity baryons are measured as the parity partner of the ground-state baryons. In addition to the flavor octet and decuplet baryons, we pay much attention to the flavor-singlet negative-parity baryon as a three-quark state and compare it with the Lambda(1405) baryon. Numerical results of the flavor octet and decuplet negative-parity baryon masses are close to experimental values of lowest-lying negative-parity baryons, while the flavor-singlet baryon is much heavier than Lambda(1405). This indicates that the Lambda(1405) would be a multi-quark state such as the N-Kbar molecule rather than the flavor-singlet 3 quark state.
We study the coupled pion-nucleon system (negative parity, isospin 1/2) based on a lattice QCD simulation for nf=2 mass degenerate light quarks. Both, standard 3-quarks baryon operators as well as meson-baryon (4+1)-quark operators are included. This is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic s-wave scattering and can derive values of the phase shift.
Five-quark (5Q) picture of Lambda(1405) is studied using quenched lattice QCD with an exotic 5Q operator of Nbar{K} type. To discreminate mere Nbar{K} and Sigmapi scattering states, Hybrid Boundary Condition (HBC), a flavor-dependent boundary condition, is imposed on the quark fields along spatial direction. 5Q mass m_{5Q}simeq 1.89 GeV is obtained after the chiral extrapolation to the physical quark mass region, which is too heavy to be identified with Lambda(1405). Then, Lambda(1405) seems neither a pure 3Q state nor a pure 5Q state, and therefore we present an interesting possibility that Lambda(1405) is a mixed state of 3Q and 5Q states.
We investigate the negative-parity baryon spectra in quenched lattice QCD. We employ the anisotropic lattice with standard Wilson gauge and O(a) improved Wilson quark actions at three values of lattice spacings with renormalized anisotropy xi=a_sigma/a_tau=4, where a_sigma and a_tau are spatial and temporal lattice spacings, respectively. The negative-parity baryons are measured with the parity projection. In particular, we pay much attention to the lowest SU(3) flavor-singlet negative-parity baryon, which is assigned as the Lambda(1405) in the quark model. For the flavor octet and decuplet negative-parity baryons, the calculated masses are close to the experimental values of corresponding lowest-lying negative-parity baryons. In contrast, the flavor-singlet baryon is found to be about 1.7 GeV, which is much heavier than the Lambda(1405). Therefore, it is difficult to identify the Lambda(1405) to be the flavor-singlet three-quark state, which seems to support an interesting picture of the penta-quark (uds qbar q) state or the N-Kbar molecule for the Lambda(1405).
We present the results of a lattice study of light-cone distribution amplitudes (DAs) of the nucleon and negative parity nucleon resonances using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to m_pi = 150 MeV. We find that the three valence quarks in the proton share their momentum in the proportion 37% : 31% : 31%, where the larger fraction corresponds to the u-quark that carries proton helicity, and determine the value of the wave function at the origin in position space, which turns out to be small compared to the existing estimates based on QCD sum rules. Higher-order moments are constrained by our data and are all compatible with zero within our uncertainties. We also calculate the normalization constants of the higher-twist DAs that are related to the distribution of quark angular momentum. Furthermore, we use the variational method and customized parity projection operators to study the states with negative parity. In this way we are able to separate the contributions of the two lowest states that, as we argue, possibly correspond to N*(1535) and a mixture of N*(1650) and the pion-nucleon continuum, respectively. It turns out that the state that we identify with N*(1535) has a very different DA as compared to both the second observed negative parity state and the nucleon, which may explain the difference in the decay patterns of N*(1535) and N*(1650) observed in experiment.
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