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Register a new userExtended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
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Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the lowest-lying multi-hadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on 24^3 x 128 and 32^3 x 256 anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as eta eta -> eta eta in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, pi-pi, and eta-eta operators is shown to be feasible.
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Recent progress in unquenched lattice QCD simulations is reviewed with emphasis on understanding of chiral behavior for light quark masses.
We present details of simulations for the light hadron spectrum in quenched QCD carried out on the CP-PACS parallel computer. Simulations are made with the Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112 lattices at four lattice spacings (a approx 0.1-0.05 fm) and the spatial extent of 3 fm. Hadronic observables are calculated at five quark masses (m_{PS}/m_V approx 0.75 - 0.4), assuming the u and d quarks being degenerate but treating the s quark separately. We find that the presence of quenched chiral singularities is supported from an analysis of the pseudoscalar meson data. We take m_pi, m_rho and m_K (or m_phi) as input. After chiral and continuum extrapolations, the agreement of the calculated mass spectrum with experiment is at a 10% level. In comparison with the statistical accuracy of 1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates a failure of the quenched approximation for the hadron spectrum: the meson hyperfine splitting is too small, and the octet masses and the decuplet mass splittings are both smaller than experiment. Light quark masses are calculated using two definitions: the conventional one and the one based on the axial-vector Ward identity. The two results converge toward the continuum limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_phi, indicating again a failure of the quenched approximation. We obtain Lambda_{bar{MS}}^{(0)}= 219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the pseudoscalar meson decay constants.
Determining the spectrum of hadronic excitations from Monte Carlo simulations requires the use of interpolating operators that couple to multi-particle states. Recent algorithmic advances have made the inclusion of multi-hadron operators in spectroscopy calculations a practical reality. In this talk, a procedure for constructing a set of multi-hadron interpolators that project onto the states of interest is described. To aid in the interpretation of simulation data, operators are designed to transform irreducibly under the lattice symmetry group. The identification of a set of optimal single-hadron interpolators for states with non-zero momenta is an essential intermediate step in this analysis.
New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalisation properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. The operators have been numerically implemented and a comparison to point sources and Jacobi smeared sources has been performed on the new CLS configurations.
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
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