Calculation of the hadron spectrum in lattice QCD

We present Monte Carlo results for the hadron mass-spectrum in lattice SU(3) using the Wilson action and the quenched approximation. We show that on a 6³· 10 lattice at β=6.0, there exist long-lived metastable states of the gauge-field, characterized by the eigenvalues of Z(3) and associated with the first-order deconfining phase transition. The hadron masses are very different in these state if the quark paths that wind around the lattice are not removed. We demonstrate two methods which eliminate a significant fraction of such quark paths. The final results for hadron masses do not agree with the experimental values. We find that the π and ?, as well as the proton and the Δ are degenerate.     

The hadron spectrum from lattice QCD

Determining the hadron spectrum and hadron properties beyond the ground states is a challenge in lattice QCD. Most of these results have been in the quenched approximation but now we are entering the dynamical era. I review some of the ideas and methods of the lattice approach, concentrating on a few examples and on results obtained for Chirally Improved (CI) fermions.     

QCD on the lattice and light hadron spectroscopy

Results in lattice Quantum Chromodynamics with fermions are reviewed. Estimates for the hadron spectrum on large lattices without and with light fermion polarization loops are discussed, and the results for different fermion regularizations are compared. The effects of the loops are found to be significant in lattice units, but to a greater part they can be reabsorbed in a redefinition of the overall scale. New estimates for the light quark masses with Wilson fermions are also presented. They differ substantially from previous estimates obtained by other methods in the continuum, and are much smaller. Finally it is argued that staggered fermions can lead to some anomalous results, which arise because of the doubling problem.     

Precise hadron mass calculations from lattice QCD

By using scalar as opposed to spin-$\text{1}\text{2}$ quarks and treating spin effects perturbatively, the masses of the lowest lying 0^- and 1^- mesons above 1 GeV (the J/Ψ, η_c, D, D¹, F, F¹, and φ) are calculated to 1%. The masses of the K¹, ?, and K are respectively obtained to 3%, 8% and 30%. Certain (spin-averaged) linear combinations of baryon masses are also computed. The nucleon-delta result differs from experiment by 8%. For heavier baryons the error is smaller. Scalar lattice QCD seems to be a promising approach to the strong interactions.     

Interacting hadron resonance gas meets lattice QCD

We present, in the framework of the interacting hadron resonance gas, an evaluation of thermodynamical quantities. The interaction is modelled via a correction for the finite size of the hadrons. We investigate the sensitivity of the model calculations on the radius of the hadrons, which is a parameter of the model. Our calculations for thermodynamical quantities as energy and entropy densities and pressure are confronted with predictions using the lattice Quantum Chromodynamics (QCD) formalism.     

Normalization of currents in lattice QCD

The normalization of vector and axial vector currents in lattice QCD with Wilson's fermion method is discussed and the numerical values of the multiplicative constants are computed to order g² and for g² → ∞.     

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.     

Hadron wave functions in lattice QCD

Coulomb gauge quark-antiquark wave functions for the pion and the rho are calculated in the valence approximation on a lattice 8³ × 16. We use gauge group SU(2) at β of 2.431 corresponding to an inverse lattice spacing of 1100 ± 100 MeV. The wave functions fall off significantly over the size of the box, are rotationally invariant except at the box's boundary, and are nearly independent of the lagrangian quark mass.     

The calculation of the hadron spectrum in lattice QCD with dynamical quarks

Hadron masses are calculated on an 8³×16 lattice using four flavors of staggered fermions to generate the gauge configurations, but using Wilson fermions to calculate the hadron propagators. The identification of a value of the Wilson hopping parameter with the value of the bare quark mass used in the simulations is discussed.     

Analytic calculation of hadron spectra by random-walk approximations in lattice QCD

We explain the detail of how to calculate the meson and baryon spectrum by a random walk approximation analytically. The results are compared with experimental values and Monte Carlo results.     

Pion structure functions from lattice QCD

We compute 〈x〉 and 〈x²〉 of the valence quarks in a pion, on the lattice using Wilson fermions in the quenced approximat We find 〈x〉 = 0.49±0.08 and 〈x²〉 = 0.02 at a scale μ ≅ 7 GeV, in a good agreement with experimental data.     

In-medium spectral functions from lattice QCD

Hadronic modes in the quark-gluon plasma and their spectral properties are discussed on the basis of the lattice QCD data analyzed by the maximum entropy method.Arrival of the final proofs: 25 March 2005PACS: 12.38.Mh, 12.38.Gc     

Parity violating vacuum currents on the random lattice

The Dirac operator is studied both with and without background gauge fieldson a three-dimensional random lattice. It is shown that the correct continuum limit for free fermions is recovered in the zero field case and the doubling problem evaded at tree level, the doubles acquiring masses of order the cut-off and decoupling from long-distance physics. The vacuum current is calculated in the presence of a nontrivial U(1) field and shown to be in agreement with continuum calculations.     

Two-point functions for flavour changing currents in QCD

We complete the calculations of two-point functions in QCD by presenting the results for the flavour changing vector current, including perturbative and non-perturbative contributions (to first order in α_s).