One flavor QCD

One flavor QCD is a rather intriguing variation on the underlying theory of hadrons. In this case quantum anomalies remove all chiral symmetries. This paper discusses the qualitative behavior of this theory as a function of its basic parameters, exploring the non-trivial phase structure expected as these parameters are varied. Comments are made on the expected changes to this structure if the gauge group is made larger and the fermions are put into higher representations.     

Hadron mass spectrum from lattice QCD

Finite temperature lattice simulations of quantum chromodynamics (QCD) are sensitive to the hadronic mass spectrum for temperatures below the "critical" temperature T(c) ≈ 160 MeV. We show that a recent precision determination of the QCD trace anomaly shows evidence for the existence of a large number of hadron states beyond those known from experiment. The lattice results are well represented by an exponentially growing mass spectrum up to a temperature T=155 MeV. Using simple parametrizations of the hadron mass spectrum we show how one may estimate the total spectral weight in these yet undermined states.     

Non-perturbative quark mass renormalization in quenched lattice QCD

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the A-parameter of the theory is obtained with a total error of 8%.     

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.     

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects.The coarse and fine lattices are of sizes 24~3×64 and 32~3×64 with inverse spacings 1/a = 1.75(4) Ge V and 2.33(5) Ge V,respectively.     

Determination of the renormalized heavy-quark mass in lattice QCD

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte Carlo data on a small 8³ × 16 lattice for β = 6. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit both the short-distance part and long-distance part of the correlator in such a small volume.     

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.     

Interquark potential with finite quark mass from lattice QCD

We present an investigation of the interquark potential determined from the q ?q Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The q ?q potential at finite quark mass m(q) can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schr?dinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a≈2.1 GeV in a range 1.0≤m(q)≤3.6 GeV. Our numerical results show that the q ?q potential in the m(q)→∞ limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the q ?q potential and the spin-spin potential are also examined.     

Twisted mass quarks and the phase structure of lattice QCD

The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable in correspondence of which the untwisted quark mass assumes positive or negative values. We provide interpretations of this phenomenon in terms of chiral symmetry breaking and the effective potential model of Sharpe and Singleton.Received: 24 August 2004, Revised: 29 October 2004, Published online: 25 January 2005     

Quark mass dependence of nucleon properties and extrapolations from lattice QCD

We summarize developments concerning the quark mass dependence of nucleon magnetic moments and the axial-vector coupling constant g_A. The aim is to explore the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD results, from the relatively large quark masses that can be handled in such computations down to the physically relevant range.     

Form factors in lattice QCD

Lattice simulations of QCD have produced precise estimates for the masses of the lowest-lying hadrons which show excellent agreement with experiment. By contrast, lattice results for the vector and axial vector form factors of the nucleon show significant deviations from their experimental determination. We present results from our ongoing project to compute a variety of form factors with control over all systematic uncertainties. In the case of the pion electromagnetic form factor we employ partially twisted boundary conditions to extract the pion charge radius directly from the linear slope of the form factor near vanishing momentum transfer. In the nucleon sector we focus specifically on the possible contamination from contributions of higher excited states. We argue that summed correlation functions offer the possibility of eliminating this source of systematic error. As an illustration of the method we discuss our results for the axial charge, g _A , of the nucleon.     

Hadron interactions in lattice QCD

Progress on the potential method, recently proposed to investigate hadron interactions in lattice QCD, is reviewed. The strategy to extract the potential in lattice QCD is explained in detail. The method is applied to extract NN potentials, hyperon potentials and the meson–baryon potentials. A theoretical investigation is made to understand the origin of the repulsive core using the operator product expansion. Some recent extensions of the method are also discussed.