String tension,gluebal masses and finite size effects in lattice SU(3)

We estimate the string tension by looking at Wilson loops and measuring the correlation between Wilson lines at g² = 1.0 for lattice SU(3). The bound $\text{Λ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}\text{?0.0087 ± 0.0011}$ is larger than the previous results. The mass of the 0⁺⁺ glueball is also estimated. The finite size effects on these quantities are shown to be large by comparing results on a 6³ × 10 lattice with those on 9⁴ lattice.     

Bootstrap calculation of the dynamical quark mass in QCD4 at finite temperature

Nonperturbative calculations of the dynamical quark mass m(T) are given in QCD₄, based on the bootstrap solution of the Schwinger-Dyson equation for the quark Green function at finite temperatures. A closed nonlinear equation is obtained for m(T) whose solution is found under some simplifying assumptions. We used a particular approximation for the effective charge and the nonperturbative expressions of the gluon magnetic and electric masses. The singular behavior of m(T) is established and its parameters are determined numerically. The singularity found is shown to correctly reproduce the chiral phase transition and the temperature limits obtained for m(T) are qualitatively correct. The complete phase diagram of QCD₄ in the (μ, T) plane is briefly discussed.     

High-loop perturbative renormalization constants for lattice QCD (I): finite constants for Wilson quark currents

We present a high order perturbative computation of the renormalization constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The computational setup is the one provided by the RI’-MOM scheme. Three- and four-loop expansions are made possible by numerical stochastic perturbation theory. Results are given for various numbers of flavors and/or (within a finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also present four-loop results. Finite-size effects are well under control, and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with the convergence properties of the series. The latter is best discussed in the framework of boosted perturbation theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of lattice QCD renormalization constants (RCs) are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, for which results are also for generic n_f up to three loops, while a four-loop result is obtained for n_f=2.     

Study for the pentaquark potential in SU(3) lattice QCD

We perform the first study of the static pentaquark (5Q) potential V(5Q) in SU(3) quenched lattice QCD with 16(3) x 32 and beta = 6.0. From the 5Q Wilson loop, V(5Q) is calculated in a gauge-invariant manner, with the smearing method to enhance the ground-state component. V(5Q) is well described by the OGE-plus-multi-Y ansatz: a sum of the one-gluon-exchange (OGE) Coulomb term and the multi-Y-type linear term proportional to the minimal total length of the flux tube linking the five quarks. Comparing with QQ and3Q potentials, we find a universality of the string tension, sigma(QQ) approximately sigma(3Q) approximately sigma(5Q), and the OGE result for Coulomb coefficients.     

Dynamical quark effects on the hadronic spectrum and qq-potential in lattice QCD

The results of a calculation which incorporates virtual quark-antiquark pairs at a coupling of β=5.7 and quark mass of 0.05 are compared with those of two quenched simulations at β=5.895 and 6. The inclusion of the dynamical quark produces no effects in the hadron mass spectrum besides an overall shift in the coupling. In contrast, the Wilson lopp factors show a non-trivial effect, in the form of a flattening of the heavy quark potential. All three studies were carried out on a 10³·32 lattice.     

The size of finite size effects in lattice gauge theories

If a quantum field is enclosed in a spatial box of finite volume, its mass spectrum depends on the box size L. For field theories in the continuum Lüscher has shown to all orders in perturbation theory that for large L this dependence is related to certain scattering amplitudes of the infinite volume theory. We derived the corresponding relations for lattice field theories. Assuming their validity for lattice gauge theory outside the perturbative region the magnitude of finite size effects on the spectrum is determined by a glueball coupling constant. This quantity is estimated by strong coupling methods.     

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.     

Gluonic excitation of the three-quark system in SU(3) lattice QCD

We present the first study of the gluonic excitation in the three-quark (3Q) system in SU(3) lattice QCD with beta=5.8 and 16(3) x 32 at the quenched level. For the spatially fixed 3Q system, we measure the gluonic excited-state potential, which is responsible for the properties of hybrid baryons. The lowest gluonic-excitation energy in the 3Q system is found to be about 1 GeV in the hadronic scale. This large gluonic-excitation energy is expected to bring about the success of the simple quark model without gluonic modes.