Positivity and topology in lattice gauge theory

The admissibility condition usually used to define the topological charge in lattice gauge theory is incompatible with a positive transfer matrix.Comment: 6 pages, revtex; revision has some clarifications and additional references, representing the final version to appear in Physical Revie

The three-loop beta function of SU(N) lattice gauge theories with Wilson fermions

We calculate the third coefficient of the lattice beta function associated with the Wilson formulation for both gauge fields and fermions. This allows us to evaluate the three-loop correction (linear in $g_0^2$) to the relation between the lattice Lambda-parameter and the bare coupling $g_0$, which is important in order to verify asymptotic scaling predictions. Our calculation also leads to the two-loop relation between the coupling renormalized in the MSbar scheme and $g_0$. The original version of this paper contained a numerical error in one of the diagrams, which has now been corrected. The calculations, as well as the layout of the paper have remained identical, but there are some important changes in the numerical results.Comment: One 14-page LaTeX file, one PostScript file containing 2 figures. Corrected a numerical error in one of the diagrams. The calculations, as well as the layout of the paper have remained unaffected, but there are some important changes in the numerical result

Hadronic decay of a scalar B meson from the lattice

We explore the transitions B$(0^+)$ to B $\pi$ and B$_s(0^+)$ to B K from lattice QCD with $N_f=2$ flavours of sea quark, using the static approximation for the heavy quark. We evaluate the effective coupling constants, predicting a B$(0^+)$ to B $\pi$ width of around 160 MeV. Our result for the coupling strength adds to the evidence that the B$_s(0^+)$ meson is not predominantly a molecular state (BK).Comment: 10 pages LATE

Non perturbative determination of the running coupling constant in quenched SU(2)

Through a finite size renormalization group technique we calculate the running coupling constant for quenched SU(2) with a few percent error over a range of energy varying by a factor thirty. The definition is based on ratio of correlations of Polyakov loops with twisted boundary conditions. The extrapolation to the continuum limit is governed by corrections due to lattice artifacts which are proportional to the square of the lattice spacing and appears rather smooth.Comment: 18 pages of ps fil

Finite temperature SU(2) gauge theory: critical coupling and universality class

We examine SU(2) gauge theory in 3+1 dimensions at finite temperature in the vicinity of critical point. For various lattice sizes in time direction ($N_\tau=1,2,4,8$) we extract high precision values of the inverse critical coupling and critical values of the 4-th order cumulant of Polyakov loops (Binder cumulant). We check the universality class of the theory by comparing the cumulant values to that of the 3D Ising model and find very good agreement. The Polyakov loop correlators for the indicated lattices are also measured and the string tension values extracted. The high precision values of critical coupling and string tension allow us to study the scaling of dimensionless $T_c/\sqrt{\sigma}$ ratio. The violation of scaling by <10% is observed as the coupling is varied from weak to strong coupling regime.Comment: 17 pages, 9 figures, minor correction

Hadronic decays from the lattice

I review the lattice QCD approach to determining hadronic decay transitions. Examples considered include rho to pi pi; b_1 to pi omega; hybrid meson decays and scalar meson decays. I discuss what lattices can provide to help understand the composition of hadrons.Comment: 6 pages, presented at QNP06, June 200

Leading Quenching Effects in the Proton Magnetic Moment

We present the first investigation of the extrapolation of quenched nucleon magnetic moments in quenched chiral effective field theory. We utilize established techniques in finite-range regularisation and compare with standard dimensional regularisation methods. Finite-volume corrections to the relevant loop integrals are also addressed. Finally, the contributions of dynamical sea quarks to the proton moment are estimated using a recently discovered phenomenological link between quenched and physical QCD.Comment: 9 pages, 11 figs; v2: revised finite volume discussio

Light Quark Mass Reweighting

We present a systematic study of the effectiveness of light quark mass reweighting. This method allows a single lattice QCD ensemble, generated with a specific value of the dynamical light quark mass, to be used to determine results for other, nearby light dynamical quark masses. We study two gauge field ensembles generated with 2+1 flavors of dynamical domain wall fermions with light quark masses m_l=0.02 (m_\pi=620 MeV) and m_l=0.01 (m_\pi=420 MeV). We reweight each ensemble to determine results which could be computed directly from the other and check the consistency of the reweighted results with the direct results. The large difference between the 0.02 and 0.01 light quark masses suggests that this is an aggressive application of reweighting as can be seen from fluctuations in the magnitude of the reweighting factor by four orders of magnitude. Never-the-less, a comparison of the reweighed topological charge, average plaquette, residual mass, pion mass, pion decay constant, and scalar correlator between these two ensembles shows agreement well described by the statistical errors. The issues of the effective number of configurations and finite sample size bias are discussed. An examination of the topological charge distribution implies that it is more favorable to reweight from heavier mass to lighter quark mass.Comment: 24 pages and 10 figure

Comparing improved actions for SU(2)

In order to help the user in choosing the right action a performance comparison is done for seven improved actions. Six of them are Symanzik improved, one at tree-level and two at one-loop, all with or without tadpole improvement. The seventh is an approximate fixed point action. Observables are static on- and off-axis two-body potentials and four-body binding energies, whose precision is compared when the same amount of computer time is used by the programs.Comment: 3 pages, 3 colour eps figures. Presented at LATTICE9

I=2 ππ\pi\pi scattering using G-parity boundary condition

To make the $\pi\pi$ state with non-zero relative momentum as the leading exponential, we impose anti-periodic boundary condition on the pion, which is implemented by imposing G-parity or H-parity on the quark fields at the boundary. With this, we calculate the I=2 $\pi\pi$ phase shift from lattice simulation by using L\"uscher's formula.Comment: Lattice 2003, 3 pages, 6 figure