Hadronic decays from the lattice

We discuss strategies to determine hadronic decay couplings from lattice studies. As an application, we explore the decay of a vector meson to two pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working with quark masses that do not allow a physical decay, we show how the transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the annihilation component of $\pi \pi \to \pi \pi$. We explore the decay amplitude for two different pion momenta and find consistent results. The coupling strength we find is in agreement with experiment. We also find evidence for a shift in the $\rho$ mass caused by mixing with two pion states.Comment: Proc. Latt03 (spectrum), 3 pages, 4 fig

Hadronic decay of a vector meson from the lattice

We explore the decay of a vector meson to two pseudoscalar mesons on the lattice with $N_f=2$ flavours of sea quark. Although we are working with quark masses that do not allow a physical decay, we show how the transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the annihilation component of $\pi \pi \to \pi \pi$. We explore the decay amplitude for two different pion momenta and find consistent results. The coupling strength we find is in agreement with experiment. We also find evidence for a shift in the $\rho$ mass caused by mixing with two pion states.Comment: 13 pages, version as accepted for Physics Letters

Hadronic transitions from the lattice

I discuss strategies to determine hadronic decay couplings from lattice studies. As a check of the methods, I explore the decay of a vector meson to two pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working with quark masses that do not allow a physical decay, I show how the transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the annihilation component of $\pi \pi \to \pi \pi$. I explore the decay amplitude for two different pion momenta and find consistent results. The coupling strength found is in agreement with experiment. I also find evidence for a shift in the $\rho$ mass caused by mixing with two pion states. I also present results for the decay of a hybrid meson, for the case of heavy valence quarks.Comment: 10 pages, 7 ps figures, proc LHP03, Cairn

Instanton size distributions from calibrated cooling

Using an under-relaxed cooling algorithm we investigated the vacuum in the $2d\ O(3)$ model and $4d$ pure gauge $SU(2)$. We calibrated the amount of cooling performed to have similar physical effect at different lattice spacings.Comment: 3 pages, (Talk given at LATTICE'94, to appear in the proceedings. Uses espcrc2.sty. 2 uuencoded compressed postscript figs appended.

Quark confinement and the bosonic string

Using a new type of simulation algorithm for the standard SU(3) lattice gauge theory that yields results with unprecedented precision, we confirm the presence of a $\gamma/r$ correction to the static quark potential at large distances $r$, with a coefficient $\gamma$ as predicted by the bosonic string theory. In both three and four dimensions, the transition from perturbative to string behaviour is evident from the data and takes place at surprisingly small distances.Comment: TeX source, 21 pages, figures include

Mass spectrum and elastic scattering in the massive SU(2)_f Schwinger model on the lattice

We calculate numerically scattering phases for elastic meson-meson scattering processes in the strongly coupled massive Schwinger-model with an SU(2) flavour symmetry. These calculations are based on Luescher's method in which finite size effects in two-particle energies are exploited. The results from Monte-Carlo simulations with staggered fermions for the lightest meson ("pion") are in good agreement with the analytical strong-coupling prediction. Furthermore, the mass spectrum of low-lying mesonic states is investigated numerically. We find a surprisingly rich spectrum in the mass region [m_\pi,4 m_\pi].Comment: 43 pages, 15 figures, LaTeX, uses feynmf.st

Numerical techniques for lattice QCD in the ϵ\epsilon--regime

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.Comment: Plain TeX source, 32 pages, figures include

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

SU(3) lattice gauge theory with a mixed fundamental and adjoint plaquette action: Lattice artefacts

We study the four-dimensional SU(3) gauge model with a fundamental and an adjoint plaquette term in the action. We investigate whether corrections to scaling can be reduced by using a negative value of the adjoint coupling. To this end, we have studied the finite temperature phase transition, the static potential and the mass of the 0^{++} glueball. In order to compute these quantities we have implemented variance reduced estimators that have been proposed recently. Corrections to scaling are analysed in dimensionless combinations such as T_c/\sqrt{\sigma} and m_{0^{++}}/T_c. We find that indeed the lattice artefacts in e.g. m_{0^{++}}/T_c can be reduced considerably compared with the pure Wilson (fundamental) gauge action at the same lattice spacing.Comment: 36 pages, 12 figure

Quark bilinear step scaling functions and their continuum limit extrapolation

Some new results on nonperturbative renormalisation of quark bilinears in quenched QCD with Schroedinger Functional techniques are presented. Special emphasis is put on a study of the universality of the continuum limit for step scaling functions computed with different levels of O(a) improvement.Comment: Lattice2003(improve), 3 pages, 3 figure