Finite size effects and scaling in lattice CP(N-1)

We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of $N$. The asymptotic scaling behaviour of alternative lattice actions is discussed along with some aspects of multigrid algorithm efficiency.Comment: 6 pages of text plus 2 pages of figures, Liverpool Preprint LTH28

Progress in building an International Lattice Data Grid

We report on progress in setting up the International Lattice Data Grid. We describe the aims and objectives of the ILDG, what has been achieved during its first year of activity and invite feedback from the community.Comment: Lattice2003(activity), 5 pages 2 figures. Edinburgh address correcte

Logarithmic Corrections to Scaling in the XY2XY_2--Model

We study the distribution of partition function zeroes for the $XY$--model in two dimensions. In particular we find the scaling behaviour of the end of the distribution of zeroes in the complex external magnetic field plane in the thermodynamic limit (the Yang--Lee edge) and the form for the density of these zeroes. Assuming that finite--size scaling holds, we show that there have to exist logarithmic corrections to the leading scaling behaviour of thermodynamic quantities in this model. These logarithmic corrections are also manifest in the finite--size scaling formulae and we identify them numerically. The method presented here can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.Comment: 3 pages, latex, 2 figure

Determination of Lambda in quenched and full QCD - an update

We present an update on our previous determination of the Lambda parameter in QCD. The main emphasis is on results for two flavours of light dynamical quarks, where we can now almost double the amount of data used, including values at smaller lattice spacings. The calculations are performed using $O(a)$ improved Wilson fermions. Little change is found to previous numerical values.Comment: Lattice2004(spectrum), Fermilab, June 21-26, 2004, 3 page

Logarithmic Corrections to Scaling in the Two Dimensional XYXY--Model

By expressing thermodynamic functions in terms of the edge and density of Lee--Yang zeroes, we relate the scaling behaviour of the specific heat to that of the zero field magnetic susceptibility in the thermodynamic limit of the $XY$--model in two dimensions. Assuming that finite--size scaling holds, we show that the conventional Kosterlitz--Thouless scaling predictions for these thermodynamic functions are not mutually compatable unless they are modified by multiplicative logarithmic corrections. We identify these logarithmic corrections analytically in the case of the specific heat and numerically in the case of the susceptibility. The techniques presented here are general and can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.Comment: 11 pages, latex, 4 figure

Systematic Regge theory analysis of omega photoproduction

Systematic analysis of available data for $\omega$-meson photoproduction is given in frame of Regge theory. At photon energies above 20 GeV the $\gamma{+}p{\to}\omega{+}p$ reaction is entirely dominated by Pomeron exchange. However, it was found that Pomeron exchange model can not reproduce the $\gamma{+}p{\to}\rho{+}p$ and $\gamma{+}p{\to}\omega{+}p$ data at high energies simultaneously with the same set of parameters. The comparison between $\rho$ and $\omega$ data indicates a large room for meson exchange contribution to $\omega$-meson photoproduction at low energies. It was found that at low energies the dominant contribution comes from $\pi$ and $f_2$-meson exchanges. There is smooth transition between the meson exchange model at low energies and Regge theory at high energies.Comment: 7 pages, 8 figures, revtex

Is the up-quark massless?

We report on determinations of the low-energy constants alpha5 and alpha8 in the effective chiral Lagrangian at O(p^4), using lattice simulations with N_f=2 flavours of dynamical quarks. Precise knowledge of these constants is required to test the hypothesis whether or not the up-quark is massless. Our results are obtained by studying the quark mass dependence of suitably defined ratios of pseudoscalar meson masses and matrix elements. Although comparisons with an earlier study in the quenched approximation reveal small qualitative differences in the quark mass behaviour, numerical estimates for alpha5 and alpha8 show only a weak dependence on the number of dynamical quark flavours. Our results disfavour the possibility of a massless up-quark, provided that the quark mass dependence in the physical three-flavour case is not fundamentally different from the two-flavour case studied here.Comment: references added, typos correcte

Chiral Perturbation Theory and Finite Size Effects on the Nucleon Mass in unquenched QCD

We calculate finite size effects on nucleon masses in chiral perturbation theory. We confront the theoretical predictions with N_f=2 lattice results and discuss chiral extrapolation formulae.Comment: talk at Lattice 03 (spectrum), 3 pages latex, 3 figures. Assignment of 2 data points to incorrect data sets in plot 1 and of 1 data point in plot 2 corrected. 1 fm lattice result updated. Conclusions unchange

A comprehensive lattice study of SU(3) glueballs

We present a study of the $SU(3)$ glueball spectrum for all $J^{PC}$ values at lattice spacings down to $a^{-1}=3.73 (6)$ GeV ($\beta=6.4$) using lattices of size up to $32^4$. We extend previous studies and show that the continuum limit has effectively been reached. The number of clearly identified $J^{PC}$ states has been substantially increased. There are no clear signals for spin-exotic glueballs below 3 GeV. A comparison with current experimental glueball candidates is made.Comment: 10 pages including 2 PS figures, Liverpool Preprint: LTH 303, Wuppertal Preprint: WUB 93-1

A Study of the \eta \pi^{0} Spectrum and Search for a J^{PC} = 1^{-+} Exotic Meson

A partial wave analysis (PWA) of the of the $\eta \pi ^0$ system (where $\eta \to \gamma \gamma$) produced in the charge exchange reaction $\pi ^-p\to \eta \pi ^0n$ at an incident momentum of 18 GeV$/c$ is presented as a function of ${\eta \pi ^0}$ invariant mass, $m_{\eta\pi^0}$, and momentum transfer squared, $t_{\pi^{-}\to\eta\pi}$, from the incident $\pi^-$ to the outgoing ${\eta\pi ^0}$ system. $S$, $P$ and $D$ waves were included in the PWA. The $a_0(980)$ and $a_2(1320)$ states are clearly observed in the overall ${\eta\pi ^0}$ effective mass distribution as well as in the amplitudes associated with $S$ wave and $D$ waves respectively after partial wave decomposition. The observed distributions in moments (averages of spherical harmonics) were compared to the results from the PWA and the two are consistent. The distribution in $t_{\pi^{-}\to\eta\pi}$ for individual $D$ waves associated with natural and unnatural parity exchange in the $t$-channel are consistent with Regge phenomenology. Of particular interest in this study is the $P$ wave since this leads to an exotic $J^{PC}=1^{-+}$ for the $\eta \pi$ system. A $P$ wave is present in the data, however attempts to describe the mass dependence of the amplitude and phase motion with respect to the $D$ wave as a Breit-Wigner resonance are problematic. This has implications regarding the existence of a reported exotic $J^{PC} = 1^{-+}$ meson decaying into $\eta \pi^0$ with a mass near 1.4 GeV$/c^2$.Comment: 19 pages, 29 figures, to appear in Phys. Rev.