The continuum limit of the quark mass step scaling function in quenched lattice QCD

The renormalisation group running of the quark mass is determined non-perturbatively for a large range of scales, by computing the step scaling function in the Schroedinger Functional formalism of quenched lattice QCD both with and without O(a) improvement. A one-loop perturbative calculation of the discretisation effects has been carried out for both the Wilson and the Clover-improved actions and for a large number of lattice resolutions. The non-perturbative computation yields continuum results which are regularisation independent, thus providing convincing evidence for the uniqueness of the continuum limit. As a byproduct, the ratio of the renormalisation group invariant quark mass to the quark mass, renormalised at a hadronic scale, is obtained with very high accuracy.Comment: 23 pages, 3 figures; minor changes, references adde

Progress on Perfect Lattice Actions for QCD

We describe a number of aspects in our attempt to construct an approximately perfect lattice action for QCD. Free quarks are made optimally local on the whole renormalized trajectory and their couplings are then truncated by imposing 3-periodicity. The spectra of these short ranged fermions are excellent approximations to continuum spectra. The same is true for free gluons. We evaluate the corresponding perfect quark-gluon vertex function, identifying in particular the ``perfect clover term''. First simulations for heavy quarks show that the mass is strongly renormalized, but again the renormalized theory agrees very well with continuum physics. Furthermore we describe the multigrid formulation for the non-perturbative perfect action and we present the concept of an exactly (quantum) perfect topological charge on the lattice.Comment: 14 pages, 17 figures, Talk presented at LATTICE96(improvement

A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence

We investigate decoupling of heavy Kaluza-Klein modes in an Abelian Higgs model with space-time topologies $\mathbb{R}^{3,1} \times S^{1}$ and $\mathbb{R}^{3,1} \times S^{1}/\mathbb{Z}_{2}$. After integrating out heavy KK modes we find the effective action for the zero mode fields. We find that in the $\mathbb{R}^{3,1} \times S^{1}$ topology the heavy modes do not decouple in the effective action, due to the zero mode of the 5-th component of the 5-d gauge field $A_{5}$. Because $A_{5}$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_{5}^{4}$ interaction terms after loop corrections. In addition, after symmetry breaking, we find new divergences in the $A_{5}$ mass that did not appear in the symmetric phase. The new divergences are traced back to the gauge-goldstone mixing that occurs after symmetry breaking. The relevance of these new divergences to Symanzik's theorem is discussed. In order to get a more sensible theory we investigate the $S^{1}/\mathbb{Z}_{2}$ compactification. With this kind of compact topology, the $A_{5}$ zero mode disappears. With no $A_{5}$, there are no new divergences and the heavy modes decouple. We also discuss the dependence of the couplings and masses on the compactification scale. We derive a set of RG-like equations for the running of the effective couplings with respect to the compactification scale. It is found that magnitudes of both couplings decrease as the scale $M$ increases. The effective masses are also shown to decrease with increasing compactification scale. All of this opens up the possibility of placing constraints on the size of extra dimensions.Comment: 35 pages, 6 figure

Finite VEVs from a Large Distance Vacuum Wave Functional

We show how to compute vacuum expectation values from derivative expansions of the vacuum wave functional. Such expansions appear to be valid only for slowly varying fields, but by exploiting analyticity in a complex scale parameter we can reconstruct the contribution from rapidly varying fields.Comment: 39 pages, 16 figures, LaTeX2e using package graphic

The numerical study of the solution of the Φ04\Phi_0^4 model

We present a numerical study of the nonlinear system of $\Phi^4_0$ equations of motion. The solution is obtained iteratively, starting from a precise point-sequence of the appropriate Banach space, for small values of the coupling constant. The numerical results are in perfect agreement with the main theoretical results established in a series of previous publications.Comment: arxiv version is already officia

Scaling, asymptotic scaling and Symanzik improvement. Deconfinement temperature in SU(2) pure gauge theory

We report on a high statistics simulation of SU(2) pure gauge field theory at finite temperature, using Symanzik action. We determine the critical coupling for the deconfinement phase transition on lattices up to 8 x 24, using Finite Size Scaling techniques. We find that the pattern of asymptotic scaling violation is essentially the same as the one observed with conventional, not improved action. On the other hand, the use of effective couplings defined in terms of plaquette expectation values shows a precocious scaling, with respect to an analogous analysis of data obtained by the use of Wilson action, which we interpret as an effect of improvement.Comment: 43 pages ( REVTeX 3.0, self-extracting shell archive, 13 PostScript figs.), report IFUP-TH 21/93 (2 TYPOS IN FORMULAS CORRECTED,1 CITATION UPDATED,CITATIONS IN TEXT ADDED

The phase diagram of twisted mass lattice QCD

We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m_\pi^2/(4\pi f_\pi)^2 ~ a \Lambda (a being the lattice spacing, and \Lambda = \Lambda_{QCD}). We then focus on the region where m_\pi^2/(4\pi f_\pi)^2 ~ (a \Lambda)^2, in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, we find two possible phase diagrams, depending on the sign of a coefficient in the chiral Lagrangian. For one sign, there is an Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is washed out into a crossover if the twisted mass is non-vanishing. For the other sign, there is a first order transition for pure Wilson fermions, and we find that this transition extends into the twisted mass plane, ending with two symmetrical second order points at which the mass of the neutral pion vanishes. We provide graphs of the condensate and pion masses for both scenarios, and note a simple mathematical relation between them. These results may be of importance to numerical simulations.Comment: 13 pages, 5 figures, small clarifying comments added in introduction, minor typos fixed. Version to be published in Phys. Rev.

Ambiguities in the up quark mass

It has long been known that no physical singularity is encountered as up quark mass is adjusted from small positive to negative values as long as all other quarks remain massive. This is tied to an additive ambiguity in the definition of the quark mass. This calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest quark.Comment: 9 pages, 1 figure. Revision as will appear in Physical Review Letters. Simplified renormalization group discussion and title change requested by PR

Extracting Semantics of Individual Places from Movement Data by Analyzing Temporal Patterns of Visits

Data reflecting movements of people, such as GPS or GSM tracks, can be a source of information about mobility behaviors and activities of people. Such information is required for various kinds of spatial planning in the public and business sectors. Movement data by themselves are semantically poor. Meaningful information can be derived by means of interactive visual analysis performed by a human expert; however, this is only possible for data about a small number of people. We suggest an approach that allows scaling to large datasets reflecting movements of numerous people. It includes extracting stops, clustering them for identifying personal places of interest (POIs), and creating temporal signatures of the POIs characterizing the temporal distribution of the stops with respect to the daily and weekly time cycles and the time line. The analyst can give meanings to selected POIs based on their temporal signatures (i.e., classify them as home, work, etc.), and then POIs with similar signatures can be classified automatically. We demonstrate the possibilities for interactive visual semantic analysis by example of GSM, GPS, and Twitter data. GPS data allow inferring richer semantic information, but temporal signatures alone may be insufficient for interpreting short stops. Twitter data are similar to GSM data but additionally contain message texts, which can help in place interpretation. We plan to develop an intelligent system that learns how to classify personal places and trips while a human analyst visually analyzes and semantically annotates selected subsets of movement data

Thermodynamics of Four-Flavour QCD with Improved Staggered Fermions

We have calculated the pressure and energy density in four-flavour QCD using improved fermion and gauge actions. We observe a strong reduction of finite cut-off effects in the high temperature regime, similar to what has been noted before for the SU(3) gauge theory. Calculations have been performed on $16^3\times 4$ and 16^4 lattices for two values of the quark mass, $ma = 0.05$ and 0.1. A calculation of the string tension at zero temperature yields a critical temperature $T_c/\sqrt{\sigma} = 0.407 \pm 0.010$ for the smaller quark mass value.Comment: 12 pages, LaTeX2e File, 11 encapsulated postscript file