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

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

Quantum Evolution of Inhomogeneities in Curved Space

We obtain the renormalized equations of motion for matter and semi-classical gravity in an inhomogeneous space-time. We use the functional Schrodinger picture and a simple Gaussian approximation to analyze the time evolution of the $\lambda\phi^4$ model, and we establish the renormalizability of this non-perturbative approximation. We also show that the energy-momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations, without the need of further geometrical counter-terms.Comment: 22 page

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

Finite Size Effects in Quark-Gluon Plasma Formation

Using lattice simulations of quenched QCD we estimate the finite size effects present when a gluon plasma equilibrates in a slab geometry, i.e., finite width but large transverse dimensions. Significant differences are observed in the free energy density for the slab when compared with bulk behavior. A small shift in the critical temperature is also seen. The free energy required to liberate heavy quarks relative to bulk is measured using Polyakov loops; the additional free energy required is on the order of $30-40 MeV$ at $2-3 T_c$.Comment: LATTICE98(hightemp), talk at Lattice 98, 3 pages, 3 encapsulated postscript figures, uses espcrc2.st

Lattice energy-momentum tensor with Symanzik improved actions

We define the energy-momentum tensor on lattice for the $\lambda \phi^4$ and for the nonlinear $\sigma$-model Symanzik tree-improved actions, using Ward identities or an explicit matching procedure. The resulting operators give the correct one loop scale anomaly, and in the case of the sigma model they can have applications in Monte Carlo simulations.Comment: Self extracting archive fil

Fractal Behaviour in the O(3) Model

We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.Comment: 6 pages + 3 figures (concatenated PS files, uuencoded gz-compressed

Finite Size Effects in the Anisotropic \lambda/4!(\phi^4_1 + \phi^4_2)_d Model

We consider the $\frac{\lambda}{4!}(\phi^{4}_{1}+\phi^{4}_{2})$ model on a d-dimensional Euclidean space, where all but one of the coordinates are unbounded. Translation invariance along the bounded coordinate, z, which lies in the interval [0,L], is broken because of the boundary conditions (BC's) chosen for the hyperplanes z=0 and z=L. Two different possibilities for these BC's boundary conditions are considered: DD and NN, where D denotes Dirichlet and N Newmann, respectively. The renormalization procedure up to one-loop order is applied, obtaining two main results. The first is the fact that the renormalization program requires the introduction of counterterms which are surface interactions. The second one is that the tadpole graphs for DD and NN have the same z dependent part in modulus but with opposite signs. We investigate the relevance of this fact to the elimination of surface divergences.Comment: 33 pages, 2 eps figure

Spontaneous Flavor and Parity Breaking with Wilson Fermions

We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase''. We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width $\Delta m_0 \sim a^3$ with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order $a$. Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.Comment: 22 pages, LaTeX, 5 figures (added several references and a comment

Precision Upsilon Spectroscopy from Nonrelativistic Lattice QCD

The spectrum of the Upsilon system is investigated using the Nonrelativistic Lattice QCD approach to heavy quarks and ignoring light quark vacuum polarization. We find good agreement with experiment for the Upsilon(1S), Upsilon(2S), Upsilon(3S) and for the center of mass and fine structure of the chi_b states. The lattice calculations predict b-bbar D-states with center of mass at (10.20 +/- 0.07 +/- 0.03)GeV. Fitting procedures aimed at extracting both ground and excited state energies are developed. We calculate a nonperturbative dispersion mass for the Upsilon(1S) and compare with tadpole-improved lattice perturbation theory.Comment: 8 pages, latex, SCRI-94-57, OHSTPY-HEP-T-94-00