title: Excited charmonium spectrum from anisotropic lattices

abstract:
  We present our final results for the excited charmonium spectrum from a
quenched calculation using a fully relativistic anisotropic lattice QCD action.
A detailed excited charmonium spectrum is obtained, including both the exotic
hybrids (with $J^{PC} = 1^{-+}, 0^{+-}, 2^{+-}$) and orbitally excited mesons
(with orbital angular momentum up to 3). Using three different lattice spacings
(0.197, 0.131, and 0.092 fm), we perform a continuum extrapolation of the
spectrum. We convert our results in lattice units to physical values using
lattice scales set by the $^1P_1-1S$ splitting. The lowest lying exotic hybrid
$1^{-+}$ lies at 4.428(41) GeV, slightly above the $D^{**}D$ (S+P wave)
threshold of 4.287 GeV. Another two exotic hybrids $0^{+-}$ and $2^{+-}$ are
determined to be 4.70(17) GeV and 4.895(88) GeV, respectively. Our finite
volume analysis confirms that our lattices are large enough to accommodate all
the excited states reported here.


title:
Hamiltonian lattice quantum chromodynamics at finite density with Wilson
  fermions

abstract:
  Quantum chromodynamics (QCD) at sufficiently high density is expected to
undergo a chiral phase transition. Understanding such a transition is of
particular importance for neutron star or quark star physics. In Lagrangian
SU(3) lattice gauge theory, the standard approach breaks down at large chemical
potential $\mu$, due to the complex action problem. The Hamiltonian formulation
of lattice QCD doesn't encounter such a problem. In a previous work, we
developed a Hamiltonian approach at finite chemical potential $\mu$ and
obtained reasonable results in the strong coupling regime. In this paper, we
extend the previous work to Wilson fermions. We study the chiral behavior and
calculate the vacuum energy, chiral condensate and quark number density, as
well as the masses of light hadrons. There is a first order chiral phase
transition at zero temperature.


title: Percolating cluster of center vortices and confinement

abstract:
  We study the role of percolating clusters of center vortices in
configurations of an Ising gauge theory in 3D. It is known that low energy
features of gauge theories can be described in terms of an ``effective string
picture'', and that confinement properties are associated with topologically
non-trivial configurations. We focus our attention upon percolating clusters of
center vortices, and present numerical evidence for the fact that these objects
play a preminent role in confinement phenomenon, since their removal sweeps off
confinement altogether. Moreover, numerical simulations show that the string
fluctuations, and in particular the Luescher term, are completely encoded in
the percolating cluster.


title: Perturbative Wilson loops with massive sea quarks on the lattice

abstract:
  We present O(g^4) calculations of both planar and non-planar Wilson loops for
various actions in the presence of sea quarks. In particular, the plaquette,
the static potential and the static self energy are calculated to this order
for massive Wilson, Sheikholeslami-Wohlert and Kogut-Susskind fermions,
including the mass and n_f dependence. The results can be used to obtain
alpha_{MS} and m_b(m_b) from lattice simulations. We compare our perturbative
calculations to simulation data of the static potential and report excellent
qualitative agreement with boosted perturbation theory predictions for
distances r<1/GeV. We are also able to resolve differences in the running of
the coupling between n_f=2 and n_f=0 static potentials. We compute perturbative
estimates of the ``beta-shifts'' of QCD with sea quarks, relative to the
quenched theory, which we find to agree within 10 % with non-perturbative
simulations. This is done by matching the respective static potentials at large
distances. The prospects of determining the QCD running coupling from low
energy hadron phenomenology in the near future are assessed. We obtain the
result $\Lambda^{(2)}_{\bar{MS}}r_0=0.69(15)$ for the two flavour QCD
Lambda-parameter from presently available lattice data where $r_0^{-1}\approx
400$ MeV and estimate $\alpha_{\bar{MS}}^{(5)}(m_Z)=0.1133(59)$.


title: Status of and performance estimates for QCDOC

abstract:
  QCDOC is a supercomputer designed for high scalability at a low cost per
node. We discuss the status of the project and provide performance estimates
for large machines obtained from cycle accurate simulation of the QCDOC ASIC.


title: Heavy Quark Physics and Lattice QCD

abstract: I review recent progress made on heavy quark physics on the lattice.


title: Speeding up the HMC: QCD with Clover-Improved Wilson Fermions

abstract:
  We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of
systems with dynamical fermions to two flavor QCD with clover-improvement. For
our smallest quark masses we see a speed-up of more than a factor of two
compared with the standard algorithm.


title: The QCD phase diagram for small chemical potentials

abstract:
  We compute derivatives of thermodynamic quantities with respect to $\mu$, at
$\mu=0$ for 2 and 3 flavors of degenerate quark masses. This allows us to
estimate the phase transition line in the $T,\mu$ plane and quantify the
influence of a non vanishing chemical potential on the equation of state by
computing lines of constant energy, pressure and density. Moreover we evaluate
the order of the QCD phase transition by measuring the Binder Cumulant of the
chiral condensate. This gives access to the chiral critical point on the phase
transition line.


title: Lattice study of the Coleman--Weinberg mass in the SU(2)-Higgs model

abstract:
  Radiative symmetry breaking is a well known phenomenon in perturbation
theory. We study the problem in a non-perturbative framework, i.e. lattice
simulations. The example of the bosonic sector of the SU(2)-Higgs model is
considered. We determine the minimal scalar mass which turns out to be higher
than the mass value given by 1-loop continuum perturbation theory.


title:
Vector spectrum and color screening in two color QCD at nonzero T and
  \mu

abstract:
  We discuss a few aspects of the phase diagram of two color lattice QCD: we
investigate the long distance screening analyzing the behavior of the
interquark potential at large distances; we present a first set of results for
vector mesons and diquarks; we note similarities and differences between
features at high temperature and high baryon density.


title: An introduction to lattice QCD at non--zero temperature and density

abstract:
  This is an informal overview of methods and results on the QCD phase diagram
and lattice termodynamics aimed at specialists in nearby fields.


title: Light Quark Simulations With FLIC Fermions

abstract:
  Hadron masses are calculated in quenched lattice QCD in order to probe the
scaling behavior of a novel fat-link clover fermion action in which only the
irrelevant operators of the fermion action are constructed using APE-smeared
links. Light quark masses corresponding to an m_pi / m_rho ratio of 0.35 are
considered to assess the exceptional configuration problem of clover-fermion
actions. This Fat-Link Irrelevant Clover (FLIC) fermion action provides scaling
which is superior to mean-field improvement and offers advantages over
nonperturbative improvement, including reduced exceptional configurations.


title: Excited Baryons from the FLIC Fermion Action

abstract:
  Masses of positive and negative parity excited nucleons and hyperons are
calculated in quenched lattice QCD using an O(a^2) improved gluon action and a
fat-link clover fermion action in which only the irrelevant operators are
constructed with fat links. The results are in agreement with earlier N*
simulations with improved actions, and exhibit a clear mass splitting between
the nucleon and its parity partner, as well as a small mass splitting between
the two low-lying J^P={1/2}^- N* states. Study of different Lambda
interpolating fields suggests a similar splitting between the lowest two
{1/2}^- Lambda* states, although the empirical mass suppression of the
Lambda*(1405) is not seen.


title: Spin-3/2 Baryons in Lattice QCD

abstract:
  We present first results for masses of spin-3/2 baryons in lattice QCD, using
a novel fat-link clover fermion action in which only the irrelevant operators
are constructed using fat links. In the isospin-1/2 sector, we observe, after
appropriate spin and parity projection, a strong signal for the J^P=3/2^-
state, and find good agreement between the 1/2^+ mass and earlier nucleon mass
simulations with a spin-1/2 interpolating field. For the isospin-3/2 Delta
states, clear mass splittings are observed between the various 1/2^+/- and
3/2^+/- channels, with the calculated level orderings in good agreement with
those observed empirically.


title: Neutron Electric Dipole Moment on the Lattice: a Theoretical Reappraisal

abstract:
  We present a strategy for a lattice evaluation of the neutron electric dipole
moment induced by the strong CP violating term of the QCD Lagrangian. Our
strategy is based on the standard definition of the electric dipole moment,
involving the charge density operator J0, in case of three flavors with
non-degenerate masses. We present a complete diagrammatic analysis showing how
the axial chiral Ward identities can be used to replace the opological charge
operator with the flavor-singlet pseudoscalar density PS. Our final result is
characterized only by disconnected diagrams, where the disconnected part can be
either the single insertion of PS or the separate insertions of both PS and J0.
The applicability of our strategy to the case of lattice formulations that
explicitly break chiral symmetry, like the Wilson and Clover actions, is
discussed.


title:
Different definitions of the chemical potential with identical partition
  function in QCD on a lattice

abstract:
  It is shown that starting from one and the same transfer matrix formulation
of QCD on a lattice, it is possible to obtain both the action of Hasenfratz and
Karsch as well as an action where the chemical potential is not coupled to the
temporal links.


title: Partially-Quenched Nucleon-Nucleon Scattering

abstract:
  Nucleon-nucleon scattering is studied to next-to-leading order in a
partially-quenched extension of an effective field theory used to describe
multi-nucleon systems in QCD. The partially-quenched nucleon-nucleon amplitudes
will play an important role in relating lattice simulations of the two-nucleon
sector to nature.


title: P-vortices, nexuses and effects of Gribov copies in the center gauges

abstract:
  We perform the careful study of the Gribov copies problem in SU(2) lattice
gauge theory for maximal direct and maximal indirect center projections. We
find that this problem is much more severe than it was thought before. The
projected string tension is not in agreement with the physical string tension.
We also show that the particle--like objects, nexuses, might be important for
the confinement dynamics.


title:
B-->pi and B-->K transitions in standard and quenched chiral
  perturbation theory

abstract:
  We study the effects of chiral logs on the heavy-->light pseudoscalar meson
transition form factors by using standard and quenched chiral perturbation
theory combined with the static heavy quark limit. The resulting expressions
are used to indicate the size of uncertainties due to the use of the quenched
approximation in the current lattice studies. They may also be used to assess
the size of systematic uncertainties induced by missing chiral log terms in
extrapolating toward the physical pion mass. We also provide the coefficient
multiplying the quenched chiral log, which may be useful if the quenched
lattice studies are performed with very light mesons.


title:
Novel Approach to Super Yang-Mills Theory on Lattice - Exact fermionic
  symmetry and "Ichimatsu" pattern -

abstract:
  We present a lattice theory with an exact fermionic symmetry, which mixes the
link and the fermionic variables. The staggered fermionic variables may be
reconstructed into a Majorana fermion in the continuum limit. The gauge action
has a novel structure. Though it is the ordinary plaquette action, two
different couplings are assigned in the ``Ichimatsu pattern'' or the checkered
pattern. In the naive continuum limit, the fermionic symmetry survives as a
continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is
proportional to the field strength multiplied by the difference of the two
gauge couplings in this limit. This work is an extension of our recently
proposed cell model toward the realization of supersymmetric Yang-Mills theory
on lattice.


title:
Simulations with different lattice Dirac operators for valence and sea
  quarks

abstract:
  We discuss simulations with different lattice Dirac operators for sea and
valence quarks. A goal of such a "mixed" action approach is to probe deeper the
chiral regime of QCD by enabling simulations with light valence quarks. This is
achieved by using chiral fermions as valence quarks while computationally
inexpensive fermions are used in the sea sector. Specifically, we consider
Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action
for this mixed theory is derived to O(a), and the appropriate low energy chiral
effective Lagrangian is constructed, including the leading O(a) contributions.
Using this Lagrangian one can calculate expressions for physical observables
and determine the Gasser-Leutwyler coefficients by fitting them to the lattice
data.


title: Charmonium with three flavors of dynamical quarks

abstract:
  We present a calculation of the charmonium spectrum with three flavors of
dynamical staggered quarks from gauge configurations that were generated by the
MILC collaboration. We use the Fermilab action for the valence charm quarks.
Our calculation of the spin-averaged 1P--1S and 2S--1S splittings yields a
determination of the strong coupling, with $\ams(M_Z) = 0.119 (4)$.


title: Fermionic topological charge of families of lattice gauge fields

abstract:
  Topological charge of families of lattice gauge fields is defined
fermionically via families index theory for the overlap Dirac operator. Certain
obstructions to gauge invariance of the overlap chiral fermion determinant, as
well as the lattice analogues of certain obstructions to gauge fixings without
the Gribov problem, have natural descriptions in this context.


title: A computational system for lattice QCD with overlap Dirac quarks

abstract:
  We outline the essential features of a Linux PC cluster which is now being
developed at National Taiwan University, and discuss how to optimize its
hardware and software for lattice QCD with overlap Dirac quarks. At present,
the cluster constitutes of 30 nodes, with each node consisting of one Pentium 4
processor (1.6/2.0 GHz), one Gbyte of PC800 RDRAM, one 40/80 Gbyte hard disk,
and a network card. The speed of this system is estimated to be 30 Gflops, and
its price/performance ratio is better than $1.0/Mflops for 64-bit (double
precision) computations in quenched lattice QCD with overlap Dirac quarks.


title:
A lattice study of interaction mechanisms in a heavy-light meson-meson
  system

abstract:
  We study mass spectra of a meson-meson system involving two light and two
heavy quarks on an anisotropic lattice. The heavy quarks are treated in the
static approximation. The dependence of the spectrum on the relative distance
of the heavy quarks is extracted from the lattice simulation using the maximum
entropy method (MEM). A correlation matrix of meson-meson operators emphasizing
quark and gluon exchange degrees of freedom is employed in an attempt to learn
about aspects of mechanisms of hadronic interaction.


title: A note on ultraviolet suppressed quasi-optimal domain wall fermions

abstract:
  In a recent work Chiu proposed to modify domain wall fermions that allow in
an optimal way fewer number of flavors than in the standard case. This is done
using a variant of doamin wall fermions, the so-called truncated overlap
fermions. In this note I discuss the possibility to implement his proposal for
the original variant of domain wall fermions. I make also some remarks on
dynamical simulations with ultraviolet suppressed domain wall fermions.


title: More chiral lattice fermions

abstract:
  Instead of the Ginsparg-Wilson relation only generalized chiral symmetry is
required. The resulting much larger class of Dirac operators for massless
fermions is investigated and a general construction for them is given. It is
also shown that the new class still leads properly to Weyl fermions and to
chiral gauge theories.


title: Charmonium at finite temperature in quenched lattice QCD

abstract:
  We study charmonium correlators in pseudoscalar and vector channels at finite
temperature using lattice QCD simulation in the quenched approximation.
Anisotropic lattices are used in order to have sufficient numbers of degrees of
freedom in the Euclidean temporal direction. We focus on the low energy
structure of the spectral function, corresponding to the ground state in the
hadron phase, by applying the smearing technique to enhance the contribution to
the correlator from this region. We employ two analysis procedures: the maximum
entropy method (MEM) for the extraction of the spectral function without
assuming a specific form, to estimate the shape of the spectral function, and
the standard $\chi^2$ fit analysis using typical forms in accordance with the
result of MEM, for a more quantitative evaluation. To verify the applicability
of the procedures, we first analyze the smeared correlators as well as the
point correlators at zero temperature. We find that by shortening the
$t$-interval used for the analysis (a situation inevitable at $T>0$) the
reliability of MEM for point correlators is lost, while it subsists for smeared
correlators. Then the smeared correlators at $T\simeq 0.9 T_c$ and $1.1 T_c$
are analyzed. At $T\simeq 0.9 T_c$, the spectral function exhibits a strong
peak, well approximated by a delta function corresponding to the ground state
with almost the same mass as at T=0. At $T\simeq 1.1 T_c$, we find that the
strong peak structure still persists at almost the same place as below $T_c$,
but with a finite width of a few hundred MeV. This result indicates that the
correlators possess a nontrivial structure even in the deconfined phase.


title: Comparison of SO(3) and SU(2) lattice gauge theory

abstract:
  The Villain form of SO(3) lattice gauge theory is studied and compared to
Wilson's SU(2) theory. The topological invariants in SO(3) which correspond to
twisted boundary conditions in SU(2) are discussed and lattice observables are
introduced for them. An apparent SO(3) phase with negative adjoint Polyakov
loop is explained in terms of these observables. The electric twist free
energy, an order parameter for the confinement-deconfinement transition, is
measured in both theories to calibrate the temperature. The results indicate
that lattices with about 700^4 sites or larger will be needed to study the
SO(3) confined phase. Alternative actions are discussed and an analytic path
connecting SO(3) and SU(2) lattice gauge theory at weak coupling is exhibited.
The relevance for confinement of the centre of the gauge group is discussed.


title: On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

abstract:
  We prove that magnetic charge does not exist as a physical observable on the
physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic
monopoles seen in lattice simulations are then interpreted as artifacts of
gauge fixing. The apparent physical scaling properties of the monopole density
in the continuum limit observed on the lattice are attributed to the correct
scaling properties of physical objects - magnetic vortices, as first argued by
Greensite et. al. We can show that a local gauge transformation of a certain
type can " create" abelian monopole-antimonopole pairs along magnetic vortices.
This gauge transformation exists in pure SU(N) gauge theory at any $N$.


title: Improving the Chiral Properties of Lattice Fermions

abstract:
  The chiral properties of lattice fermions can be improved by altering either
their fermion-gauge coupling or the pure gauge part of the action (or both).
  Using both perturbation theory and nonperturbative simulation, we compare a
simple alteration of the gauge action (which encompasses the Wilson, Symanzik,
Iwasaki, and DBW2 actions), and HYP-blocked links in the fermion action.
Perturbative tests include calculations of the potential, flavor-changing quark
scattering amplitudes, and matching factors for currents. Non-perturbative
tests include the potential, measurements of flavor symmetry breaking for
staggered fermions, the behavior of topological objects, and properties of
overlap actions. Our results display the bad properties of these actions as
well as their good ones.


title: Dynamical Simulations with Smeared Link Staggered Fermions

abstract:
  One of the most serious problems of the staggered fermion lattice action is
flavor symmetry violation. Smeared link staggered fermions can improve flavor
symmetry by an order of magnitude relative to the standard thin link action.
Over the last few years different smearing transformations have been proposed,
both with perturbatively and non-perturbatively determined coefficients. What
hindered the acceptance and more general use of smeared link fermions until now
is the relative difficulty of dynamical simulations and the lack of
perturbative calculations with these actions. In both areas there have been
significant improvement lately, that I will review in this paper.


title:
The N_t=4 finite temperature phase transition for lattice QCD with a
  weak chiral 4-fermion interaction

abstract:
  We study the finite temperature phase transition of lattice QCD with an
irrelevant chiral 4-fermion interaction and two massless quark flavours, on
$8^3 \times 4$ and $12^2 \times 24 \times 4$ lattices. The strength of the
4-fermion interaction was reduced to half the minimum value used in previous
simulations, to study how the nature of this phase transition depends on this
additional interaction. We find that the transition remains first order as the
4-fermion coupling is reduced. Extending our earlier studies indicates that for
sufficiently large 4-fermion coupling, the transition is probably second order.


title: Exact Chiral Symmetry on the Lattice: QCD Applications

abstract:
  I review recent progress and results in lattice QCD obtained using fermions
with exact chiral symmetry.


title:
Behavior of Hadrons at Finite Density -- Lattice Study of Color SU(2)
  QCD

abstract:
  Using two-color lattice QCD with Wilson fermions, we report a study of the
finite baryon number density system with two-flavors. First we investigate the
Polyakov line and thermodynamical uantities in the $(\kappa,\mu)$ plane, where
$\kappa$ and $\mu$ are the hopping parameter and chemical potential in the
fermion action, respectively. Then we calculate propagators of meson
($\bar{q}\Gamma q$) and baryon ($q\Gamma q$) states. We find that the vector
meson propagators are strongly modified in large $\mu$ regions, indicating the
reduction of the mass. This anomalous behavior of the vector meson is observed
for the first time in lattice QCD.


title:
The renormalised quark mass in the Schrodinger functional of lattice QCD
  - a one-loop calculation with a non-vanishing background field

abstract:
  The critical quark mass, at which the renormalised mass vanishes, is computed
in the Schrodinger functional scheme with a non vanishing background field at
one-loop order of perturbation theory. Further one-loop calculations are done
for the renormalisation constant of the pseudo scalar density and for several
discretisation errors and compared to results obtained with a vanishing
background field.


title: String effects in the 3d gauge Ising model

abstract:
  We compare the predictions of the effective string description of confinement
with a set of Montecarlo data for the 3d gauge Ising model at finite
temperature. Thanks to a new algorithm which makes use of the dual symmetry of
the model we can reach very high precisions even for large quark-antiquark
distances. We are thus able to explore the large R regime of the effective
string. We find that for large enough distances and low enough temperature the
data are well described by a pure bosonic string. As the temperature increases
higher order corrections become important and cannot be neglected even at large
distances. These higher order corrections seem to be well described by the
Nambu-Goto action truncated at the first perturbative order.


title:
Calculation of weak matrix elements in domain-wall QCD with the DBW2
  gauge action

abstract:
  We report the details of our ongoing quenched calculations of weak matrix
elements using the combination of domain-wall fermions and the DBW2 gauge
action on lattices with $a^{-1}\approx 3$ GeV. A strategy to avoid the problem
of fixed topological charge is introduced in generating gauge configurations.
After studying the basic run parameters and elemental quantities, we present a
preliminary result for the kaon B-parameter ($B_K$).


title: Heavy-light mesons with staggered light quarks

abstract:
  We demonstrate the viability of improved staggered light quarks in studies of
heavy-light systems. Our method for constructing heavy-light operators exploits
the close relation between naive and staggered fermions. The new approach is
tested on quenched configurations using several staggered actionsn combined
with nonrelativistic heavy quarks. The B_s meson kinetic mass, the hyperfine
and 1P-1S splittings in B_s, and the decay constant f_{B_s} are calculated and
compared to previous quenched lattice studies. An important technical detail,
Bayesian curve-fitting, is discussed at length.


title:
Valence quarks in the QCD plasma: quark number susceptibilities and
  screening

abstract:
  We have investigated the quark sector of quenched QCD for 1.5\le T/Tc\le3 in
the continuum limit, using two different lattice discretisations of quarks and
extrapolating from lattice spacings between 1/4T and 1/14T. At these
temperatures, the flavour off-diagonal susceptibility, chi_{ud}/T^2, is
compatible with zero at each lattice spacing, and hence also in the continuum
limit. In the continuum limit, the light quark susceptibilities are about 10%
less than the ideal gas results even at the highest T, in agreement with hard
thermal loop predictions but marginally below a resummed perturbative
computation. For the mass range appropriate to the strange quark, the flavour
diagonal susceptibility is significantly smaller. Our estimate of the
Wroblewski parameter is compatible with observations at RHIC and SPS. The
continuum limit of screening masses in all (local) quark-bilinears is very
close to the ideal gas results.


title: Generalized Parton Distributions and the Spin Structure of the Nucleon

abstract:
  Generalized parton distributions are a new type of hadronic observables which
has recently stimulated great interest among theorists and experimentalists
alike. Introduced to delineate the spin structure of the nucleon, the orbital
angular momentum of quarks in particular, the new distributions contain vast
information about the internal structure of the nucleon, with the usual
electromagnetic form factors and Feynman parton distributions as their special
limits. While new perturbative QCD processes, such as deeply virtual Compton
scattering and exclusive meson production, have been found to measure the
distributions directly in experiments, lattice QCD offers a great promise to
provide the first-principle calculations of these interesting observables.


title:
Quark Contributions to Baryon Magnetic Moments in Full, Quenched and
  Partially Quenched QCD

abstract:
  The chiral nonanalytic behaviour of quark-flavor contributions to the
magnetic moments of octet baryons are determined in full, quenched and
partially-quenched QCD, using an intuitive and efficient diagrammatic
formulation of quenched and partially-quenched chiral perturbation theory. The
technique provides a separation of quark-sector magnetic-moment contributions
into direct sea-quark loop, valence-quark, indirect sea-quark loop and quenched
valence contributions, the latter being the conventional view of the quenched
approximation. Both meson and baryon mass violations of SU(3)-flavor symmetry
are accounted for. Following a comprehensive examination of the individual
quark-sector contributions to octet baryon magnetic moments, numerous
opportunities to observe and test the underlying structure of baryons and the
nature of chiral nonanalytic behavior in QCD and its quenched variants are
discussed. In particular, the valence u-quark contribution to the proton
magnetic moment provides the optimal opportunity to directly view nonanalytic
behavior associated with the meson cloud of full QCD and the quenched meson
cloud of quenched QCD. The u quark in Sigma^+ provides the best opportunity to
display the artifacts of the quenched approximation.


title: Lattice gauge theory with baryons at strong coupling

abstract:
  We study the effective Hamiltonian for strong-coupling lattice QCD in the
case of non-zero baryon density. In leading order the effective Hamiltonian is
a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and
the spins belong to a representation that depends on the local baryon number.
Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to
U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model
which we analyze in a 1/N_c expansion. In the vacuum sector we recover
spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn
theories. For non-zero baryon density we study the nearest-neighbor theory
only, and show that the pattern of spontaneous symmetry breaking depends on the
baryon density.


title: Calculation of Nucleon Electromagnetic Form Factors

abstract:
  The fomalism is developed to express nucleon matrix elements of the
electromagnetic current in terms of form factors consistent with the
translational, rotational, and parity symmetries of a cubic lattice. We
calculate the number of these form factors and show how appropriate linear
combinations approach the continuum limit.


title: Finite-Size Scaling of Vector and Axial Current Correlators

abstract:
  Using quenched chiral perturbation theory, we compute the long-distance
behaviour of two-point functions of flavour non-singlet axial and vector
currents in a finite volume, for small quark masses, and at a fixed gauge-field
topology. We also present the corresponding predictions for the unquenched
theory at fixed topology. These results can in principle be used to measure the
low-energy constants of the chiral Lagrangian, from lattice simulations in
volumes much smaller than one pion Compton wavelength. We show that quenching
has a dramatic effect on the vector correlator, which is argued to vanish to
all orders, while the axial correlator appears to be a robust observable only
moderately sensitive to quenching.


title:
Continuum Extrapolation of Moments of Nucleon Quark Distributions in
  Full QCD

abstract:
  Moments of light cone quark density, helicity, and transversity distributions
are calculated in unquenched lattice QCD at $\beta = 5.5$ and $\beta = 5.3$
using Wilson fermions on $ 16^3 \times 32 $ lattices. These results are
combined with earlier calculations at $\beta = 5.6$ using SESAM configurations
to study the continuum limit.


title:
Understanding Parton Distributions from Lattice QCD: Present Limitations
  and Future Promise

abstract:
  This talk will explain how ground state matrix elements specifying moments of
quark density and spin distributions in the nucleon have been calculated in
full QCD, show how physical extrapolation to the chiral limit including the
physics of the pion cloud resolves previous apparent conflicts with experiment,
and describe the computational resources required for a definitive comparison
with experiment.


title: Domain wall fermions with improved gauge actions

abstract:
  We study the chiral properties of quenched domain wall fermions with several
gauge actions. We demonstrate that the residual chiral symmetry breaking, which
is present for a finite number of lattice sites in the fifth dimension ($L_s$),
can be substantially suppressed using improved gauge actions. In particular the
Symanzik action, the Iwasaki action, and a renormalization group improved gauge
action, called doubly blocked Wilson (DBW2), are studied and compared to the
Wilson action. All improved gauge actions studied show a reduction in the
additive residual quark mass, $\mres$. Remarkably, in the DBW2 case $\mres$ is
roughly two orders of magnitude smaller than the Wilson gauge action at
$a^{-1}=2$ GeV and $L_s=16$. Significant reduction in $\mres$ is also realized
at stronger gauge coupling corresponding to $a^{-1}=1.3$ GeV. As our numerical
investigation indicates, this reduction is achieved by reducing the number of
topological lattice dislocations present in the gauge field configurations. We
also present detailed results for the quenched light hadron spectrum and the
pion decay constant using the DBW2 gauge action.


title: The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction

abstract:
  Compact lattice Quantum Electrodynamics (QED) with four species of fermions
is simulated with massless quarks by using the $\chi$QED scheme of adding a
four-fermi interaction to the action. Simulations directly in the chiral limit
of massless quarks are done with high statistics on $8^4$, and $16^4$ lattices,
and the phase diagram, parameterized by the gauge and the four-fermi couplings,
is mapped out. The line of monopole condensation transitions is separate from
the line of chiral symmetry restoration. The simulation results indicate that
the monopole condensation transition is first order while the chiral transition
is second order. The challenges in determining the Universality class of the
chiral transition are discussed. If the scaling region for the chiral
transition is sufficiently wide, the $16^4$ simulations predict critical
indices far from mean field values. We discuss a speculative scenario in which
anti-screening provided by double-helix strands of monopole and anti-monopole
loops are the agent that balances the screening of fermion anti-fermion pairs
to produce an ultra-violet fixed point in the electric coupling.


title: Spin on the lattice

abstract:
  I review the current status of hadronic structure computations on the
lattice. I describe the basic lattice techniques and difficulties and present
some of the latest lattice results; in particular recent results of the RBC
group using domain wall fermions are also discussed.


title: String breaking and monopoles

abstract:
  The string breaking is discussed in U(1)^{N-1} Abelian effective theories of
QCD. When a screening is expected, the static potential shows a flattening in
the long-range region and a linear behavior in the intermediate region. We show
why the screening is better observed in the Polyakov-loop correlators than in
the Wilson loops. The breaking of the adjoint string is explained without the
Z(N) picture.


title: Instanton and Monopole in External Chromomagnetic Fields

abstract:
  We study properties of instanton and monopole in an external chromomagnetic
field. Generally, the 't Hooft ansatz is no longer a solution of the Yang-Mills
field equation in the presence of external fields. Therefore, we investigate a
stabilized instanton solution with minimal total Yang-Mills action in a
nontrivial topological sector. With this aim, we consider numerical
minimization of the action with respect to the global color orientation, the
anisotropic scale transformation and the local gauge-like transformation
starting from a simple superposed gauge field of the 't Hooft ansatz and the
external color field. Here, the external color field is, for simplicity, chosen
to be a constant Abelian magnetic field along a certain direction. Then, the
4-dimensional rotational symmetry O(4) of the instanton solution is reduced to
two 2-dimensional rotational symmetries $O(2)\times O(2)$ due to the effect of
a homogeneous external field. In the space $\mib{R}^{3}$ at fixed $t$, we find
a quadrupole deformation of this instanton solution. In the presence of a
magnetic field $\vec{H}$, a prolate deformation occurs along the direction of
$\vec{H}$. Contrastingly, in the presence of an electric field $\vec{E}$ an
oblate deformation occurs along the direction of $\vec{E}$. We further discuss
the local correlation between the instanton and the monopole in the external
field in the maximally Abelian gauge. The external field affects the appearance
of the monopole trajectory around the instanton. In fact, a monopole and
anti-monopole pair appears around the instanton center, and this monopole loop
seems to partially screen the external field.


title: Dimensional reduction of Lattice Gauge Theory in (2+1)D

abstract:
  This is my Ph.D. thesis defended earlier this year. It contains mostly
information already presented in previous Bielefeld/Saclay papers on this
subject, though in more detailed form. It also includes actual calculations and
some unpublished material on phase structure of the reduced model.


title: Heavy Quark Free Energies and Screening in SU(2) Gauge Theory

abstract:
  We investigate the singlet, triplet and colour average heavy quark free
energies in SU(2) pure gauge theory at various temperatures T. We focus on the
long distance behaviour of the free energies, studying in particular the
temperature dependence of the string tension and the screening masses. The
results are qualitatively similar to the SU(3) scenario, except near the
critical temperature Tc of the deconfining transition. Finally we test a
recently proposed method to renormalize the Polyakov loop.


title: Low-Lying Fermion Modes: Dynamical versus Quenched

abstract:
  We compare the low-lying eigenmodes of the O(a) improved Wilson-Dirac
operator on quenched and dynamical configurations and investigate methods of
probing the topological properties of gauge configurations


title: Status of the apeNEXT project

abstract:
  We present the current status of the apeNEXT project. Aim of this project is
the development of the next generation of APE machines which will provide
multi-teraflop computing power. Like previous machines, apeNEXT is based on a
custom designed processor, which is specifically optimized for simulating QCD.
We discuss the machine design, report on benchmarks, and give an overview on
the status of the software development.


title: Locality of optimal lattice domain-wall fermions

abstract:
  It is shown that the effective 4D lattice Dirac operator of optimal lattice
domain-wall fermions with finite N_s (in the fifth dimension) is exponentially
local for sufficiently smooth gauge background.


title: Interpreting the lattice monopoles in the continuum terms

abstract:
  We review briefly current interpretation of the lattice monopoles, defined
within the Maximal Abelian Projection, in terms of the continuum theory. We
emphasize, in particular, that the lattice data, at the presently available
lattices, indicate that the monopoles are associated with singular fields. This
note is prompted by a recent analysis hep-lat/0211005 which is based on an
implicit assumption that the fields are regular.


title:
Non-Perturbative Determination of $c_{\rm SW}$ in Three-flavor Dynamical
  QCD

abstract:
  We present a fully non-perturbative determination of the $O(a)$ improvement
coefficient $c_{\rm SW}$ in three-flavor dynamical QCD for the RG improved as
well as the plaquette gauge actions, using the Schr\"odinger functional scheme.
Results are compared with one-loop estimates at weak gauge coupling.


title: QCD and the eta prime Mass: Instantons or Confinement?

abstract:
  We argue that lattice calculations of the $\eta'$ mass in QCD with $N_c=2$
colors performed at non-zero baryon chemical potential can be used to study the
mechanism responsible for the mass of the $\eta'$. QCD with two colors is an
ideal laboratory because it exhibits confinement, chiral symmetry breaking and
a would-be $U(1)_A$ Goldstone boson at all densities. Since the instanton
density and the confinement scale vary with density in a very different way,
instantons are clearly distinguishable from other possible mechanisms. There is
an instanton prediction for the $\eta'$ mass at large density that can be
compared to lattice results. The density dependence of the instanton
contribution is a simple consequence of the integer topological charge carried
by the instanton. We also argue that $N_c=3$ color QCD at finite isospin
density can be used in order to study the origin of OZI-violation in the scalar
sector.


title: Lattice Perturbation Theory

abstract:
  The consideration of quantum fields defined on a spacetime lattice provides
computational techniques which are invaluable for studying gauge theories
nonperturbatively from first principles. Perturbation theory is an essential
aspect of computations on the lattice, especially for investigating the
behavior of lattice theories near the continuum limit. Particularly important
is its role in connecting the outcome of Monte Carlo simulations to continuum
physical results. For these matchings the calculation of the renormalization
factors of lattice matrix elements is required. In this review we explain the
main methods and techniques of lattice perturbation theory, focusing on the
cases of Wilson and Ginsparg-Wilson fermions. We will illustrate, among other
topics, the peculiarities of perturbative techniques on the lattice, the use of
computer codes for the analytic calculations and the computation of lattice
integrals. Discussed are also methods for the computation of 1-loop integrals
with very high precision. The review presents in a pedagogical fashion also
some of the recent developments in this kind of calculations. The coordinate
method of L\"uscher and Weisz is explained in detail. Also discussed are the
novelties that Ginsparg-Wilson fermions have brought from the point of view of
perturbation theory. Particular emphasis is given throughout the paper to the
role of chiral symmetry on the lattice and to the mixing of lattice operators
under renormalization. The construction of chiral gauge theories regularized on
the lattice, made possible by the recent advances in the understanding of
chiral symmetry, is also discussed. Finally, a few detailed examples of lattice
perturbative calculations are presented.


title: The Second Moment of the Pion Light Cone Wave Function

abstract:
  We present a preliminary result for second moment of the light cone wave
function of the pion. This parameter is the subject of a discrepancy between
theoretical predictions (coming from lattice and sum rules) and a recent
experimental result (that remarkably agrees with purely perturbative
predictions). In this work we exploit lattice hypercubic symmetries to remove
power divergences and, moreover, implement a full 1-loop matching for all the
contributing operators.


title: The string spectrum from large Wilson loops

abstract:
  We look at energies of the low lying states of the hadronic string in three
dimensional SU(2) lattice gauge theory by forming correlation matrices among
different sources. We are able to go to previously inaccessible time
separations. This is made possible by using a new algorithm proposed by
L\"{u}scher and Weisz which lets us measure the exponentially small values of
large Wilson loops with sufficient accuracy.


title:
The Quark-Gluon Mixed Condensate g<\bar{q} sigma G q> in SU(3)c Quenched
  Lattice QCD

abstract:
  Using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched
level, we study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is
another chiral order parameter. For each current quark mass of m_q=21, 36, 52
MeV, we generate 100 gauge configurations in the 16^4 lattice with \beta = 6.0,
and perform the measurement of the mixed condensate at 16 points in each gauge
configuration. Using the 1600 data for each m_q, we find the ratio between the
mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q>/
<\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale in the chiral limit. The large
value of the mixed condensate suggests its importance in the operator product
expansion in QCD.


title:
Flavor Singlet Meson Mass in the Continuum Limit in Two-Flavor Lattice
  QCD

abstract:
  We present results for the mass of the eta-prime meson in the continuum limit
for two-flavor lattice QCD, calculated on the CP-PACS computer, using a
renormalization-group improved gauge action, and Sheikholeslami and Wohlert's
fermion action with tadpole-improved csw. Correlation functions are measured at
three values of the coupling constant beta corresponding to the lattice spacing
a approx. 0.22, 0.16, 0.11 fm and for four values of the quark mass parameter
kappa corresponding to mpi over mrho approx. 0.8, 0.75, 0.7 and 0.6. For each
beta, kappa pair, 400-800 gauge configurations are used. The two-loop diagrams
are evaluated using a noisy source method. We calculate eta-prime propagators
using local sources, and find that excited state contributions are much reduced
by smearing. A full analysis for the smeared propagators gives
metaprime=0.960(87)+0.036-0.248 GeV, in the continuum limit, where the second
error represents the systematic uncertainty coming from varying the functional
form for chiral and continuum extrapolations.


title: Results for the Etaprime Mass from Two-Flavor Lattice QCD

abstract:
  We present results for the mass of the etaprime meson for two-flavor lattice
QCD in the continuum limit, calculated on the CP-PACS computer, using an
RG-improved gauge action and clover fermion action with tadpole-improved csw.
Measurements are made at three couplings corresponding to a approx. 0.22, 0.16,
0.11 fm for four quark masses corresponding to mpi over mrho approx. 0.8, 0.75,
0.7, 0.6. Thw two-loop diagrams are evaluated using a noisy source method.
Quark smearing for both one- and two- loop diagrams is successfully applied to
obtain ground state signals in the etaprime channel. We obtain
metaprime=0.960(87)+0.036-0.286GeV in the continuum limit, where the second
error represents the systematic uncertainty coming from varying the functional
form for chiral and continuum extrapolations.


title: Speeding up Lattice QCD simulations with clover-improved Wilson Fermions

abstract:
  We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of
systems with dynamical fermions to two flavour QCD with clover-improvement. The
basic idea of our proposal is to split the fermion matrix into two factors with
a reduced condition number each. In the effective action, for both factors a
pseudo-fermion field is introduced. For our smallest quark masses we see a
speed-up of more than a factor of two compared with the standard algorithm.


title: Finite-Volume Two-Pion Amplitudes in the I=0 Channel

abstract:
  We perform a calculation in one-loop chiral perturbation theory of the
two-pion matrix elements and correlation functions of an I=0 scalar operator,
in finite and infinite volumes for both full and quenched QCD. We show that
major difficulties arise in the quenched theory due to the lack of unitarity.
Similar problems are expected for quenched lattice calculations of $K \to \pi
\pi$ amplitudes with $\Delta I=1/2$. Our results raise the important question
of whether it is consistent to study $K\to\pi\pi$ amplitudes beyond leading
order in chiral perturbation theory in quenched or partially quenched QCD.


title:
Abelian representation for nonabelian Wilson loops and the Non - Abelian
  Stokes theorem on the lattice

abstract:
  We derive the Abelian - like expression for the lattice SU(N) Wilson loop in
arbitrary irreducible representation. The continuum Abelian representation of
the SU(N) Wilson loop (for the loop without selfintersections) that has been
obtained by Diakonov and Petrov appears to be a continuum limit of this
expression. We also obtain the lattice variant of a non - Abelian Stokes
theorem and present the explicit expression for the matrix $\cal H$ used in the
Diakonov - Petrov approach.


title: Mass Generation without Phase Coherence at Nonzero Temperature

abstract:
  We present results from numerical simulations of the 2+1d SU(2)xSU(2) Nambu -
Jona-Lasinio model with N_f=4 fermion flavours at zero and nonzero temperature
T. At zero temperature, critical exponents are extracted from the scaling of
the order parameter and fermion mass and are found to be consistent with
next-to-leading order predictions of the 1/N_f expansion. At nonzero
temperature we observe fermion mass generation despite the lack of chiral
symmetry breaking, which is forbidden by the Colemann-Mermin-Wagner theorem for
all T>0. We study the effects of lattice discretisation and finite volume on
the dynamically generated fermion mass. By study of the lattice dispersion
relation we also show that in the hot phase there is no significant temperature
induced modification to the speed of light. Studies of the equation of state
are made by measuring the pressure as a function of temperature and comparison
is made with large-N_f predictions.


title: Fine tuned vortices in lattice SU(2) gluodynamics

abstract:
  We report measurements of the action associated with center vortices in SU(2)
pure lattice gauge theory. In the lattice units the excess of the action on the
plaquettes belonging to the vortex is approximately a constant, independent on
the lattice spacing 'a'. Therefore the action of the center vortex is of order
'A/a^2', where 'A' is its area. Since the area 'A' is known to scale in the
physical units, the measurements imply that the suppression due to the surface
action is balanced, or fine tuned to the entropy factor which is to be an
exponential of 'A/a^2'.


title:
Monopole creation operators as confinement--deconfinement order
  parameters

abstract:
  We study numerically two versions of the monopole creation operators proposed
by Frohlich and Marchetti. The disadvantage of the old version of the monopole
creation operator is due to visibility of the Dirac string entering the
definition of the creation operator in the theories with coexisting electric
and magnetic charges. This problem does not exist for the new creation operator
which is rather complicated. Using the Abelian Higgs model with a compact gauge
field we show that both definitions of the monopole creation operator can serve
as order parameters for the confinement--deconfinement phase transition. The
value of the monopole condensate for the old version depends on the length of
Dirac string. However, as soon as the length is fixed the old operator
certainly discriminates between the phases with condensed and non--condensed
monopoles.


title:
More on String Breaking in the 3D Abelian Higgs Model: the Photon
  Propagator

abstract:
  We study the Landau gauge photon propagator in the three--dimensional Abelian
Higgs model with compact gauge field and fundamentally charged matter in the
London limit. The total gauge field is split into singular and regular parts.
On the confinement side of the string breaking crossover the momentum
dependence of the total propagator is characterized by an anomalous dimension
similarly to 3D compact QED. At the crossover and throughout the Higgs region
the anomalous dimension disappears. This result perfectly agrees with recent
observations that the monopole--antimonopole plasma leads to nonzero anomalous
dimension and the presence of the matter fields causes monopole pairing into
dipole bound states. The Yukawa mass characterizing the propagator part from
regular gauge fields is non-vanishing at the Higgs side and coincides with the
mass found for the total propagator. The regular gauge field without anomalous
dimension becomes massless at the crossover and in the confinement region.


title: Quark-Gluon Mixed Condensate (anti-Q sigma G Q) from Lattice QCD

abstract:
  We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is
another chiral order parameter, in SU(3)c lattice QCD with the Kogut-Susskind
fermion at the quenched level. Using 100 gauge configurations on the 16^4
lattice with \beta = 6.0, we measure the mixed condensate at 16 points in each
gauge configuration for each current-quark mass of m_q=21, 36, 52 MeV. From the
1600 data for each m_q, we find the ratio between the mixed condensate and the
quark condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at
the lattice scale of 1/a \simeq 2 GeV in the chiral limit. The large value of
the mixed condensate suggests its importance in the operator product expansions
in QCD. We also show our preliminary results of the mixed condensate at finite
temperature.


title: Charmonium near the deconfining transition on the lattice

abstract:
  We study the charmonium properties at finite temperature using quenched
lattice QCD simulations. Although a simple potential model analysis indicates
no bound state at $T>1.05T_c$, our analyses of the spatial correlation between
quark and anti-quark and the spectral function indicate that a bound-state-like
structure may survive even above $T_c$.


title:
On the effects of (partial) quenching on penguin contributions to K-> pi
  pi

abstract:
  Recently, we pointed out that chiral transformation properties of strong
penguin operators change in the transition from unquenched to (partially)
quenched QCD. As a consequence, new penguin-like operators appear in the
(partially) quenched theory, along with new low-energy constants, which should
be interpreted as a quenching artifact. Here, we extend the analysis to the
contribution of the new low-energy constants to the K^0 -> pi^+ pi^- amplitude,
at leading order in chiral perturbation theory, and for arbitrary (momentum
non-conserving) kinematics. Using these results, we provide a detailed
discussion of the intrinsic systematic error due to this (partial) quenching
artifact. We also give a simple recipe for the determination of the
leading-order low-energy constant parameterizing the new operators in the case
of strong $LR$ penguins.


title:
Partially Quenched Chiral Perturbation Theory and a Massless Up Quark: A
  Lattice Calculation of the Light-Quark-Mass Ratio

abstract:
  The nontrivial topological structure of the QCD gauge vacuum generates a CP
breaking term in the QCD Lagrangian. However, measurements of the neutron
electric dipole moment have demonstrated that the term's coefficient is
unnaturally small, a dilemma known as the strong CP problem. A massless up
quark is one potential solution, as the term could then be absorbed through
chiral rotations. Through the light-quark-mass ratio m_u / m_d, leading order
Chiral Perturbation Theory appears to rule this scenario out. However, the
Kaplan-Manohar ambiguity demonstrates that certain strong next-to-leading order
corrections are indistinguishable from an up quark mass. Only a direct
calculation of the Gasser-Leutwyler coefficient combination 2 L_8 - L_5 can
resolve the issue. We carry out such a calculation, using partially quenched
N_f = 3 staggered fermions and hypercubic blocking, and make a quantitative
assessment of our systematic error. We find 2 L_8 - L_5 = (0.22 +/- 0.14) x
10^-3, which corresponds to a light-quark-mass ratio of m_u / m_d = 0.408 +/-
0.035. Thus, the massless-up-quark solution to the strong CP problem is ruled
out. This is the first calculation of its type to use a physical number of
light quarks, N_f = 3, and the first determination of 2 L_8 - L_5 to include a
comprehensive study of statistical error.


title:
The Thermal Glueball at Finite Temperature in SU(3) Anisotropic Lattice
  QCD

abstract:
  The thermal glueball is studied at finite temperature by using SU(3)
anisotropic lattice QCD with beta_{lat}=6.25, the renormalized anisotropy xi =
a_s/a_t = 4 over the lattice of the size 20^3xN_t with various N_t at the
quenched level. While the narrow peak ansatz leads to the significant polemass
reduction of about 300 MeV near the critical temperature T_c, Breit-Wigner
ansatz which can take into account the possible appearance of the thermal width
leads to the significant thermal width broadening of about 300 MeV with a
modest reduction of the peak center of about 100 MeV.


title: The nonperturbative quark-gluon vertex

abstract:
  We show results for the quark-gluon vertex in the Landau gauge, using a
mean-field improved Sheikholeslami-Wohlert fermion action. We compute all the
three non-zero form factors of the vertex at zero gluon momentum, and compare
them to the abelian vertex. The quark mass dependence of the vertex is also
investigated and found to be negligible for the range of masses considered.


title: Numerical techniques for lattice QCD in the $\epsilon$--regime

abstract:
  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.


title: Uncovering Low-Dimensional Topological Structure in the QCD Vacuum

abstract:
  Recently, we have pointed out that sign-coherent 4-dimensional structures can
not dominate topological charge fluctuations in QCD vacuum at all scales. Here
we show that an enhanced lower-dimensional coherence is possible. In pure SU(3)
lattice gauge theory we find that in a typical equilibrium configuration about
80% of space-time points are covered by two oppositely-charged connected
structures built of elementary 3-dimensional coherent hypercubes. The
hypercubes within the structure are connected through 2-dimensional common
faces. We suggest that this coherence is a manifestation of a low-dimensional
order present in the QCD vacuum. The use of a topological charge density
associated with Ginsparg-Wilson fermions ("chiral smoothing") is crucial for
observing this structure.


title:
Correlators of left charges and weak operators in finite volume chiral
  perturbation theory

abstract:
  We compute the two-point correlator between left-handed flavour charges, and
the three-point correlator between two left-handed charges and one strangeness
violating \Delta I=3/2 weak operator, at next-to-leading order in finite volume
SU(3)_L x SU(3)_R chiral perturbation theory, in the so-called epsilon-regime.
Matching these results with the corresponding lattice measurements would in
principle allow to extract the pion decay constant F, and the effective chiral
theory parameter g_27, which determines the \Delta I = 3/2 amplitude of the
weak decays K to \pi\pi as well as the kaon mixing parameter B_K in the chiral
limit. We repeat the calculations in the replica formulation of quenched chiral
perturbation theory, finding only mild modifications. In particular, a properly
chosen ratio of the three-point and two-point functions is shown to be
identical in the full and quenched theories at this order.


title: B_K from quenched overlap QCD

abstract:
  We present an exploratory calculation of the standard model Delta S=2 matrix
element relevant for indirect CP violation in K -> pi pi decays. The
computation is performed with overlap fermions in the quenched approximation at
beta=6.0 on a 16^3x32 lattice. The resulting bare matrix element is
renormalized non-perturbatively. Our preliminary result is B_K^{NDR}(2
GeV)=0.61(7), where the error does not yet include an estimate of systematic
uncertainties.


title: Some remarks on cyclization and periodicity

abstract:
  Conditions when application of cyclization procedure does not lead to the
periodic function are specified. Sufficient conditions under which obtained
function is periodic are stated.


title:
The measurement, fitting and interpretation of the radial distributions
  of Heavy-Light mesons calculated on a lattice with dynamical fermions

abstract:
  In our earlier work, the charge and matter radial distributions of
heavy-light mesons were measured on a 16^3 times 24 lattice with a lattice
spacing of a = 0.17 fm and a light quark mass about that of the strange quark.
  Several major improvements have now been made: 1) Dynamical fermions are used
with a approximately 0.14 fm; 2) More gauge configurations are included (78 vs
20); 3) Off-axis, in addition to on-axis, insertions are made; 4) The data
analysis is much more complete. In particular, distributions involving excited
states are extracted.


title:
Lattice calculation of the lowest order hadronic contribution to the
  muon anomalous magnetic moment

abstract:
  We present a quenched lattice calculation of the lowest order (alpha^2)
hadronic contribution to the anomalous magnetic moment of the muon which arises
from the hadronic vacuum polarization. A general method is presented for
computing entirely in Euclidean space, obviating the need for the usual
dispersive treatment which relies on experimental data for e^+e^- annihilation
to hadrons. While the result is not yet of comparable accuracy to those
state-of-the-art calculations, systematic improvement of the quenched lattice
computation to this level of accuracy is straightforward and well within the
reach of present computers. Including the effects of dynamical quarks is
conceptually trivial, the computer resources required are not.


title: More on Electric and Magnetic Fluxes in SU(2)

abstract:
  The free energies of static charges and center monopoles are given by their
fluxes. While electric fluxes show the universal behaviour of the deconfinement
transition, the monopole free energies vanish in the thermodynamic limit at all
temperatures and are thus irrelevant for the transition. Magnetic fluxes may,
however, be used to measure the topological susceptibility without cooling.


title: Hadronic decay of a vector meson from the lattice

abstract:
  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.


title: Chiral fermion operators on the lattice

abstract:
  We only require generalized chiral symmetry and $\gamma_5$-hermiticity, which
leads to a large class of Dirac operators describing massless fermions on the
lattice, and use this framework to give an overview of developments in this
field. Spectral representations turn out to be a powerful tool for obtaining
detailed properties of the operators and a general construction of them. A
basic unitary operator is seen to play a central r\^ole in this context. We
discuss a number of special cases of the operators and elaborate on various
aspects of index relations. We also show that our weaker conditions lead still
properly to Weyl fermions and to chiral gauge theories.


title: Remarks on the reweighting method in the chemical potential direction

abstract:
  We comment on the reweighting method in the chemical potential $(\mu_{\rm
q})$ direction. We study the fluctuation of the reweighting factor during
Monte-Carlo steps. We find that it is the absolute value of the reweighting
factor that mainly contributes to the shift of the phase transition line
$(\beta_c)$ by the presence of $\mu_{\rm q}$. The phase fluctuation is a cause
of the sign problem, but the effect on $\beta_c$ seems to be small. We also
discuss $\beta_c$ for Iso-vector chemical potential and $\beta_c$ determined
from simulations with imaginary chemical potential.


title:
The profile of the broken string in the confined and deconfined phase in
  full QCD

abstract:
  We study the profile of the broken string (flux tube) in the maximally
abelian gauge below and above the finite temperature phase transition in full
QCD. In the deconfinement phase, the flux tube disappears and the electric
field apperas to be Coulomb-like. In the confinement phase, but near $T_c$, at
shorter distances a flux tube is formed like at zero temperature, while at
larger distances the tube disappears similar to the deconfinement phase.


title: The flux distribution of the three quark system in SU(3)

abstract:
  We study the abelian color-flux distribution of the three quark system in the
maximally abelian gauge on SU(3) lattices. The distribution of the color
electric field suggests $Y Ansatz$, which might be interpreted through the dual
superconductor picture as the result of the vacuum pressure in the confined
phase. In order to clarify the flux structure, we investigate the color
electric field in the three quark system also in the monopole part and in the
photon part.


title:
Lattice QCD study for the Quark-Gluon Mixed Condensate (anti-Q sigma G
  Q)

abstract:
  We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is
another chiral order parameter, using the SU(3)c lattice QCD with the
Kogut-Susskind(KS) fermion at the quenched level. We generate 100 gauge
configurations on the 16^4 lattice with \beta = 6.0, and measure the mixed
condensate at 16 points in each gauge configuration for each current-quark mass
of m_q=21, 36, 52 MeV. From the 1600 data for each m_q, we find the ratio
between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma
G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in
the chiral limit. The large value of the mixed condensate suggests its
importance in the operator product expansions in QCD.


title: High Spin Glueballs from the Lattice

abstract:
  We discuss the principles underlying higher spin glueball calculations on the
lattice. For that purpose, we develop numerical techniques to rotate Wilson
loops by arbitrary angles in lattice gauge theories close to the continuum. As
a first application, we compute the glueball spectrum of the SU(2) gauge theory
in 2+1 dimensions for both parities and for spins ranging from 0 up to 4
inclusive. We measure glueball angular wave functions directly, decomposing
them in Fourier modes and extrapolating the Fourier coefficients to the
continuum. This allows a reliable labelling of the continuum states and gives
insight into the way rotation symmetry is recovered. As one of our results, we
demonstrate that the D=2+1 SU(2) glueball conventionally labelled as J^P = 0^-
is in fact 4^- and that the lightest ``J=1'' state has, in fact, spin 3.


title: Vortices, Confinement and Higgs fields

abstract:
  We review lattice evidence for the vortex mechanism of quark confinement and
study the influence of charged matter fields on the vortex distribution.


title:
Some peculiarities of transition from discrete to continuum Fourier
  series in lattice theories

abstract:
  Transition from discrete to continuous Fourier series is studied for the
functions becoming singular in the transition. Conditions are specified when
summing replacement by integration is inadmissible.


title: New findings for topological excitations in SU(3) lattice gauge theory

abstract:
  We probe the SU(3) vacuum using eigenvectors of the Dirac operator with an
arbitrary phase for the temporal boundary condition. We consider configurations
with topological charge |Q| = 1 near the QCD phase transition and at low
temperatures on a torus. For all our ensembles we show that the zero-mode of
the Dirac operator changes its position as one changes the phase of the
boundary condition. For ensembles near the QCD phase transition our results
closely resemble the behavior of zero-modes for Kraan - van Baal solutions of
the classical Yang-Mills equations where the individual lumps are interpreted
as monopoles. Our findings near T_c and on the torus show that for both cases
an excitation with topological charge |Q| = 1 is built from several separate
lumps.


title: The BlueGene/L Supercomputer

abstract:
  The architecture of the BlueGene/L massively parallel supercomputer is
described. Each computing node consists of a single compute ASIC plus 256 MB of
external memory. The compute ASIC integrates two 700 MHz PowerPC 440 integer
CPU cores, two 2.8 Gflops floating point units, 4 MB of embedded DRAM as cache,
a memory controller for external memory, six 1.4 Gbit/s bi-directional ports
for a 3-dimensional torus network connection, three 2.8 Gbit/s bi-directional
ports for connecting to a global tree network and a Gigabit Ethernet for I/O.
65,536 of such nodes are connected into a 3-d torus with a geometry of
32x32x64. The total peak performance of the system is 360 Teraflops and the
total amount of memory is 16 TeraBytes.


title: Convergence of chiral effective field theory

abstract:
  We formulate the expansion for the mass of the nucleon as a function of pion
mass within chiral perturbation theory using a number of different ultra-violet
regularisation schemes; including dimensional regularisation and various
finite-ranged regulators. Leading and next-to-leading order non-analytic
contributions are included through the standard one-loop Feynman graphs. In
addition to the physical nucleon mass, the expansion is constrained by recent,
extremely accurate, lattice QCD data obtained with two flavors of dynamical
quarks. The extent to which different regulators can describe the chiral
expansion is examined, while varying the range of quark mass over which the
expansions are matched. Renormalised chiral expansion parameters are recovered
from each regularisation prescription and compared. We find that the
finite-range regulators produce consistent, model-independent results over a
wide range of quark mass sufficient to solve the chiral extrapolation problem
in lattice QCD.


title: Lattice effective theory and the phase transition at finite densities

abstract:
  The transition from the hadronic phase to the phase of
color-superconductivity at large densities is addressed by an effective theory
which incorporates the Yang-Mills dynamics in addition to the di-quark degree
of freedom. A toy version of this theory is studied by lattice simulations. A
first order phase transition separates the regime of broken color-electric flux
tubes from the color superconducting phase. My findings suggest that the quark
and gluon liberation occurs at the same critical chemical potential.


title: Massless QED_3 with explicit fermions

abstract:
  We study dynamical mass generation in QED in (2+1) dimensions using
Hamiltonian lattice methods. We use staggered fermions, and perform simulations
with explicit dynamical fermions in the chiral limit. We demonstrate that a
recently developed method to reduce the fermion sign problem can successfully
be applied to this problem. Our results are in agreement with both the strong
coupling expansion and with Euclidean lattice simulations.


title: Direct simulations of small multi-fermion systems

abstract:
  I explore computer simulations of the dynamics of small multi-fermion lattice
systems. The method is more general, but I concentrate on Hubbard type models
where the fermions hop between a small number of connected sites. I use the
natural mapping of fermion occupation numbers onto computer bits. Signs from
fermion interchange are reduced to bit counting. The technique inherently
requires computer resources growing exponentially with the system volume; so,
it restricted to modestly small systems. Large volume results would require
combining these techniques with further approximations, perhaps in a recursive
renormalization group manner.


title: Non-perturbative Methods in Modal Field Theory

abstract:
  Several issues in the modal approach to quantum field theory are discussed.
Within the formalism of spherical field theory, differential renormalization is
presented and shown to result in a finite number of renormalization parameters.
Computations of the massless Thirring model in 1+1 dimensions are presented
using this approach.
  Diagonalization techniques in periodic field theory are demonstrated. Issues
of very large Hilbert spaces are considered and several approaches are
presented. The quasi sparse eigenvector (QSE) approach takes advantage of the
relatively small number of basis states that typically contribute significantly
to any particular eigenvector. Stochastic correction methods use Monte Carlo
calculations to calculate higher order corrections to the quasi sparse result.
  The quasi sparse eigenvector method and stochastic error correction are
applied to the Hubbard model. With U/t=4, the shift in the ground energy below
the U=0 value is found to within 1% for the 8x8 Hubbard model with 25/64
filling.


title: Flux Tubes of Two- and Three-Quark System in Full QCD

abstract:
  We study the abelian color flux of two- and three-quark systems in the
maximally abelian gauge in lattice QCD with dynamical fermions. We find that
the abelian flux tube formed between quark and antiquark is very much the same
as in quenched QCD up to quark separations of $R$$\sim$ 2fm. The profile of the
color electric field in three-quark system suggests $Y$ ansatz, which might be
interpreted as the result of the vacuum pressure in the confined phase. In
order to clarify the flux structure, we investigate the color electric field of
the three-quark system splittting the abelian gauge field into the monopole and
photon parts.


title: Interactions between Lattice Hadrons

abstract:
  The effective residual interaction for a system of hadrons has a long
tradition in theoretical physics. It has been mostly addressed in terms of
boson exchange models. The aim of this review is to describe approaches based
on lattice field theory and numerical simulation. At the present time this
subject matter is in an exploratory stage. A large array of problems waits to
be tackled, so that known features of hadron-hadron interactions will
eventually be understood in a model-independent way. The lattice formulation,
being capable of dealing with the nonperturbative regime, describes
strong-interaction physics from first principles, i.e. quantum chromodynamics
(QCD). Although the physics of hadron-hadron interactions may be intrinsically
complicated, the methods used in lattice simulations are simple: For the most
part they are based on standard mass calculations. This chapter addresses
commonly used techniques, within QCD and also simpler lattice models, describes
important results, and also gives some insight into numerical methods for
multi-quark systems.


title: Lattice QCD, gauge fixing, and the transition to the perturbative regime

abstract:
  Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads
to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD
action. In the asymptotic regime, where perturbative QCD is relevant, Gribov
copies can be neglected. In the nonperturbative regime, one must adopt either a
nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain
local BRST invariance at the expense of admitting Gribov copies. These issues
are explored and discussed. In addition, the relationship between recent
Dyson-Schwinger based calculations of the infrared behavior of QCD Green's
functions and the lattice calculation of these quantities is examined.


title:
Light hadron spectroscopy with two flavors of $O(a)$-improved dynamical
  quarks

abstract:
  We present a high statistics study of the light hadron spectrum and quark
masses in QCD with two flavors of dynamical quarks. Numerical simulations are
carried out using the plaquette gauge action and the O(a)-improved Wilson quark
action at \beta=5.2, where the lattice spacing is found to be a=0.0887(11)fm
from \rho meson mass, on a 20^3\times 48 lattice. At each of five sea quark
masses corresponding to m_{PS}/m_{V} \simeq 0.8-0.6, we generate 12000
trajectories using the symmetrically preconditioned Hybrid Monte Carlo
algorithm. Finite spatial volume effects are investigated employing 12^3 \times
48, 16^3 \times 48 lattices. We also perform a set of simulations in quenched
QCD with the same lattice actions at a similar lattice spacing to those for the
full QCD runs. In the meson sector we find clear evidence of sea quark effects.
The J parameter increases for lighter sea quark masses, and the full QCD meson
masses are systematically closer to experiment than in quenched QCD. Careful
finite-size studies are made to ascertain that these are not due to finite-size
effects. Evidence of sea quark effects is less clear in the baryon sector due
to larger finite-size effects. We also calculate light quark masses and find
m_{ud}^{MS}(2GeV) =3.223(+0.046/-0.069)MeV and
m_s^{MS}(2GeV)=84.5(+12.0/-1.7)MeV which are about 20% smaller than in quenched
QCD.


title: The scaling region of the lattice O(N) sigma model at finite temperature

abstract:
  We present results from numerical studies of the finite temperature phase
transition of the $(3+1)d$ O(N)-symmetric non-linear sigma model for $N=1,2$
and 3. We study the dependence of the width of the 3d critical region on $N$
and we show that the broken phase scaling region is much wider for N=2 and 3
than for N=1. We also compare the widths of the critical region in the low $T$
and high $T$ phases of the O(2) model and we show that the scaling region in
the broken phase is much wider than in the symmetric phase. We also report
results for the width of the scaling regions in the low $T$ phase$ (2+1)d$
Ising model and we show that the spatial correlation length has to be
approximately twice the lattice temporal extent before the 2d scaling region is
reached.


title: Opportunities, Challenges, and Fantasies in Lattice QCD

abstract:
  Some important problems in quantitative QCD will certainly yield to hard work
and adequate investment of resources, others appear difficult but may be
accessible, and still others will require essentially new ideas. Here I
identify several examples in each class.


title: Interpolating the Free Energy Density Differences of Reweighting Methods

abstract:
  A discussion of the overlap problem of reweighting approaches to evaluating
critical phenomenon in fermionic systems is motivated by highlighting the
divergence of the joint probability density function of a general ratio. By
identifying the bounds for which this integral can be expressed in closed form,
we establish criteria for accurately mapping the joint ratio distribution of
two disjoint ensembles through interpolation. The approach is applied to QCD
with four staggered flavours to evaluate the critical line in the $\beta-\mu$
plane.


title: Heavy quark potential in lattice QCD at finite temperature

abstract:
  Results of the study of lattice QCD with two flavors of nonperturbatively
improved Wilson fermions at finite temperature are presented. The transition
temperature for m_{\pi}/m_{\rho} \sim 0.8 and lattice spacing a \sim 0.12 fm is
determined. A two-exponent ansatz is successfully applied to describe the heavy
quark potential in the confinement phase.


title:
Finite temperature phase transition in lattice QCD with N_f=2
  nonperturbatively improved Wilson fermions at N_t=8

abstract:
  The finite temperature lattice QCD with N_f=2 nonperturbatively improved
Wilson fermions is studied on 16^3 8 lattice. Using abelian projection after
fixing to MA gauge we determine the transition temperature for m_{\pi}/m_{\rho}
\sim 0.8.


title: Dynamical generation of a gauge symmetry in the Double-Exchange model

abstract:
  It is shown that a bosonic formulation of the double-exchange model, one of
the classical models for magnetism, generates dynamically a gauge-invariant
phase in a finite region of the phase diagram. We use analytical methods, Monte
Carlo simulations and Finite-Size Scaling analysis. We study the transition
line between that region and the paramagnetic phase. The numerical results show
that this transition line belongs to the Universality Class of the
Antiferromagnetic RP(2) model. The fact that one can define a Universality
Class for the Antiferromagnetic RP(2) model, different from the one of the O(N)
models, is puzzling and somehow contradicts naive expectations about
Universality.


title:
Quark Mass Dependence of Nucleon Properties and Extrapolation from
  Lattice QCD

abstract:
  We summarize developments concerning the quark mass dependence of nucleon
magnetic moments and the axial-vector coupling constant g_A. The aim is to
explore the feasibility of chiral effective field theory methods for the
extrapolation of lattice QCD results, from the relatively large quark masses
that can be handled in such computations down to the physically relevant range.


title: The electrical conductivity and soft photon emissivity of the QCD plasma

abstract:
  The electrical conductivity in the hot phase of the QCD plasma is extracted
from a quenched lattice measurement of the Euclidean time vector correlator for
1.5 < T/T_c < 3. The spectral density in the vicinity of the origin is examined
using a method specially adapted to this region, and a peak at small energies
is seen. The continuum limit of the electrical conductivity, and the closely
related soft photon emissivity of the QCD plasma, are then extracted from a fit
to the Fourier transform of the temporal vector correlator.


title: The Gribov problem and its solution from a toy model point of view

abstract:
  The standard Faddeev Popov gauge fixing procedure is put on solid grounds by
taking into account a topological factor which corrects for the number of
Gribov copies within the first Gribov horizon. Zwanziger's stochastic approach
to gauge fixed Yang-Mills theory is briefly reviewed. A simple toy model is
presented which illustrates both methods. Within the toy model, I show that a
stochastic drift force can be constructed with which the gauged configurations
are attracted by the fundamental modular region. The toy model shows that an
action which gives rise to the drift force can be found. This makes a ``heat
bath'' simulation possible, which is seen to be superior to the Langevin
approach at the numerical level.


title: Evidence for Dyonic Structure of SU(2) Lattice Gauge Fields Below $T_c$

abstract:
  We report the observation of calorons with nontrivial holonomy and fractional
topological charge objects in cooled lattice samples derived from SU(2)
equilibrium ensembles at $T<T_c$.


title: In Medium Hadron Properties

abstract:
  We discuss modifications of hadron properties in the heat bath extracted from
Euclidian correlation functions and spectral functions r econstructed with the
Maximum Entropy Method. To investigate the cut-off dependencies we perform
simulation on various lattice sizes and present the result of an analytic
calculation of the mesonic spectral functions in the infinite temperature
limit.


title:
Confinement, deconfinement and the photon propagator in 3D cQED on the
  lattice

abstract:
  We report on a lattice study of the gauge boson propagator of 3D compact QED
in Landau gauge at zero and finite temperature. Non-perturbative effects are
reflected by the generation of a mass m and by an anomalous dimension alpha.
These effects can be attributed to monopoles and are absent in the propagator
of the regular part of the gauge field.


title: A hidden symmetry in the Standard Model

abstract:
  We found an additional symmetry hidden in the fermion and Higgs sectors of
the Standard Model. It is connected to the centers of the SU(3) and SU(2)
subgroups of the gauge group. A lattice regularization of the whole Standard
Model is constructed that possesses this symmetry.


title: The Use of the Monte Carlo Hamiltonian

abstract:
  In order to solve quantum field theory in a non-perturbative way, Lagrangian
lattice simulations have been very successful. Here we discuss a recently
proposed alternative Hamiltonian lattice formulation - the Monte Carlo
Hamiltonian. In order to show its working in the case of the scalar
$\Phi^{4}_{1+1}$ model, we have computed thermodynamic functions like free
energy, average energy, entropy and specific heat. We find good agreement
between the results from the Monte Carlo Hamiltonian and standard Lagrangian
lattice computations. However, the Monte Carlo Hamiltonian results show less
fluctuations under variation of temperature. We address properties of the MC
Hamiltonian, like a finite temperature window, and scaling properties. Also we
discuss possible future applications - like quantum chaos in many-body systems,
the non-perturbative computation of wave functions of elementary particles, as
well as scattering amplitudes in high energy physics.


title: Numerical simulation with light Wilson-quarks

abstract:
  The computational cost of numerical simulations of QCD with light dynamical
Wilson-quarks is estimated by determining the autocorrelation of various
quantities. In test runs the expected qualitative behaviour of the pion mass
and coupling at small quark masses is observed.


title: On the renormalization of the Polyakov loop

abstract:
  We discuss a non-perturbative renormalization of n-point Polyakov loop
correlation functions by explicitly introducing a renormalization constant for
the Polyakov loop operator on a lattice deduced from the short distance
properties of 2-point correlators. We calculate this constant for the
SU(3)gauge theory.


title: Renormalized quark-anti-quark free energy

abstract:
  We present results on the renormalized quark-anti-quark free energy in SU(3)
gauge theory at finite temperatures. We discuss results for the singlet, octet
and colour averaged free energies and comment on thermal relations which allow
to extract separately the potential energy and entropy from the free energy.


title:
Critical behaviour and Scaling functions for the three-dimensional O(6)
  spin model with external field

abstract:
  We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3
lattices. From Binder's cumulant at vanishing magnetic field we obtain the
critical coupling J_c=1.42865(5) and verify this value with the \chi^2-method.
The universal value of Binder's cumulant at this point is
g_r(J_c)=-1.94456(10). At the critical coupling we find the critical exponents
\nu=0.818(5), \beta=0.425(2) and \gamma=1.604(6) from a finite size scaling
analysis. We also determine the finite-size-scaling function on the critical
line and the equation of state. Our O(6)-result for the equation of state is
compared to the Ising, O(2) and O(4) results.


title:
Matrix model correlation functions and lattice data for the QCD Dirac
  operator with chemical potential

abstract:
  We apply a complex chiral random matrix model as an effective model to QCD
with a small chemical potential at zero temperature. In our model the
correlation functions of complex eigenvalues can be determined analytically in
two different limits, at weak and strong non-Hermiticity. We compare them to
the distribution of the smallest Dirac operator eigenvalues from quenched QCD
lattice data for small values of the chemical potential, appropriately rescaled
with the volume. This confirms the existence of two different scaling regimes
from lattice data.


title: Scaling behavior of the overlap quark propagator in Landau gauge

abstract:
  The properties of the momentum space quark propagator in Landau gauge are
examined for the overlap quark action in quenched lattice QCD. Numerical
calculations are done on three lattices with different lattice spacings and
similar physical volumes to explore the approach of the quark propagator toward
the continuum limit. We have calculated the nonperturbative momentum-dependent
wave function renormalization function Z(p) and the nonperturbative mass
function M(p) for a variety of bare quark masses and perform an extrapolation
to the chiral limit. We find the behavior of Z(p) and M(p) are in reasonable
agreement between the two finer lattices in the chiral limit, however the data
suggest that an even finer lattice is desirable. The large momentum behavior is
examined to determine the quark condensate.


title:
Critical Slowing-Down in SU(2) Landau-Gauge-Fixing Algorithms at beta =
  infinity

abstract:
  We evaluate numerically and analytically the dynamic critical exponent $z$
for five gauge-fixing algorithms in SU(2) lattice Landau-gauge theory by
considering the case $\beta = \infty$. Numerical data are obtained in two,
three and four dimensions. Results are in agreement with those obtained
previously at finite $\beta$ in two dimensions. The theoretical analysis, valid
for any dimension $d$, helps us clarify the tuning of these algorithms. We also
study generalizations of the overrelaxation algorithm and of the stochastic
overrelaxation algorithm and verify that we cannot have a dynamic critical
exponent $z$ smaller than 1 with these local algorithms. Finally, the analytic
approach is applied to the so-called $\lambda$-gauges, again at $\beta =
\infty$, and verified numerically for the two-dimensional case.


title:
Coupling of the light vector meson to the vector and to the tensor
  current

abstract:
  We present results for the coupling of the light vector mesons to the tensor
current, relative to the standard vector meson decay constants. From an
O(a)-improved lattice study, performed at three values of the lattice spacing
in the quenched approximation, our final values (in the continuum limit), in
the MS-scheme at 2 GeV, are: (f^T/f)_rho =0.72(2)(+2/-0), (f^T/f)_K* =0.74(2),
(f^T/f)_phi =0.76(1).


title: Chiral extrapolations of nucleon properties from lattice QCD

abstract:
  We report on recent work about the study of quark mass dependence of nucleon
magnetic moments and axial-vector coupling constant. We examine the feasibility
of chiral effective field theory methods for the extrapolation of lattice QCD
data obtained at relative large pion masses down to the physical values.


title: A lattice study of $\Lambda_b$ semileptonic decay

abstract:
  We present results from a lattice study of the semileptonic decay $\Lambda_b
\to \Lambda_c l \nu_l $. We use $O(a^2, \alpha_s a^2)$ improved quenched
lattices of the MILC collaboration, with lattice spacing $\sim 0.13$ fm. For
the valence quarks, the tadpole-improved clover action is used, with the
Fermilab method employed for the heavy quarks. Form factors are extracted from
the vector as well as the axial-vector part of the current.


title: The Confinement Problem in Lattice Gauge Theory

abstract:
  I review investigations of the quark confinement mechanism that have been
carried out in the framework of SU(N) lattice gauge theory. The special role of
Z(N) center symmetry is emphasized.


title:
Lattice calculation of $1^{-+}$ hybrid mesons with improved
  Kogut-Susskind fermions

abstract:
  We report on a lattice determination of the mass of the exotic $1^{-+}$
hybrid meson using an improved Kogut-Susskind action. Results from both
quenched and dynamical quark simulations are presented. We also compare with
earlier results using Wilson quarks at heavier quark masses. The results on
lattices with three flavors of dynamical quarks show effects of sea quarks on
the hybrid propagators which probably result from coupling to two meson states.
We extrapolate the quenched results to the physical light quark mass to allow
comparison with experimental candidates for the $1^{-+}$ hybrid meson. The
lattice result remains somewhat heavier than the experimental result, although
it may be consistent with the $\pi_1(1600)$.


title: Supersymetry on the Noncommutative Lattice

abstract:
  Built upon the proposal of Kaplan et.al. [hep-lat/0206109], we construct
noncommutative lattice gauge theory with manifest supersymmetry. We show that
such theory is naturally implementable via orbifold conditions generalizing
those used by Kaplan {\sl et.al.} We present the prescription in detail and
illustrate it for noncommutative gauge theories latticized partially in two
dimensions. We point out a deformation freedom in the defining theory by a
complex-parameter, reminiscent of discrete torsion in string theory. We show
that, in the continuum limit, the supersymmetry is enhanced only at a
particular value of the deformation parameter, determined solely by the size of
the noncommutativity.


title: Lattice chiral symmetry, CP-violation and Majorana fermions

abstract:
  A brief summary of lattice fermions defined by the general Ginsparg-Wilson
algebra is first given. It is then shown that those general class of fermion
operators have a conflict with CP invariance in chiral gauge theory and with
the definition of Majorana fermions in the presence of chiral-symmetric Yukawa
couplings. The same conclusion holds for the domain-wall fermion also.


title: Lattice QCD at non-vanishing density: phase diagram, equation of state

abstract:
  We propose a method to study lattice QCD at non-vanishing temperature (T) and
chemical potential (\mu). We use n_f=2+1 dynamical staggered quarks with
semi-realistic masses on L_t=4 lattices. The critical endpoint (E) of QCD on
the Re(\mu)-T plane is located. We calculate the pressure (p), the energy
density (\epsilon) and the baryon density (n_B) of QCD at non-vanishing T and
\mu.


title: Lattice Supersymmetry and Topological Field Theory

abstract:
  It is known that certain theories with extended supersymmetry can be
discretized in such a way as to preserve an exact fermionic symmetry. In the
simplest model of this kind, we show that this residual supersymmetric
invariance is actually a BRST symmetry associated with gauge fixing an
underlying local shift symmetry. Furthermore, the starting lattice action is
then seen to be entirely a gauge fixing term. The corresponding continuum
theory is known to be a topological field theory. We look, in detail, at one
example - supersymmetric quantum mechanics which possesses two such BRST
symmetries. In this case, we show that the lattice theory can be obtained by
blocking out of the continuum in a carefully chosen background metric. Such a
procedure will not change the Ward identities corresponding to the BRST
symmetries since they correspond to topological observables. Thus, at the
quantum level, the continuum BRST symmetry is preserved in the lattice theory.
Similar conclusions are reached for the two-dimensional complex Wess-Zumino
model and imply that all the supersymmetric Ward identities are satisfied {\it
exactly} on the lattice. Numerical results supporting these conclusions are
presented.


title: Renormalization group improved action on anisotropic lattices

abstract:
  We study a block spin transformation in the SU(3) lattice gauge theory on
anisotropic lattices to obtain Iwasaki's renormalization group improved action
for anisotropic cases. For the class of actions with plaquette and $1\times2$
rectangular terms, we determine the improvement parameters as functions of the
anisotropy $\xi= a_s/a_t$. We find that the program of improvement works well
also on anisotropic lattices. From a study of an indicator which estimates the
distance to the renormalized trajectory, we show that, for the range of the
anisotropy $\xi \approx 1$--4, the coupling parameters previously determined
for isotropic lattices improve the theory considerably.


title: Exotics

abstract:
  We review lattice QCD results for glueballs (including a discussion of mixing
with scalar mesons), hybrid mesons and other exotic states (such as $B_s B_s$
molecules).


title:
Abelian dominance and gluon propagators in the Maximally Abelian gauge
  of SU(2) lattice gauge theory

abstract:
  Propagators of the diagonal and the off-diagonal gluons are studied
numerically in the Maximal Abelian gauge of SU(2) lattice gauge theory. It is
found that in the infrared region the propagator of the diagonal gluon is
strongly enhanced in comparison with the off--diagonal one. The enhancement
factor is about 50 at our smallest momentum 325 MeV. We have also applied
various fits to the propagator formfactors.


title: CP symmetry and lattice chiral gauge theories

abstract:
  The CP symmetry is a fundamental discrete symmetry in chiral gauge theory.
Therefore this symmetry is expected to be kept also on the lattice. However, it
has been pointed out by Hasenfratz that the chiral fermion action in Luscher's
formulation of lattice chiral gauge theory is not invariant under CP
transformation. In this thesis, we first review the method of constructing
chiral gauge theory on the lattice. Then we generalize the analysis of
Hasenfratz and show that CP symmetry is not manifestly implemented for the
local and doubler-free Ginsparg-Wilson operator under rather general
assumptions for chiral projection operators. We next calculate the fermion
generating functional and precisely identify where the effects of this CP
breaking appear in this formulation. The basics of lattice gauge theory are
briefly summarized in Appendix.A.


title: The spectrum of screening masses near T_c: predictions from universality

abstract:
  We discuss the spectrum of screening masses in a pure gauge theory near the
deconfinement temperature from the point of view of the dimensionally reduced
model describing the spontaneous breaking of the center symmetry. Universality
arguments can be used to predict the values of the mass ratios in the scaling
region of the deconfined phase when the transition is of second order. One such
prediction is that the scalar sector of the screening spectrum in SU(2) pure
gauge theory contains a bound state of the fundamental excitation,
corresponding through universality to the bound state found in the 3D Ising
model and phi^4 theory in the broken symmetry phase. A Monte Carlo evaluation
of the screening masses in the gauge theory confirms the validity of the
prediction. We briefly discuss the possibility of using similar arguments for
first order deconfinement transitions, and in particular for the physically
relevant case of SU(3).


title: QCD at Fixed Topology

abstract:
  Since present Monte Carlo algorithms for lattice QCD may become trapped in a
fixed topological charge sector, it is important to understand the effect of
calculating at fixed topology. In this work, we show that although the
restriction to a fixed topological sector becomes irrelevant in the infinite
volume limit, it gives rise to characteristic finite size effects due to
contributions from all $\theta$-vacua. We calculate these effects and show how
to extract physical results from numerical data obtained at fixed topology.