title:
Thermal effects on quark-gluon mixed condensate g<\bar{q} \sigma G q>
  from lattice QCD

abstract:
  We present the first study of the thermal effects on 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
the lattices at \beta=6.0, 6.1, 6.2 in high statistics, we calculate the mixed
condensate as well as the quark condensate in the chiral limit for the
temperature 0MeV <= T <= 500MeV. Except for the sharp decrease of both the
condensates around T_c \simeq 280MeV, the thermal effects are found to be weak
below T_c. We also find that the ratio m_0^2 = g<\bar{q} \sigma G q>/
<\bar{q}q> is almost independent of the temperature even in the very vicinity
of T_c. This result indicates nontrivial similarity in the chiral behaviors of
the two different condensates.


title:
Critical point of QCD at finite T and \mu, lattice results for physical
  quark masses

abstract:
  A critical point (E) is expected in QCD on the temperature (T) versus
baryonic chemical potential (\mu) plane. Using a recently proposed lattice
method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of
physical masses on L_t=4 lattices. Our result for the critical point is T_E=162
\pm 2 MeV and \mu_E= 360 \pm 40 MeV. For the critical temperature at \mu=0 we
obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and
S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark
masses (m_{u,d}) by a factor of three down to their physical values.
Furthermore, in order to approach the thermodynamical limit we increase our
largest volume by a factor of three. As expected, decreasing m_{u,d} decreased
\mu_E. Note, that the continuum extrapolation is still missing


title:
Supersymmetry breaking in two dimensions: the lattice N=1 Wess-Zumino
  model

abstract:
  We study dynamical supersymmetry breaking by non perturbative lattice
techniques in a class of two-dimensional N=1 Wess-Zumino models. We work in the
Hamiltonian formalism and analyze the phase diagram by analytical
strong-coupling expansions and explicit numerical simulations with Green
Function Monte Carlo methods.


title:
Topological lumps and Dirac zero modes in SU(3) lattice gauge theory on
  the torus

abstract:
  We compute eigenmodes of the lattice Dirac operator for quenched SU(3) gauge
configurations on the 4-torus with topological charge 1. We find a strong
dependence of the zero modes on the boundary conditions which we impose for the
Dirac operator. The lumps seen by the eigenmodes often change their position
when changing the boundary conditions, while the local chirality of the lumps
remains the same. Our results show that the zero mode of a charge 1
configuration can couple to more than one object. We address the question
whether these objects could be fractionally charged lumps.


title: An alternate smearing method for Wilson loops in lattice QCD

abstract:
  A gauge field link smearing method developed for calculations with staggered
fermions, namely the use of unitarized fat7 links, is applied to mesonic and
baryonic Wilson loop calculations. This method is found to be very effective
for reducing statistical fluctuations for large Wilson loops. Examination of
chromo-electric field distributions shows that self-interactions of the static
sources are reduced when unitarized fat7 smearing is used but long-distance
inter-quark effects are unchanged.


title:
Recombination of dyons into calorons in SU(2) lattice fields at low
  temperatures

abstract:
  By cooling of equilibrium lattice fields at finite temperature in SU(2) gauge
theory it has been shown that topological objects (calorons) observed on the
lattice in the confined phase possess a dyonic substructure which becomes
visible under certain circumstances. Here we show that, with decreasing
temperature of the equilibrium ensemble, the distribution in the caloron
parameter space is modified such that the calorons appear non-dissociated into
constituent dyons. Still the calorons have nontrivial holonomy which is
demonstrated by the Polyakov line behaviour for these configurations. At
vanishing temperature (on a symmetric lattice) topological lumps obtained by
cooling possess rotational symmetry in 4D and a characteristic double peak
structure of Polyakov lines (defined with respect to temporal and spatial
directions) with non-trivial asymptotics.


title: Lattice formulation of chiral gauge theories

abstract:
  We present a general formulation of chiral gauge theories, which admits Dirac
operators with more general spectra, reveals considerably more possibilities
for the structure of the chiral projections, and nevertheless allows
appropriate realizations. In our analyses we use two forms of the correlation
functions which both also apply in the presence of zero modes and for any value
of the index. To account properly for the conditions on the bases the concept
of equivalence classes of pairs of them is introduced. The behaviors under
gauge transformations and under CP transformations are unambiguously derived.


title:
An estimate of the flavour singlet contributions to the hyperfine
  splitting in charmonium

abstract:
  We explore the splitting between flavour singlet and non-singlet mesons in
charmonium. This has implications for the hyperfine splitting in charmonium.


title: Monopoles in Real Time for Classical U(1) Gauge Field Theory

abstract:
  U(1) gauge fields are decomposed into a monopole and photon part across the
phase transition from the confinement to the Coulomb phase. We analyze the
leading Lyapunov exponents of such gauge field configurations on the lattice
which are initialized by quantum Monte Carlo simulations. We observe that the
monopole field carries the same Lyapunov exponent as the original U(1) field.
As a long awaited result, we show that monopoles are created and annihilated in
pairs as a function of real time in excess to a fixed average monopole number.


title: Full Spectrum of Lyapunov Exponents in Gauge Field Theory

abstract:
  We analyze the Lyapunov exponents of U(1) gauge fields across the phase
transition from the confinement to the Coulomb phase on the lattice which are
initialized by quantum Monte Carlo simulations. We observe all features of a
strange attractor with a tendency to regularity towards the continuum limit.
Results are also displayed for the full spectrum of Lyapunov exponents of the
SU(2) gauge system.


title: Quantum chaos in supersymmetric QCD at finite density

abstract:
  We investigate the distribution of the spacings of adjacent eigenvalues of
the lattice Dirac operator. At zero chemical potential $\mu$, the
nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of
random matrix theory both in the confinement and in the deconfinement phase.
This is indicative of quantum chaos. At nonzero chemical potential, the
eigenvalues of the Dirac operator become complex and we discuss how $P(s)$ can
be defined in the complex plane. Numerical results from an SU(2) simulation
with staggered fermions in fundamental and adjoint representations are compared
with predictions from non-hermitian random matrix theory, and agreement with
the Ginibre ensemble is found for $\mu\approx 0.5$.


title: Hybrid Meson Spectrum from the FLIC action

abstract:
  The spectral properties of hybrid meson interpolating fields are
investigated. The quantum numbers of the meson are carried by smeared-source
fermion operators and highly-improved chromo-electric and -magnetic field
operators composed with APE-smeared links. The effective masses of standard and
hybrid operators indicate that the ground state meson is effectively isolated
using both standard and hybrid interpolating fields. Focus is placed on
interpolating fields in which the large spinor components of the quark and
antiquark fields are merged. In particular, the effective mass of the exotic
$1^{-+}$ meson is reported. Further, we report some values for excited mesonic
states using a variational process.


title:
Properties of P-vortex and monopole clusters in lattice SU(2) gauge
  theory

abstract:
  We study the action and geometry of P-vortices, discriminating between the
percolating and finite clusters. We also discuss the interrelation of the
monopoles and P-vortices. To define P-vortices we use both the direct maximal
center projection and indirect maximal center projection. We find, in
particular, that the action density of the P-vortices in short clusters is
substantially higher than in the percolating cluster. The surface of the
percolating cluster appears random at short distances, with action density
depending on the shape.


title: A novel probe of the vacuum of the lattice gluodynamics

abstract:
  We introduce a notion of minimal number of negative links on the lattice for
a given original configuration of SU(2) fields. Negative links correspond to a
large potential, not necessarily large action. The idea is that the minimal
number of negative links is a gauge invariant notion. To check this hypothesis
we measure correlator of two negative links, averaged over all the directions,
as function of the distance between the links. The inverse correlation length
coincides within the error bars with the lightest glueball mass.


title:
Dynamic critical behavior of the Swendsen--Wang Algorithm for the
  three-dimensional Ising model

abstract:
  We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model
at the critical point. For the dynamic critical exponents associated to the
integrated autocorrelation times of the "energy-like" observables, we find
z_{int,N} = z_{int,E} = z_{int,E'} = 0.459 +- 0.005 +- 0.025, where the first
error bar represents statistical error (68% confidence interval) and the second
error bar represents possible systematic error due to corrections to scaling
(68% subjective confidence interval). For the "susceptibility-like"
observables, we find z_{int,M^2} = z_{int,S_2} = 0.443 +- 0.005 +- 0.030. For
the dynamic critical exponent associated to the exponential autocorrelation
time, we find z_{exp} \approx 0.481. Our data are consistent with the
Coddington-Baillie conjecture z_{SW} = \beta/\nu \approx 0.5183, especially if
it is interpreted as referring to z_{exp}.

categories: hep-lat cond-mat.stat-mech math-ph math.MP


title: On the stability of Dirac sheet configurations

abstract:
  Using cooling for SU(2) lattice configurations, purely Abelian constant
magnetic field configurations were left over after the annihilation of
constituents that formed metastable Q=0 configurations. These so-called Dirac
sheet configurations were found to be stable if emerging from the confined
phase, close to the deconfinement phase transition, provided their Polyakov
loop was sufficiently non-trivial. Here we show how this is related to the
notion of marginal stability of the appropriate constant magnetic field
configurations. We find a perfect agreement between the analytic prediction for
the dependence of stability on the value of the Polyakov loop (the holonomy) in
a finite volume and the numerical results studied on a finite lattice in the
context of the Dirac sheet configurations.


title: Duality and scaling in 3-dimensional scalar electrodynamics

abstract:
  Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry,
is believed to be dual to a scalar theory with a global U(1) symmetry, near the
phase transition point. The conjectured duality leads to definite predictions
for the scaling exponents of the gauge theory transition in the type II region,
and allows thus to be scrutinized empirically. We review these predictions, and
carry out numerical lattice Monte Carlo measurements to test them: a number of
exponents, characterising the two phases as well as the transition point, are
found to agree with expectations, supporting the conjecture. We explain why
some others, like the exponent characterising the photon correlation length,
appear to disagree with expectations, unless very large system sizes and the
extreme vicinity of the transition point are considered. Finally, we remark
that in the type I region the duality implies an interesting quantitative
relationship between a magnetic flux tube and a 2-dimensional non-topological
soliton.


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

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


title: B to rho ell nu form factors in lattice QCD

abstract:
  We present results from quenched lattice QCD for the form factors for the
decay $B\to\rho l\nu$. The calculations are performed using a nonperturbatively
improved action and operators at two values of the lattice spacing. The bottom
quark mass is reached by extrapolation from simulations performed with heavy
quark masses around the charm mass. Our primary result is for the partially
integrated decay rate $\Gamma_{PI}$ over the range $12.7\gev^2 < q^2 <
18.2\gev^2$:
  \Gamma_PI = (4.9^{+12}_{-10}{+0}_{-14}) X 10^12 s^-1


title: From the Abelian projected flux tube to the dual Abelian Higgs model

abstract:
  A recent detailed study of the Q-anti-Q flux tube and its DAHM analysis is
reported.


title:
I=2 $\pi\pi$ Scattering Phase Shift with two Flavors of $O(a)$ Improved
  Dynamical Quarks

abstract:
  We present a lattice QCD calculation of phase shift including the chiral and
continuum extrapolations in two-flavor QCD. The calculation is carried out for
I=2 S-wave $\pi\pi$ scattering. The phase shift is evaluated for two momentum
systems, the center of mass and laboratory systems, by using the finite volume
method proposed by L\"uscher in the center of mass system and its extension to
general systems by Rummukainen and Gottlieb. The measurements are made at three
different bare couplings $\beta = 1.80$, 1.95 and 2.10 using a renormalization
group improved gauge and a tadpole improved clover fermion action, and
employing a set of configurations generated for hadron spectroscopy in our
previous work. The illustrative values we obtain for the phase shift in the
continuum limit are $\delta$(deg.) $= - 3.50(64)$, $ - 9.5(30)$ and $ -
16.9(64)$ for $\sqrt{s}({\rm GeV})$ $=0.4$, $ 0.6$ and $ 0.8$, which are
consistent with experiment.


title:
Lattice QCD calculation of the proton decay matrix element in the
  continuum limit

abstract:
  We present a quenched lattice QCD calculation of the \alpha and \beta
parameters of the proton decay matrix element. The simulation is carried out
using the Wilson quark action at three values of the lattice spacing in the
range a\approx 0.1-0.064 fm to study the scaling violation effect. We find only
mild scaling violation when the lattice scale is determined by the nucleon
mass. We obtain in the continuum limit,
|\alpha(NDR,2GeV)|=0.0090(09)(^{+5}_{-19})GeV^3 and
|\beta(NDR,2GeV)|=0.0096(09)(^{+6}_{-20})GeV^3 with \alpha and \beta in a
relatively opposite sign, where the first error is statistical and the second
is due to the uncertainty in the determination of the physical scale.


title: Topological susceptibility in full QCD with Ginsparg-Wilson fermions

abstract:
  We show that, if the formula for the topological charge density operator
suggested by fermions obeying the Ginsparg-Wilson relation is employed, it is
possible to give a precise and unambiguous definition of the topological
susceptibility in full QCD, chi_tL, for finite quark masses on the lattice. The
lattice expression of chi_tL looks like the formal continuum one, in the sense
that no power divergent subtractions are needed for its proper definition. As a
consequence, the small mass behaviour of chi_tL leads directly to a
multiplicative renormalizable definition of the chiral condensate that does not
require any power divergent subtraction.


title: Lattice representation of vector and chiral gauge theories

abstract:
  A lattice derivative is defined as a discrete Fourier transform of momentum
on a finite lattice. Species doublers are removed with anti-periodic boundary
conditions. U(1) chiral transformation is modified to reproduce chiral anomaly.
Chiral gauge theories can be constructed on the lattice using a single Weyl
fermion as a building block.


title: Hadronic Electromagnetic Properties at Finite Lattice Spacing

abstract:
  Electromagnetic properties of the octet mesons as well as the octet and
decuplet baryons are augmented in quenched and partially quenched chiral
perturbation theory to include O(a) corrections due to lattice discretization.
We present the results for the SU(3) flavor group in the isospin limit as well
as the results for SU(2) flavor with non-degenerate quarks. These corrections
will be useful for extrapolation of lattice calculations using Wilson valence
and sea quarks, as well as calculations using Wilson sea quarks and
Ginsparg-Wilson valence quarks.


title:
Light hadrons with improved staggered quarks: approaching the continuum
  limit

abstract:
  We have extended our program of QCD simulations with an improved
Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09
fm. Also, the simulations with a approximately 0.12 fm have been extended to
smaller quark masses. In this paper we describe the new simulations and
computations of the static quark potential and light hadron spectrum. These
results give information about the remaining dependences on the lattice
spacing. We examine the dependence of computed quantities on the spatial size
of the lattice, on the numerical precision in the computations, and on the step
size used in the numerical integrations. We examine the effects of
autocorrelations in "simulation time" on the potential and spectrum. We see
effects of decays, or coupling to two-meson states, in the 0++, 1+, and 0-
meson propagators, and we make a preliminary mass computation for a radially
excited 0- meson.


title:
Non-Commutativity of the Zero Chemical Potential Limit and the
  Thermodynamic Limit in Finite Density Systems

abstract:
  Monte Carlo simulations of finite density systems are often plagued by the
complex action problem. We point out that there exists certain
non-commutativity in the zero chemical potential limit and the thermodynamic
limit when one tries to study such systems by reweighting techniques. This is
demonstrated by explicit calculations in a Random Matrix Theory, which is
thought to be a simple qualitative model for finite density QCD. The
factorization method allows us to understand how the non-commutativity, which
appears at the intermediate steps, cancels in the end results for physical
observables.


title: Unquenched Gluon Propagator in Landau Gauge

abstract:
  Using lattice quantum chromodynamics (QCD) we perform an unquenched
calculation of the gluon propagator in Landau gauge. We use configurations
generated with the AsqTad quark action by the MILC collaboration for the
dynamical quarks and compare the gluon propagator of quenched QCD (i.e., the
pure Yang-Mills gluon propagator) with that of 2+1 flavor QCD. The effects of
the dynamical quarks are clearly visible and lead to a significant reduction of
the nonperturbative infrared enhancement relative to the quenched case.


title:
Perturbation theory vs. simulation for tadpole improvement factors in
  pure gauge theories

abstract:
  We calculate the mean link in Landau gauge for Wilson and improved SU(3)
anisotropic gauge actions, using two loop perturbation theory and Monte Carlo
simulation employing an accelerated Langevin algorithm. Twisted boundary
conditions are employed, with a twist in all four lattice directions
considerably improving the (Fourier accelerated) convergence to an improved
lattice Landau gauge. Two loop perturbation theory is seen to predict the mean
link extremely well even into the region of commonly simulated gauge couplings
and so can be used remove the need for numerical tuning of self-consistent
tadpole improvement factors. A three loop perturbative coefficient is inferred
from the simulations and is found to be small. We show that finite size effects
are small and argue likewise for (lattice) Gribov copies and double Dirac
sheets.


title: Wess-Zumino model with exact supersymmetry on the lattice

abstract:
  A lattice formulation of the four dimensional Wess-Zumino model that uses
Ginsparg-Wilson fermions and keeps exact supersymmetry is presented. The
supersymmetry transformation that leaves invariant the action at finite lattice
spacing is determined by performing an iterative procedure in the coupling
constant. The closure of the algebra, generated by this transformation is also
showed.


title:
Computational methods for the fermion determinant and the link between
  overlap and domain wall fermions

abstract:
  This paper reviews the most popular methods which are used in lattice QCD to
compute the determinant of the lattice Dirac operator: Gaussian integral
representation and noisy methods. Both of them lead naturally to matrix
function problems. We review the most recent development in Krylov subspace
evaluation of matrix functions. The second part of the paper reviews the formal
relationship and algebraic structure of domain wall and overlap fermions. We
review the multigrid algorithm to invert the overlap operator. It is described
here as a preconditioned Jacobi iteration where the preconditioner is the Schur
complement of a certain block of the truncated overlap matrix.


title: Dynamical fat link fermions

abstract:
  The use of APE smearing or other blocking techniques in fermion actions can
provide many advantages. There are many variants of these fat link actions in
lattice QCD currently, such as FLIC fermions. Frequently, fat link actions make
use of the APE blocking technique in combination with a projection of the
blocked links back into the special unitary group. This reunitarisation is
often performed using an iterative maximisation of a gauge invariant measure.
This technique is not differentiable with respect to the gauge field and thus
prevents the use of standard Hybrid Monte Carlo simulation algorithms. The use
of an alternative projection technique circumvents this difficulty and allows
the simulation of dynamical fat link fermions with standard HMC and its
variants.


title: Approximation Theory for Matrices

abstract:
  We review the theory of optimal polynomial and rational Chebyshev
approximations, and Zolotarev's formula for the sign function over the range
(\epsilon \leq |z| \leq1). We explain how rational approximations can be
applied to large sparse matrices efficiently by making use of partial fraction
expansions and multi-shift Krylov space solvers.


title: Fast Evaluation of Zolotarev Coefficients

abstract:
  We review the theory of elliptic functions leading to Zolotarev's formula for
the sign function over the range (\epsilon \leq|x| \leq1). We show how Gauss'
arithmetico-geometric mean allows us to evaluate elliptic functions cheaply,
and thus to compute Zolotarev coefficients ``on the fly'' as a function of
(\epsilon). This in turn allows us to calculate the matrix functions (\sgn H),
(\sqrt H), and (1/\sqrt H) both quickly and accurately for any Hermitian matrix
(H) whose spectrum lies in the specified range.


title: Critical slowing down of topological modes

abstract:
  We investigate the critical slowing down of the topological modes using local
updating algorithms in lattice 2-d CP^(N-1) models. We show that the
topological modes experience a critical slowing down that is much more severe
than the one of the quasi-Gaussian modes relevant to the magnetic
susceptibility, which is characterized by $\tau_{\rm mag} \sim \xi^z$ with
$z\approx 2$. We argue that this may be a general feature of Monte Carlo
simulations of lattice theories with non-trivial topological properties, such
as QCD, as also suggested by recent Monte Carlo simulations of 4-d SU(N)
lattice gauge theories.


title: Infrared and ultraviolet properties of the Landau gauge quark propagator

abstract:
  We present a current summary of a program to study the quark propagator using
lattice QCD. We use the Overlap and ``Asqtad'' quark actions on a number of
lattice ensembles to assess systematic errors. We comment on the place of this
work amongst studies of QCD Green's functions in other formulations. A
preliminary calculation of the running quark mass is presented.


title: The overlap Dirac operator as a continued fraction

abstract:
  We use a continued fraction expansion of the sign-function in order to obtain
a five dimensional formulation of the overlap lattice Dirac operator. Within
this formulation the inverse of the overlap operator can be calculated by a
single Krylov space method and nested conjugate gradient procedures are
avoided. We point out that the five dimensional linear system can be made well
conditioned using equivalence transformations on the continued fractions.


title: Short distance behaviour of the effective string

abstract:
  We study the Polyakov loop correlator in the (2+1) dimensional Z_2 gauge
model. An algorithm that we have presented recently, allows us to reach high
precision results for a large range of distances and temperatures, giving us
the opportunity to test predictions of the effective Nambu-Goto string model.
Here we focus on the regime of low temperatures and small distances. In
contrast to the high temperature, large distance regime, we find that our
numerical results are not well described by the two loop-prediction of the
Nambu-Goto model. In addition we compare our data with those for the SU(2) and
SU(3) gauge models in (2+1) dimensions obtained by other authors. We generalize
the result of L\"uscher and Weisz for a boundary term in the interquark
potential to the finite temperature case.


title: Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD

abstract:
  We demonstrate how to make rigorous predictions for electroweak matrix
elements in nuclear systems directly from QCD. More precisely, we show how to
determine the short-distance contributions to low-momentum transfer electroweak
matrix elements in the two-nucleon sector from lattice QCD. In potential model
descriptions of multi-nucleon systems, this is equivalent to uniquely
determining the meson-exchange currents, while in the context of nuclear
effective field theory, this translates into determining the coefficients of
local, gauge-invariant, multi-nucleon-electroweak current operators. The
energies of the lowest-lying states of two nucleons on a finite volume lattice
with periodic boundary conditions in the presence of a background magnetic
field are sufficient to determine the local four-nucleon operators that
contribute to the deuteron magnetic moment and to the threshold cross-section
of n + p -> d + gamma. Similarly, the energy-levels of two nucleons immersed in
a background isovector axial weak field can be used to determine the
coefficient of the leading local four-nucleon operator contributing to the
neutral- and charged-current break-up of the deuteron. This is required for the
extraction of solar neutrino fluxes at SNO and future neutrino experiments.


title: Effective Field Theories and Quantum Chromodynamics on the Lattice

abstract:
  We give a selection of results on spectrum and decay constants of light and
heavy-light hadrons. Effective field theories relevant for their lattice
calculation, namely non-relativistic QCD (NRQCD) for heavy quarks on the
lattice and Chiral Perturbation Theory for light quarks, are briefly discussed.


title: Improved Wilson QCD simulations with light quark masses

abstract:
  We present results from simulations using 2 flavours of O(a)-improved Wilson
quarks whose masses are about 1/3 of the physical strange quark mass. We
present new data on the mass of the singlet pseudoscalar meson and evidence of
the onset of chiral logarithms in the pion decay constant. The previously
observed suppression of the topological susceptibility at lighter quark masses
is confirmed. We report on the performance of the hybrid Monte Carlo algorithm
at light quark masses.


title:
Density matrix renormalization group in a two-dimensional
  $\lambda\phi^4$ Hamiltonian lattice model

abstract:
  Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional
$\lambda\phi^4$ model. Spontaneous breakdown of discrete $Z_2$ symmetry is
studied numerically using vacuum wavefunctions. We obtain the critical coupling
$(\lambda/\mu^2)_{\rm c}=59.89\pm 0.01$ and the critical exponent
$\beta=0.1264\pm 0.0073$, which are consistent with the Monte Carlo and the
exact results, respectively. The results are based on extrapolation to the
continuum limit with lattice sizes $L=250,500$, and 1000. We show that the
lattice size L=500 is sufficiently close to the the limit $L\to\infty$.


title: Finite size effects of a pion matrix element

abstract:
  We investigate finite size effects of the pion matrix element of the
non-singlet, twist-2 operator corresponding to the average momentum of
non-singlet quark densities. Using the quenched approximation, they come out to
be surprisingly large when compared to the finite size effects of the pion
mass. As a consequence, simulations of corresponding nucleon matrix elements
could be affected by finite size effects even stronger which could lead to
serious systematic uncertainties in their evaluation.


title:
Systematic errors due to linear congruential random-number generators
  with the Swendsen-Wang algorithm: A warning

abstract:
  We show that linear congruential pseudo-random-number generators can cause
systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm,
if the lattice size is a multiple of a very large power of 2 and one random
number is used per bond. These systematic errors arise from correlations within
a single bond-update half-sweep. The errors can be eliminated (or at least
radically reduced) by updating the bonds in a random order or in an aperiodic
manner. It also helps to use a generator of large modulus (e.g. 60 or more
bits).


title: Signals of confinement in Green functions of SU(2) Yang-Mills theory

abstract:
  The vortex picture of confinement is employed to explore the signals of
confinement in Yang-Mills Green functions. By using SU(2) lattice gauge theory,
it has been well established that the removal of the center vortices from the
lattice configurations results in the loss of confinement. The running coupling
constant, the gluon and the ghost form factors are studied in Landau gauge for
both cases, the full and the vortex removed theory. In the latter case, a
strong suppression of the running coupling constant and the gluon form factor
at low momenta is observed. At the same time, the singularity of the ghost form
factor at vanishing momentum disappears. This observation establishes an
intimate correlation between the ghost singularity and confinement. The result
also shows that a removal of the vortices generates a theory for which
Zwanziger's horizon condition for confinement is no longer satisfied.


title: Heavy meson chiral perturbation theory in finite volume

abstract:
  We study finite volume effects in heavy quark systems in the framework of
heavy meson chiral perturbation theory for full, quenched, and partially
quenched QCD. A novel feature of this investigation is the role played by the
scales Delta and delta_s, where Delta is the mass difference between the
heavy-light vector and pseudoscalar mesons of the same quark content, and
delta_s is the mass difference due to light flavour SU(3) breaking. The primary
conclusion of this work is that finite volume effects arising from the
propagation of Goldstone particles in the effective theory can be altered by
the presence of these scales. Since Delta varies significantly with the heavy
quark mass, these volume effects can be amplified in both heavy and light quark
mass extrapolations (interpolations). As an explicit example, we present
results for B parameters of neutral B meson mixing matrix elements and
heavy-light decay constants to one-loop order in finite volume heavy meson
chiral perturbation theory for full, quenched, and N_f=2+1 partially quenched
QCD. Our calculation shows that for high-precision determinations of the
phenomenologically interesting SU(3) breaking ratios, finite volume effects are
significant in quenched and not negligible in partially quenched QCD, although
they are generally small in full QCD.


title:
On projection (in)dependence of monopole condensate in lattice SU(2)
  gauge theory

abstract:
  We study the temperature dependence of the monopole condensate in different
Abelian projections of the SU(2) lattice gauge theory. Using the
Frohlich-Marchetti monopole creation operator we show numerically that the
monopole condensate depends on the choice of the Abelian projection. Contrary
to the claims in the current literature we observe that in the Abelian Polyakov
gauge and in the field strength gauge the monopole condensate does not vanish
at the critical temperature and thus is not an order parameter.


title:
Quark mass dependence of pseudoscalar masses and decay constants on a
  lattice

abstract:
  Our previous calculations of the sea- and valence-quark mass dependence of
the pseudoscalar meson masses and decay constants is repeated on a 16^3x32
lattice which allows for a better determination of the quantities in question.
  The conclusions are similar as before on the 16^4 lattice [1].
  The two light dynamical quark flavours we simulate have masses in the range
1/4 m_s < m_{u,d} < 2/3 m_s.
  The sea quark mass dependence of f_pi and m_pi^2/m_q is well described by the
next-to-leading order (NLO) Chiral Perturbation Theory (ChPT) formulas and
clearly shows the presence of chiral logarithms.
  The valence quark mass dependence requires the presence of NNLO contributions
in Partially Quenched ChPT (PQChPT) -- in addition to the NLO terms.
  The O(a) lattice artifacts in these quantities turn out to be small.


title: Nucleon Masses and Magnetic Moments in a Finite Volume

abstract:
  We compute finite-size corrections to nucleon masses and magnetic moments in
a periodic, spatial box of size L, both in QCD and in partially-quenched QCD.


title:
News from Lattice QCD on Heavy Quark Potentials and Spectral Functions
  of Heavy Quark States

abstract:
  We discuss recent lattice results on in-medium properties of hadrons and
focus on thermal properties of heavy quark bound states. We will clarify the
relation between heavy quark free energies and potentials used to analyze the
melting of heavy quark bound states. Furthermore, we present calculations of
meson spectral functions which indicate that the charmonium ground states,
J/psi and eta_c, persist in the quark gluon plasma as well defined resonances
with no significant change of their zero temperature masses at least up to T ~
1.5 T_c. We also briefly comment on the current status of lattice calculations
at non-vanishing baryon number density.


title: Charmonium systems after the deconfinement transition

abstract:
  The behavior of charmonia after the deconfinement transition is investigated
on quenched lattices. Analysis of temporal correlators on fine lattices at
temperatures upto 3 T_c show that the J/psi and eta_c survive the deconfinement
transition with little significant changes, and survive as bound states at
least upto 2.25 T_c. The spatially excited chi_c states suffer serious system
modifications, maybe dissolution, already a little above T_c.


title: A novel improved action for SU(3) lattice gauge theory

abstract:
  SU(3) lattice gauge theory is studied by means of an improved action where a
$2 \times 2$ Wilson loop is supplemented to the standard plaquette term. By
contrast to earlier studies using a tree level improvement, the prefactor of
the $2 \times 2$ Wilson term is determined by minimizing the breaking of
rotational symmetry detected from the static quark-antiquark potential. On
coarse lattices, the novel action is superior to the Iwasaki action and
comparable with DBW2 action. The scaling behavior of the novel action is
studied by using the static quark potential and the ratio of the deconfinement
temperature and the string tension.


title: Hybrid Monte Carlo with Fat Link Fermion Actions

abstract:
  The use of APE smearing or other blocking techniques in lattice fermion
actions can provide many advantages. There are many variants of these fat link
actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion
formalism makes use of the APE blocking technique in combination with a
projection of the blocked links back into the special unitary group. This
reunitarisation is often performed using an iterative maximisation of a gauge
invariant measure. This technique is not differentiable with respect to the
gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation
algorithms. The use of an alternative projection technique circumvents this
difficulty and allows the simulation of dynamical fat link fermions with
standard HMC and its variants. The necessary equations of motion for FLIC
fermions are derived, and some initial simulation results are presented. The
technique is more general however, and is straightforwardly applicable to other
smearing techniques or fat link actions.


title: Dimensional reduction in QCD: Lessons from lower dimensions

abstract:
  In this contribution we present the results of a series of investigations of
dimensional reduction, applied to SU(3) gauge theory in 2 + 1 dimensions. We
review earlier results, present a new reduced model with Z(3) symmetry, and
discuss the results of numerical simulations of this model.


title:
What the Gribov copy tells on the confinment and the theory of dynamical
  chiral symmetry breaking

abstract:
  We performed lattice Landau gauge QCD simulation on \beta=6.0, 16^4, 24^4,
32^4 and \beta=6.4, 32^4, 48^4 and 56^4 by adopting the gauge fixing that
minimizes the norm of the gauge field, and measured the running coupling by
using the gluon propagator and the ghost propagator. In view of ambiguity in
the vertex renormalization factor \tilde Z_1 in the lattice, we adjust the
normalization of the running coupling by the perturbative QCD results near the
highest momentum point. It has a maximum \alpha_s(q)~ 2.1(3) at around q=0.5
GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached
-0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is
\alpha_G=0.20 but there is an exceptional Gribov copy with \alpha_G=0.27. The
features of the exceptional Gribov copy are investigated by measuring four
one-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to
each lattice axis. We observe, in general, correlation between absolute value
of the Kugo-Ojima parameter and the degree of reflection positivity violation
in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov
copy has an axis whose gluon propagator manifestly violates reflection
positivity, and the average of the Cartan subalgebra components of the
Kugo-Ojima parameter along this axis is consistent to -1. The running coupling
of the enemble average shows a suppression at 0 momentum, but when the ghost
propagator of the exceptional Gribov copy is adopted, the suppression
disappears and the data implies presence of the infrared fixed point
\alpha_s(0)~ 2.5(5) and \kappa=0.5 suggested by the Dyson-Schwinger approach in
the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and
N_f=2 unquenched SU(3) QCD are also made.


title: Locality with staggered fermions

abstract:
  We address the locality problem arising in simulations, which take the square
root of the staggered fermion determinant as a Boltzmann weight to reduce the
number of dynamical quark tastes. A definition of such a theory necessitates an
underlying local fermion operator with the same determinant and the
corresponding Green's functions to establish causality and unitarity. We
illustrate this point by studying analytically and numerically the square root
of the staggered fermion operator. Although it has the correct weight, this
operator is non-local in the continuum limit. Our work serves as a warning that
fundamental properties of field theories might be violated when employing
blindly the square root trick. The question, whether a local operator
reproducing the square root of the staggered fermion determinant exists, is
left open.


title: What can Lattice QCD theorists learn from NMR spectroscopists?

abstract:
  Euclidean-time hadron correlation functions computed in Lattice QCD (LQCD)
are modeled by a sum of decaying exponentials, reminiscent of the exponentially
damped sinusoid models of free induction decay (FID) in Nuclear Magnetic
Resonance (NMR) spectroscopy. We present our initial progress in studying how
data modeling techniques commonly used in NMR perform when applied to LQCD
data.


title:
Theta vacuum effects on the chiral condensation and the eta^prime meson
  correlators in the two-flavor massive QED_2 on the lattice

abstract:
  We study the scalar and pseudoscalar condensations and the eta^prime meson
correlators of the two-flavor massive Schwinger model in the non-zero theta
vacuum. Exploiting our new method which was developed to investigate
topological effects in the previous work, we find that the pseudoscalar
condensation is non-zero and there exists a long-range correlation of the
eta^prime meson. This phenomenon is well described by the clustering property.
We also find that even in theta=0 case the cancellation of the long-range
correlation is nontrivial and requires accurate contributions from higher
topological sectors. Our results imply that the fluctuation of the
``disconnected'' diagram originates from the pseudoscalar condensation in each
topological sector.


title: An asymptotic formula for the pion decay constant in a large volume

abstract:
  We derive an asymptotic formula a la Luscher for the finite volume correction
to the pion decay constant: this is expressed as an integral over the < 3 \pi |
A_\mu|0 > amplitude after proper subtraction of the pion pole contribution. We
analyze the formula numerically at leading and next-to-leading order in the
chiral expansion.


title: Gribov copies, Lattice QCD and the gluon propagator

abstract:
  We address the problem of Gribov copies in lattice QCD. The gluon propagator
is computed, in the Landau gauge, using 302 ($\beta = 5.8$) $12^4$
configurations gauge fixed to different copies. The results of the simulation
shows that: i) the effect of Gribov copies is small (less than 10%); ii) Gribov
copies change essentially the lowest momenta components ($q < 2.6$ GeV); iii)
within the statistical accuracy of our simulation, the effect of Gribov copies
is resolved if statistical errors are multiplied by a factor of two or three.
Moreover, when modelling the gluon propagator, different sets of Gribov copies
produce different sets of parameters not, necessarily, compatible within one
standard deviation. Finally, our data supports a gluon propagator which, for
large momenta, behaves like a massive gluon propagator with a mass of 1.1 GeV.


title: A Gauge Theory of Wilson Lines as a Dimensionally Reduced Model of QCD_3

abstract:
  We analyze a two dimensional SU(3) gauge model of Wilson lines as a
dimensionally reduced model of high temperature QCD_3. In contrast to
perturbative dimensional reduction it has an explicit global Z(3) symmetry in
the action. The phase diagram of the model is studied in the space of two free
parameters used to describe the self interaction of the Wilson lines. In
addition to the confinement-deconfinement transition, the model also exhibits a
new Z(3)-breaking phase. These findings are obtained by numerical simulations,
and supported by a perturbative calculation to one loop. A screening mass from
Polyakov loop correlations is calculated numerically. It matches the known
QCD_3 mass in a domain of parameters belonging to the normal deconfined phase.


title: Lattice study on kaon pion scattering length in the $I=3/2$ channel

abstract:
  Using the tadpole improved Wilson quark action on small, coarse and
anisotropic lattices, $K\pi$ scattering length in the $I=3/2$ channel is
calculated within quenched approximation. The results are extrapolated towards
the chiral and physical kaon mass region. Finite volume and finite lattice
spacing errors are also analyzed and a result in the infinite volume and
continuum limit is obtained. Our result is compared with the results obtained
using Roy equations, Chiral Perturbation Theory, dispersion relations and the
experimental data.


title: Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory

abstract:
  We write the SU(2) lattice gauge theory Hamiltonian in (d+1) dimensions in
terms of prepotentials which are the SU(2) fundamental doublets of harmonic
oscillators. The Hamiltonian in terms of prepotentials has $SU(2) \otimes U(1)$
local gauge invariance. In the strong coupling limit, the color confinement in
this formulation is due to the U(1) gauge group. We further solve the $SU(2)
\otimes U(1)$ Gauss law to characterize the physical Hilbert space in terms of
a set of gauge invariant integers. We also obtain certain novel gauge invariant
operators in terms of the above oscillators. The corresponding prepotential
formulation of SU(N) lattice gauge theory is also simple and discussed.


title: In Search of the Chiral Regime

abstract:
  A critical appraisal is given of a recent analysis of the quark-mass and
finite-size dependence of unquenched lattice QCD data for the nucleon mass. We
use this forum to estimate the boundary of the chiral regime for nucleon
properties.


title:
Two Particle States in an Asymmetric Box and the Elastic Scattering
  Phases

abstract:
  The exact two-particle energy eigenstates in a generic asymmetric rectangular
box with periodic boundary conditions in all three directions are studied.
Their relation with the elastic scattering phases of the two particles in the
continuum are obtained for both $D_4$ and $D_2$ symmetry. These results can be
viewed as a generalization of the corresponding formulae in a cubic box
obtained by L\"uscher before. In particular, the s-wave scattering length is
related to the energy shift in the finite box. Possible applications of these
formulae are also discussed.


title:
Long-distance behavior of $q\bar{q}$ color dependent potentials at
  finite temperature

abstract:
  SU(3) heavy quark potentials at finite temperature are studied with quenched
lattice QCD using the stochastic gauge-fixing method. In addition to the
standard color average channel, we investigate $q\bar{q}$ potentials in singlet
and octet channels. % We obtain clear signals in all cases. The singlet
$q\bar{q}$ channel yields an attractive force, while the octet $q\bar{q}$
potential is repulsive; the corresponding color average channel also results in
an attractive force. %As the temperature increases, these forces are weakened
and As the temperature increases, these forces become weak and their variations
are very small; at $T/T_c=1.8-5.6$, % the singlet attractive force is not so
weakened even for long distances. the singlet attractive force survives over $R
\sim 1/T$. The singlet and octet potentials calculated with this algorithm have
a small gauge dependence when the gauge parameter $\alpha$ is changed from 0.6
to 1.3.


title: 3-d Lattice QCD Free Energy to Four Loops

abstract:
  We compute the expansion of the 3-d Lattice QCD free energy to four loop
order by means of Numerical Stochastic Perturbation Theory. The first and
second order are already known and are correctly reproduced. The third and
fourth order coefficients are new results. The known logarithmic divergence in
the fourth order is correctly identified. We comment on the relevance of our
computation in the context of dimensionally reduced finite temperature QCD.


title: The Volume Source Technique for flavor singlets: a second look

abstract:
  We reconsider the Volume Source Technique (VST) for the determination of
flavor singlet quantities on the lattice. We point out a difficulty arising in
the case of fermions in real representations of the gauge group and propose an
improved version of the method (IVST) based on random gauge transformations of
the background configuration. We compare the performance of IVST with the
method based on stochastic estimators (SET). We consider the case of the N=1
Supersymmetric Yang-Mills Theory (SYM), where just one fermionic flavor is
present, the gluino in the adjoint representation, and only flavor singlet
states are possible. The work is part of an inclusive analysis of the spectrum
of the lightest particles of the theory, based on the simulation of the model
on a $16^3\cdot32$ lattice with dynamical gluinos in the Wilson scheme.


title:
Insight into nucleon structure from lattice calculations of moments of
  parton and generalized parton distributions

abstract:
  This talk presents recent calculations in full QCD of the lowest three
moments of generalized parton distributions and the insight they provide into
the behavior of nucleon electromagnetic form factors, the origin of the nucleon
spin, and the transverse structure of the nucleon. In addition, new exploratory
calculations in the chiral regime of full QCD are discussed.


title:
Renormalization of bilinear quark operators for the chirally improved
  lattice Dirac operator

abstract:
  We compute non-perturbative renormalization constants of fermionic bilinears
for the chirally improved lattice fermions in the quenched approximation of
QCD. We address finite size effects and the influence of Gribov copies. Our
results are presented in the RI' and MSbar schemes as well as in RGI form and
we discuss relations between the renormalization constants implied by chiral
symmetry. After publication we corrected the numerator of the first coefficient
of \alpha_s^3 in (24) from 3696847 to 3890527, which yields a 0.2% higher value
of the conversion coefficient at \mu=2 GeV.


title:
One-loop renormalisation of quark bilinears for overlap fermions with
  improved gauge actions

abstract:
  We compute lattice renormalisation constants of local bilinear quark
operators for overlap fermions and improved gauge actions. Among the actions we
consider are the Symanzik, L\"uscher-Weisz, Iwasaki and DBW2 gauge actions. The
results are given for a variety of $\rho$ parameters. We show how to apply mean
field (tadpole) improvement to overlap fermions. The question, what is a good
gauge action, is discussed from the perturbative point of view. Finally, we
show analytically that the gauge dependent part of the self-energy and the
amputated Green functions are independent of the lattice fermion
representation, using either Wilson or overlap fermions.


title:
Glueballs and k-strings in SU(N) gauge theories : calculations with
  improved operators

abstract:
  We test a variety of blocking and smearing algorithms for constructing
glueball and string wave-functionals, and find some with much improved overlaps
onto the lightest states. We use these algorithms to obtain improved results on
the tensions of k-strings in SU(4), SU(6), and SU(8) gauge theories. We
emphasise the major systematic errors that still need to be controlled in
calculations of heavier k-strings, and perform calculations in SU(4) on an
anisotropic lattice in a bid to minimise one of these. All these results point
to the k-string tensions lying part-way between the `MQCD' and `Casimir
Scaling' conjectures, with the power in 1/N of the leading correction lying in
[1,2]. We also obtain some evidence for the presence of quasi-stable strings in
calculations that do not use sources, and observe some near-degeneracies
between (excited) strings in different representations. We also calculate the
lightest glueball masses for N=2, ...,8, and extrapolate to N=infinity,
obtaining results compatible with earlier work. We show that the N=infinity
factorisation of the Euclidean correlators that are used in such mass
calculations does not make the masses any less calculable at large N.


title: A strange property of lattices with an even number of sites

abstract:
  By examining the behaviour of the "SLAC" lattice derivative operators, it is
found that lattices with an even number of sites have a somewhat strange
self-consistency requirement for extra structure in the spatial derivative
operator, which is not needed by lattices having an odd number of sites, and
which is not at all obvious from a first-principles derivation. The general
implications of this extra required structure are not, as yet, completely
clear.


title: Hadronic decay of a scalar B meson from the lattice

abstract:
  We explore the transitions B$(0^+)$ to B $\pi$ and B$_s(0^+)$ to B K from
lattice QCD with $N_f=2$ flavours of sea quark, using the static approximation
for the heavy quark. We evaluate the effective coupling constants, predicting a
B$(0^+)$ to B $\pi$ width of around 160 MeV. Our result for the coupling
strength adds to the evidence that the B$_s(0^+)$ meson is not predominantly a
molecular state (BK).


title: SU(N) chiral gauge theories on the lattice

abstract:
  We extend the construction of lattice chiral gauge theories based on
non-perturbative gauge fixing to the non-abelian case. A key ingredient is that
fermion doublers can be avoided at a novel type of critical point which is only
accessible through gauge fixing, as we have shown before in the abelian case.
The new ingredient allowing us to deal with the non-abelian case as well is the
use of equivariant gauge fixing, which handles Gribov copies correctly, and
avoids Neuberger's no-go theorem. We use this method in order to gauge fix the
non-abelian group (which we will take to be SU(N)) down to its maximal abelian
subgroup. Obtaining an undoubled, chiral fermion content requires us to
gauge-fix also the remaining abelian gauge symmetry. This modifies the
equivariant BRST identities, but their use in proving unitarity remains intact,
as we show in perturbation theory. On the lattice, equivariant BRST symmetry as
well as the abelian gauge invariance are broken, and a judiciously chosen
irrelevant term must be added to the lattice gauge-fixing action in order to
have access to the desired critical point in the phase diagram. We argue that
gauge invariance is restored in the continuum limit by adjusting a finite
number of counter terms. We emphasize that weak-coupling perturbation theory
applies at the critical point which defines the continuum limit of our lattice
chiral gauge theory.


title: Lambda(1405) and Negative-Parity Baryons in Lattice QCD

abstract:
  We review briefly recent studies of the Lambda(1405) spectrum in Lattice QCD.
Ordinary three-quark pictures of the Lambda(1405) in quenched Lattice QCD fail
to reproduce the mass of the experimental value, which seems to support the
penta-quark picture for the Lambda(1405) such as a Kbar-N molecule-like state.
It is also noted that the present results suffer from relatively large
systematic uncertainties coming from the finite volume effect, the chiral
extrapolation and the quenching effect.


title: Non-Compact QED_3 with N_f=1 and N_f=4

abstract:
  We present numerical results for non-compact three-dimensional QED for
numbers of flavors N_f=1 and N_f=4.In particular, we address the issue of
whether chiral symmetry is spontaneously broken in the continuum limit, and
obtain a positive answer for N_f=1, with a dimensionless condensate estimated
to be beta^2<psibarpsi> ~= O(10^-3), implying that the critical number of
flavors N_fc>1. We also compare the N_f=1 and N_f=4 models by analysing the
transition from strong to weak coupling behaviour using an equation of state
based on a continuous phase transition. While some qualitative differences
emerge, it appears difficult to determine whether N_f=4 lies above or below
N_fc.


title: Light hadron spectroscopy in two-flavor QCD with small sea quark masses

abstract:
  We extend the study of the light hadron spectrum and the quark mass in
two-flavor QCD to smaller sea quark mass, corresponding to
$m_{PS}/m_{V}=0.60$--0.35. Numerical simulations are carried out using the
RG-improved gauge action and the meanfield-improved clover quark action at
$\beta=1.8$ ($a = 0.2$ fm from $\rho$ meson mass). We observe that the light
hadron spectrum for small sea quark mass does not follow the expectation from
chiral extrapolations with quadratic functions made from the region of
$m_{PS}/m_{V}=0.80$--0.55. Whereas fits with either polynomial or continuum
chiral perturbation theory (ChPT) fails, the Wilson ChPT (WChPT) that includes
$a^2$ effects associated with explicit chiral symmetry breaking successfully
fits the whole data: In particular, WChPT correctly predicts the light quark
mass spectrum from simulations for medium heavy quark mass, such as $m_{PS}/m_V
\simgt 0.5$. Reanalyzing the previous data %at $m_{PS}/m_{V}=0.80$--0.55 with
the use of WChPT, we find the mean up and down quark mass being smaller than
the previous result from quadratic chiral extrapolation by approximately 10%,
$m_{ud}^{\bar{\rm MS}}(\mu=2 {GeV}) = 3.11(17)$ [MeV] in the continuum limit.


title:
Critical or tricritical point in mixed-action SU(2) lattice gauge
  theory?

abstract:
  An analysis of scaling along the first-order bulk transition line in
fundamental-adjoint SU(2) lattice gauge theory strongly supports the
first-order endpoint being a tricritical point, and is inconsistent with it
being an ordinary critical point as is usually assumed. If tricritical, the
transition must continue from the endpoint further into the phase diagram as a
second-order bulk transition and extend to and beyond the Wilson axis.
Observations indicate that this is most likely the same transition that has
been traditionally considered a finite-temperature transition.


title:
Contribution of disconnected diagrams to the hyperfine splitting of
  charmonium

abstract:
  We discuss the contribution of OZI-suppressed diagrams to the hyperfine
splitting of charmonium in lattice QCD. We study valence quark mass regions
from strange to charm quark masses. No contribution of the disconnected diagram
is seen in the vector meson channel. In the pseudo-scalar channel and for
valence quark masses around the strange quark, the disconnected contribution
induces a considerable increase of the meson mass. This contribution quickly
decreases as the quark mass increases. For charmonium the effect is very small
although a decrease of the pseudoscalar mass induced by the disconnected
contribution cannot be ruled out.


title: I=2 Pion scattering length with improved actions on anisotropic lattices

abstract:
  $\pi\pi$ scattering length in the I=2 channel is calculated within quenched
approximation using improved gauge and improved Wilson fermion actions on
anisotropic lattices. The results are extrapolated towards the chiral, infinite
volume and continuum limit. This result improves our previous result on the
scattering length. In the chiral, infinite volume and continuum limit, we
obtain $a^{(2)}_0m_\pi=-0.0467(45)$, which is consistent with the result from
Chiral Perturbation Theory, the experiment and results from other lattice
calculations.


title:
Chiral extrapolations of baryon masses for unquenched three-flavor
  lattice simulations

abstract:
  We have analyzed the chiral expansion of the baryon masses to second order in
the quark masses, including strong isospin violation. The calculations are
performed in Lorentz-invariant baryon chiral perturbation theory. Chiral
extrapolation functions for three-flavor unquenched lattice simulations are
derived. The matching to the two-flavor case and the sigma terms are also
considered.


title: The aliasing problem in lattice field theory

abstract:
  The intrinsically nonlinear nature of quantum field theory provides a
fundamental complication for lattice calculations, when the physical
implications of the subtleties of Fourier theory are taken into account. Even
though the fundamental fields are constrained to the first Brillouin zone,
Fourier theory tells us that the high-momentum components of products of these
fields "bleed into" neighbouring Brillouin zones, where they "alias" (or
"masquerade") as low-momentum contributions, violating the conservation of
energy and momentum, and fundamentally distorting calculations. In this paper I
offer a general strategy for eliminating the artefacts of aliasing in practical
calculations.


title: Finite Temperature QCD with Domain Wall Fermions

abstract:
  Domain wall fermions are a new lattice fermion formulation which preserves
the full chiral symmetry of the continuum at finite lattice spacing, up to
terms exponentially small in an extra parameter. We discuss the main features
of the formulation and its application to study of QCD with two light fermions
of equal mass. We also present numerical studies of the two flavor QCD
thermodynamics with aT = 1/4.


title:
Non-perturbative renormalization of meson decay constants in quenched
  QCD for a renormalization group improved gauge action

abstract:
  Renormalization constants ($Z$-factors) of vector and axial-vector currents
are determined non-perturbatively in quenched QCD for a renormalization group
improved gauge action and a tadpole improved clover quark action using the
Schr\"odinger functional method. Non-perturbative values of $Z$-factors turn
out to be smaller than one-loop perturbative values by $O(15%)$ at lattice
spacing of $a^{-1}\approx$ 1 GeV. The pseudoscalar and vector meson decay
constants calculated with the non-perturbative $Z$-factors show a much better
scaling behavior compared to previous results obtained with tadpole improved
one-loop $Z$-factors. In particular, the non-perturbative $Z$-factors
normalized at infinite physical volume show that scaling violation of the decay
constants are within about 10% up to the lattice spacing $a^{-1}\sim 1$ GeV.
The continuum estimates obtained from data in the range $a^{-1}=$ 1 -- 2 GeV
agree with those determined from finer lattices ($a^{-1}\sim 2-4$ GeV) with the
standard action.


title:
The Sequential Empirical Bayes Method: An Adaptive Constrained-Curve
  Fitting Algorithm for Lattice QCD

abstract:
  We introduce the ``Sequential Empirical Bayes Method'', an adaptive
constrained-curve fitting procedure for extracting reliable priors. These are
then used in standard augmented-$\chi^2$ fits on separate data. This better
stabilizes fits to lattice QCD overlap-fermion data at very low quark mass
where {\it a priori} values are not otherwise known. Lessons learned (including
caveats limiting the scope of the method) from studying artificial data are
presented. As an illustration, from local-local two-point correlation
functions, we obtain masses and spectral weights for ground and first-excited
states of the pion, give preliminary fits for the $a_0$ where ghost states (a
quenched artifact) must be dealt with, and elaborate on the details of fits of
the Roper resonance and $S_{11}(N^{1/2-})$ previously presented elsewhere. The
data are from overlap fermions on a quenched $16^3\times 28$ lattice with
spatial size $La=3.2 {\rm fm}$ and pion mass as low as $\sim 180 {\rm MeV}$.


title: On the discretization of physical momenta in lattice QCD

abstract:
  The adoption of two distinct boundary conditions for two fermions species on
a finite lattice allows to deal with arbitrary relative momentum between the
two particle species, in spite of the momentum quantization rule due to a
limited physical box size. We test the physical significance of this
topological momentum by checking in the continuum limit the validity of the
expected energy-momentum dispersion relations.


title: Numerical Methods for the QCD Overlap Operator:III. Nested Iterations

abstract:
  The numerical and computational aspects of chiral fermions in lattice quantum
chromodynamics are extremely demanding. In the overlap framework, the
computation of the fermion propagator leads to a nested iteration where the
matrix vector multiplications in each step of an outer iteration have to be
accomplished by an inner iteration; the latter approximates the product of the
sign function of the hermitian Wilson fermion matrix with a vector. In this
paper we investigate aspects of this nested paradigm. We examine several Krylov
subspace methods to be used as an outer iteration for both propagator
computations and the Hybrid Monte-Carlo scheme. We establish criteria on the
accuracy of the inner iteration which allow to preserve an a priori given
precision for the overall computation. It will turn out that the accuracy of
the sign function can be relaxed as the outer iteration proceeds. Furthermore,
we consider preconditioning strategies, where the preconditioner is built upon
an inaccurate approximation to the sign function. Relaxation combined with
preconditioning allows for considerable savings in computational efforts up to
a factor of 4 as our numerical experiments illustrate. We also discuss the
possibility of projecting the squared overlap operator into one chiral sector.


title:
A finite temperature investigation of dual superconductivity in the
  modified SO(3) lattice gauge theory

abstract:
  We study the SO(3) lattice gauge theory in 3+1 dimensions with the adjoint
Wilson action modified by a $\mathbb{Z}_2$ monopole suppression term and by
means of the Pisa disorder operator. We find evidence for a finite temperature
deconfinement transition driven by the condensation of U(1) magnetic charges. A
finite-size scaling test shows consistency with the critical exponents of the
3D Ising model.


title:
Phase Structure and Gauge Boson Propagator in the radially active 3D
  compact Abelian Higgs Model

abstract:
  Unfreezing the radial degree of freedom, we study the three-dimensional
Abelian Higgs model with compact gauge field and fundamentally charged matter.
For small quartic Higgs self coupling and finite gauge coupling the model
possesses a first order transition from the confined/symmetric phase to the
deconfined/Higgs phase separated at some hopping parameter $\kappa_c$. Latent
heat and surface tension are obtained in the first order regime. At larger
quartic coupling the first order transition ceases to exist, and the behavior
becomes similar to that known from the London limit. These observations are
complemented by a study of the photon propagator in Landau gauge in the two
different regimes. The problems afflicting the gauge fixing procedure are
carefully investigated. We propose an improved gauge fixing algorithm which
uses a finite subgroup in a preselection/preconditioning stage. The
computational gain in the expensive confinement region is a speed-up factor
around 10. The propagator in momentum space has a non-zero anomalous dimension
in the confined phase whereas it vanishes in the Higgs phase. As far as the
gauge boson propagator is concerned, we find that the radially active Higgs
field provides qualitatively no new effect compared to the radially frozen
Higgs field studied before.


title: Spatially improved operators for excited hadrons on the lattice

abstract:
  We present a new approach for determining spatially optimized operators that
can be used for lattice spectroscopy of excited hadrons. Jacobi smeared quark
sources with different widths are combined to construct hadron operators with
different spatial wave functions. We use the variational method to determine
those linear combinations of operators that have optimal overlap with ground
and excited states. The details of the new approach are discussed and we
demonstrate the power of the method using examples from quenched baryon and
meson spectroscopy. In particular we study the Roper state and rho(1450) and
discuss some physical implications of our tests.


title: Octet Baryon Masses in Partially Quenched Chiral Perturbation Theory

abstract:
  The mass spectrum of the lowest lying octet baryons is calculated to
next-to-next-to-leading order in heavy baryon chiral perturbation theory and
partially quenched heavy baryon chiral perturbation theory. We work in the
isospin limit and treat the decuplet baryons as dynamical fields. These results
are necessary for extrapolating QCD and partially quenched QCD lattice
simulations of the octet baryon masses.


title: The Physical Hilbert Space of SU(2) Lattice Gauge Theory

abstract:
  We solve the Gauss law of SU(2) lattice gauge theory using the harmonic
oscillator prepotential formulation. We construct a generating function of a
manifestly gauge invariant and orthonormal basis in the physical Hilbert space
of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal
physical states are given in closed form. The generalization to SU(N) gauge
group is discussed.


title:
Free energy of a static quark anti-quark pair and the renormalized
  Polyakov loop in three flavor QCD

abstract:
  We study the free energy of a static quark anti-quark pair at finite
temperature in three flavor QCD with degenerate quark masses using N_tau=4 and
6 lattices with Asqtad staggered fermion action. The static free energy was
calculated for different values of the quark mass and the entropy contribution
at large distances has been extracted. We also calculate the renormalized
Polyakov loop following the approach by Kaczmarek et al.


title: Hadronic property at finite density

abstract:
  We report on three topics on finite density simulations: (i) the derivative
method for hadronic quantities, (ii) phase fluctuations in the vicinity of the
critical temperature and (iii) the density of states method at finite isospin
density.


title: Dynamics of Phase Transitions: The 3D 3-state Potts model

abstract:
  In studies of the QCD deconfining phase transition or cross-over by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. In this paper we extend our previous
study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model,
which serves as an effective model for some QCD properties. We investigate the
linear theory of spinodal decomposition in some detail. It describes the early
time evolution of the 3D model under a quench from the disordered into the
ordered phase well, but fails in 2D. Further, the quench leads to competing
vacuum domains, which are difficult to equilibrate, even in the presence of a
small external magnetic field. From our hysteresis study we find, as before, a
dynamics dominated by spinodal decomposition. There is evidence that some
effects survive in the case of a cross-over. But the infinite volume
extrapolation is difficult to control, even with lattices as large as $120^3$.


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

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


title:
Anisotropic Goldstone bosons of strong-coupling lattice QCD at high
  density

abstract:
  We calculate the spectrum of excitations in strong-coupling lattice QCD in a
background of fixed baryon density, at a substantial fraction of the saturation
density. We employ a next-nearest-neighbor fermion formulation that possesses
the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find two types
of massless excitations: type I Goldstone bosons with linear dispersion
relations and type II Goldstone bosons with quadratic dispersion relations.
Some of the type I bosons originate as type II bosons of the nearest-neighbor
theory. Bosons of either type can develop anisotropic dispersion relations,
depending on the value of N_f and the baryon density.


title: Computing Electromagnetic Effects in Fully Unquenched QCD

abstract:
  The inclusion of electromagnetic effects in unquenched QCD can be
accomplished using ensembles generated in dynamical simulations with pure QCD
provided the change in the quark determinant induced by a weak electromagnetic
field can be efficiently computed. A stochastic technique for achieving this in
the case of dynamical domain wall calculations is described.


title: Scaling of FLIC Fermions

abstract:
  Hadron masses are calculated in quenched lattice QCD on a variety of lattices
in order to probe the scaling behavior of the Fat-Link Irrelevant Clover (FLIC)
fermion action, a fat-link clover fermion action in which the purely irrelevant
operators of the fermion action are constructed using APE-smeared links. The
scaling analysis indicates FLIC fermions provide a new form of nonperturbative
O(a) improvement where near-continuum results are obtained at finite lattice
spacing.


title:
Phase diagram of the lattice Wess-Zumino model from rigorous lower
  bounds on the energy

abstract:
  We study the lattice N=1 Wess-Zumino model in two dimensions and we construct
a sequence $\rho^{(L)}$ of exact lower bounds on its ground state energy
density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds
$\rho^{(L)}$ can be computed numerically on a finite lattice with $L$ sites and
can be exploited to discuss dynamical symmetry breaking. The transition point
is determined and compared with recent results based on large-scale Green
Function Monte Carlo simulations with good agreement.


title:
Impact of large cutoff-effects on algorithms for improved Wilson
  fermions

abstract:
  As a feasibility study for a scaling test we investigate the behavior of
algorithms for dynamical fermions in the N_f=2 Schroedinger functional at an
intermediate volume of 1 fm^4. Simulations were performed using HMC with two
pseudo-fermions and PHMC at lattice spacings of approximately 0.1 and 0.07 fm.
We show that some algorithmic problems are due to large cutoff-effects in the
spectrum of the improved Wilson-Dirac operator and disappear at the smaller
lattice spacing. The problems discussed here are not expected to be specific to
the Schroedinger functional.


title: Thick vortices in SU(2) lattice gauge theory

abstract:
  Three dimensional SU(2) lattice gauge theory is studied after eliminating
thin monopoles and the smallest thick monopoles. Kinematically this constraint
allows the formation of thick vortex loops which produce Z(2) fluctuations at
longer length scales. The thick vortex loops are identified in a three
dimensional simulation. A condensate of thick vortices persists even after the
thin vortices have all disappeared. The thick vortices decouple at a slightly
lower temperature (higher beta) than the thin vortices and drive a phase
transition.


title:
Tricritical point of lattice QCD with Wilson quarks at finite
  temperature and density

abstract:
  First principle study of QCD at finite temperature $T$ and chemical potential
$\mu$ is essential for understanding a wide range of phenomena from heavy-ion
collisions to cosmology and neutron stars. However, in the presence of finite
density, the critical behavior lattice gauge theory without species doubling,
is unknown. At strong coupling, we examine the phase structure on the $(\mu,T)$
plane, using Hamiltonian lattice QCD with Wilson fermions. A tricritical point
is found, separating the first and second order chiral phase transitions. Such
a tricritical point at finite $T$ has not been found in previous work in the
Hamiltonian formalism with Kogut-Susskind fermions or naive fermions.


title: Quark mass dependence of the pseudoscalar hairpin vertex

abstract:
  In a recent investigation of chiral behavior in quenched lattice QCD, the
flavor-singlet pseudoscalar ``hairpin'' vertex associated with the eta prime
mass was studied for pion masses ranging from approximately 275 to 675 MeV.
Throughout this mass range, the quark-disconnected pseudoscalar correlator is
well-described by a pure double-pion-pole diagram with a p^2 independent mass
insertion. The residue of the double pole was found to exhibit a significant
quark mass dependence, evidenced by a negative slope of the effective mass
insertion (m_0^{eff})^2 as a function of m_{\pi}^2. It has been observed by
Sharpe that, with a consistent NLO calculation in quenched chiral perturbation
theory, this mass dependence is uniquely predicted in terms of the single-pole
coefficient \alpha_{\Phi} and the Leutwyler parameter L_5. Since \alpha_{\Phi}
is found to be approximately zero, the chiral slope of the double-pole residue
determines a value for L_5. This provides a consistency check between the
chiral slope of the hairpin mass insertion and that of the pion decay constant.
We investigate the consistency of these mass dependences in our Monte Carlo
results at two values of lattice spacing. Within statistics, the slopes are
found to be consistent with the Q\chiPT prediction, confirming that the
observed negative slope of m_0^{eff} arises as an effect of the L_5 Leutwyler
term.


title:
Deconstruction, 2d lattice super-Yang-Mills, and the dynamical lattice
  spacing

abstract:
  We study expectation values related to the dynamical lattice spacing that
occurs in the recent 2d lattice super-Yang-Mills constructions of Cohen et al.
[hep-lat/0307012]. The corresponding observable in the fully-quenched ensemble
would appear to indicate a difficulty with the proposed continuum limit.
However, we find that the same observable in the phase-quenched ensemble takes
a very different, perhaps encouraging, average value. Unfortunately, we are not
able to obtain results for the full theory, due to the nearly flat distribution
of the complex phase of the fermion determinant in the phase-quenched ensemble.


title:
First determination of the strange and light quark masses from full
  lattice QCD

abstract:
  We compute the strange quark mass $m_s$ and the average of the $u$ and $d$
quark masses $\hat m$ using full lattice QCD with three dynamical quarks
combined with experimental values for the pion and kaon masses. The simulations
have degenerate $u$ and $d$ quarks with masses $m_u=m_d\equiv \hat m$ as low as
$m_s/8$, and two different values of the lattice spacing. The bare lattice
quark masses obtained are converted to the $\msbar$ scheme using perturbation
theory at $O(alpha_s)$. Our results are: $m_s^\msbar$(2 GeV) = 76(0)(3)(7)(0)
MeV, $\hat m^\msbar$(2 GeV) = 2.8(0)(1)(3)(0) MeV and $m_s/\hat m$ =
27.4(1)(4)(0)(1), where the errors are from statistics, simulation,
perturbation theory, and electromagnetic effects, respectively.


title:
Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical
  Dimension

abstract:
  A finite size scaling theory for the partition function zeros and
thermodynamic functions of O(N) phi^4-theory in four dimensions is derived from
renormalization group methods. The leading scaling behaviour is mean-field like
with multiplicative logarithmic corrections which are linked to the triviality
of the theory. These logarithmic corrections are independent of N for odd
thermodynamic quantities and associated zeros and are N dependent for the even
ones. Thus a numerical study of finite size scaling in the Ising model serves
as a non-perturbative test of triviality of phi^4_4-theories for all N.


title: An Introduction to Chiral Symmetry on the Lattice

abstract:
  The $SU(N_f)_L \otimes SU(N_f)_R$ chiral symmetry of QCD is of central
importance for the nonperturbative low-energy dynamics of light quarks and
gluons. Lattice field theory provides a theoretical framework in which these
dynamics can be studied from first principles. The implementation of chiral
symmetry on the lattice is a nontrivial issue. In particular, local lattice
fermion actions with the chiral symmetry of the continuum theory suffer from
the fermion doubling problem. The Ginsparg-Wilson relation implies L\"uscher's
lattice variant of chiral symmetry which agrees with the usual one in the
continuum limit. Local lattice fermion actions that obey the Ginsparg-Wilson
relation have an exact chiral symmetry, the correct axial anomaly, they obey a
lattice version of the Atiyah-Singer index theorem, and still they do not
suffer from the notorious doubling problem. The Ginsparg-Wilson relation is
satisfied exactly by Neuberger's overlap fermions which are a limit of Kaplan's
domain wall fermions, as well as by Hasenfratz and Niedermayer's classically
perfect lattice fermion actions. When chiral symmetry is nonlinearly realized
in effective field theories on the lattice, the doubling problem again does not
arise. This review provides an introduction to chiral symmetry on the lattice
with an emphasis on the basic theoretical framework.


title: Chiral symmetry breaking at large N_c

abstract:
  We present numerical evidence for the hypothesis that, in the planar limit,
four dimensional Euclidean Yang-Mills theory on a finite symmetrical four-torus
breaks chiral symmetry spontaneously when the length of the sides l is larger
than a critical value l_c with a bilinear condensate whose value is independent
of l. Therefore spontaneous symmetry breaking occurs at finite volume and
infinite N_c reduction holds for the chiral condensate.


title: Improved chiral properties of FLIC fermions

abstract:
  The chiral properties of the fat-link irrelevant clover (FLIC) fermion action
are examined. The improved chiral properties of fermion actions incorporating
smoothed links are realized in the FLIC action where only the irrelevant
operators of the fermion action are constructed with smoothed links. In
particular, the histogram of the additive mass renormalization encountered in
chiral-symmetry breaking Wilson-type fermion actions is seen to narrow upon
introducing fat-links in the irrelevant operators. The exceptional
configuration problem of quenched QCD is reduced, enabling access to the light
quark mass regime of $m_{\pi} / m_{\rho} \sim 0.35$. In particular, quenched
chiral non-analytic behavior is revealed in the light quark mass dependence of
the $\Delta$-baryon mass. FLIC fermions offer a promising approach to revealing
the properties of full QCD at light quark masses.


title:
Non-perturbative Pion Matrix Element of a twist-2 operator from the
  Lattice

abstract:
  We give a continuum limit value of the lowest moment of a twist-2 operator in
pion states from non-perturbative lattice calculations. We find that the
non-perturbatively obtained renormalization group invariant matrix element is
<x>_{RGI} = 0.179(11), which corresponds to <x>^{MSbar}(2 GeV) = 0.246(15). In
obtaining the renormalization group invariant matrix element, we have
controlled important systematic errors that appear in typical lattice
simulations, such as non-perturbative renormalization, finite size effects and
effects of a non-vanishing lattice spacing. The crucial limitation of our
calculation is the use of the quenched approximation. Another question that
remains not fully clarified is the chiral extrapolation of the numerical data.


title: Twisted mass QCD and lattice approaches to the $\Delta I = 1/2$ rule

abstract:
  Twisted mass lattice QCD (tmQCD), generalised to four Wilson quark flavours,
can be used for the computation of some weak matrix elements related to $\Delta
I=1/2$ transitions. Besides eliminating unphysical zero modes, tmQCD may
alleviate long-standing renormalisation problems of the four-quark operators
which contribute to CP-conserving $K\to\pi$ transitions. With an active charm
quark, the renormalisation of the $K\to\pi$ matrix elements requires at most
the subtraction of a linearly divergent counterterm. Furthermore, in the
(partially) quenched approximation the twist angles can be chosen so that only
a finite counterterm needs to be subtracted.


title: QCD Thermodynamics with Three Flavors of Improved Staggered Quarks

abstract:
  We report on a study of QCD thermodynamics with three flavors of quarks,
using a Symanzik improved gauge action and the Asqtad O(a^2) improved staggered
quark action. Simulations were carried out with lattice spacings 1/4T, 1/6T and
1/8T both for three degenerate quarks with masses less than or equal to the
strange quark mass, m_s, and for degenerate up and down quarks with masses in
the range 0.1 m_s \leq m_{u,d} \leq 0.6 m_s, and the strange quark mass fixed
near its physical value. We present results for standard thermodynamics
quantities, such as the Polyakov loop, the chiral order parameter and its
susceptibility. For the quark masses studied to date we find a rapid crossover
rather than a bona fide phase transition. We have carried out the first
calculations of quark number susceptibilities with three flavors of sea quarks.
These quantities are of physical interest because they are related to
event-by-event fluctuations in heavy ion collision experiments. Comparison of
susceptibilities at different lattice spacings show that our results are close
to the continuum values.


title:
A non-perturbative study of the action parameters for
  anisotropic-lattice quarks

abstract:
  A quark action designed for highly anisotropic lattice simulations is
discussed. The mass-dependence of the parameters in the action is studied and
the results are presented. Applications of this action in studies of heavy
quark quantities are described and results are presented from simulations at an
anisotropy of six, for a range of quark masses from strange to bottom.


title:
Two Geometric Approaches To Study The Deconfinement Phase Transition in
  (3+1)-Dimensional $Z_2$ Gauge Theories

abstract:
  We have simulated $(3+1)-$dimensional finite temperature $Z_2$ gauge theory
by using Metropolis algorithm. We aimed to observe the deconfinement phase
transitions by using geometric methods. In order to do so we have proposed two
different methods which can be applied to $3-$dimensional effective spin model
consisting of Polyakov loop variables. The first method is based on studies of
cluster structures of each configuration. For each temperature, configurations
are obtained from a set of bond probability ($P$) values. At a certain
probability, percolating clusters start to emerge. Unless the probability value
coincides with the Coniglio-Klein probability value, the fluctuations are less
than the actual fluctuations at the critical point. In this method the task is
to identify the probability value which yields the highest peak in the
diverging quantities on finite lattices. The second method uses the scaling
function based on the surface renormalization which is of geometric origin.
Since this function is a scaling function, the measurements done on
different-size lattices yield the same value at the critical point, apart from
the correction to scaling terms. The linearization of the scaling function
around the critical point yields the critical point and the critical exponents.


title: Leading Quenching Effects in the Proton Magnetic Moment

abstract:
  We present the first investigation of the extrapolation of quenched nucleon
magnetic moments in quenched chiral effective field theory. We utilize
established techniques in finite-range regularisation and compare with standard
dimensional regularisation methods. Finite-volume corrections to the relevant
loop integrals are also addressed. Finally, the contributions of dynamical sea
quarks to the proton moment are estimated using a recently discovered
phenomenological link between quenched and physical QCD.


title: Precise determination of the strangeness magnetic moment of the nucleon

abstract:
  By combining the constraints of charge symmetry with new chiral extrapolation
techniques and recent low mass lattice QCD simulations of the individual quark
contributions to the magnetic moments of the nucleon octet, we obtain a precise
determination of the strange magnetic moment of the proton. The result, namely
G_M^s = -0.046 +/- 0.019 mu_N, is consistent with the latest experimental
measurements but an order of magnitude more precise. This poses a tremendous
challenge for future experiments.


title: The strangeness magnetic moment of the nucleon from FLIC fermions

abstract:
  By imposing the constraints of charge symmetry we show that the strangeness
magnetic moment of the nucleon can be expressed in terms of empirical magnetic
moments and ratios of valence quark magnetic moments. The latter are determined
using modern chiral extrapolation techniques and recent low mass lattice QCD
simulations of the individual quark contributions to the magnetic moments of
the nucleon octet. The result is a precise determination of G_M^s, namely
-0.043 +/- 0.026 mu_N, which is consistent with the latest experimental
measurements.


title: Recent Developments in Quark Nuclear Physics

abstract:
  We provide an overview of recent work exploring the quark-mass dependence of
hadronic observables and the associated role of chiral nonanalytic behavior due
to the meson-cloud of hadrons. In particular, we address an issue of great
current interest, namely the degree of model independence of results obtained
through a controlled extrapolation of lattice QCD simulation results. Physical
insights gained from this research are highlighted. We emphasize how chiral
effective field theory formulated with a finite-range regulator provides a
reliable and model-independent extrapolation to the physical world.


title:
Equation of State for Spin Systems with Goldstone Bosons: the 3d O(4)
  Case

abstract:
  We propose an improved parametric form for the equation of state of
three-dimensional O(N) spin systems. The proposed form is a series expansion
with two sets of terms, which contribute (mainly) separately to the description
of the high- and low-temperature regions of the phase diagram. Our goal is a
better description of the low-temperature phase at zero magnetic field (i.e.
the coexistence line), characterized by singularities induced by Goldstone
modes. We test our proposed form by comparison with existing Monte Carlo data
for the N=4 case, which is of interest in studies of the QCD phase transition
and for which the Goldstone-mode effects are quite pronounced. We find that the
description of the numerical equation of state is indeed improved with respect
to other fitting forms. In all cases considered we determine the coefficients
nonperturbatively, from fits to the data. As a consequence, we are able to
obtain a very precise characterization of the pseudo-critical line for the
model.


title: Blocking from continuum and monopoles in gluodynamics

abstract:
  We review the method of blocking of topological defects from continuum used
as a non--perturbative tool to construct effective actions for these defects.
The actions are formulated in the continuum limit while the couplings of these
actions can be derived from simple observables calculated numerically on
lattices with a finite lattice spacing. We demonstrate the success of the
method in deriving the effective actions for Abelian monopoles in the pure
SU(2) gauge models in an Abelian gauge. In particular, we discuss the
gluodynamics in three and four space--time dimensions at zero and non--zero
temperatures. Besides the action the quantities of our interest are the
monopole density, the magnetic Debye mass and the monopole condensate.


title: Yang-Mills fields and the lattice

abstract:
  The Yang-Mills theory lies at the heart of our understanding of elementary
particle interactions. For the strong nuclear forces, we must understand this
theory in the strong coupling regime. The primary technique for this is the
lattice. While basically an ultraviolet regulator, the lattice avoids the use
of a perturbative expansion. I discuss some of the historical circumstances
that drove us to this approach, which has had immense success, convincingly
demonstrating quark confinement and obtaining crucial properties of the strong
interactions from first principles.


title:
Static quark potential and effective string corrections in the (2+1)-d
  SU(2) Yang-Mills theory

abstract:
  We report on a very accurate measurement of the static quark potential in
SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections
to the linear behaviour. We perform numerical simulations at zero and finite
temperature comparing our results with the corrections given by the effective
string picture in these two regimes. We also check for universal features
discussing our results together with those recently published for the (2+1)-d
Z(2) and SU(3) pure gauge theories.


title: Transport Coefficients of Gluon Plasma

abstract:
  Transport coefficients of gluon plasma are calculated for a SU(3) pure gauge
model by lattice QCD simulations on $16^3 \times 8$ and $24^3 \times 8$
lattices. Simulations are carried out at a slightly above the deconfinement
transition temperature $T_c$, where a new state of matter is currently being
pursued in RHIC experiments. Our results show that the ratio of the shear
viscosity to the entropy is less than one and the bulk viscosity is consistent
with zero in the region, $1.4 \leq T/T_c \leq 1.8 $.


title:
The Index Theorem and Universality Properties of the Low-lying
  Eigenvalues of Improved Staggered Quarks

abstract:
  We study various improved staggered quark Dirac operators on quenched gluon
backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We
find a clear separation of the spectrum into would-be zero modes and others.
The number of would-be zero modes depends on the topological charge as expected
from the Index Theorem, and their chirality expectation value is large
(approximately 0.7). The remaining modes have low chirality and show clear
signs of clustering into quartets and approaching the random matrix theory
predictions for all topological charge sectors. We conclude that improvement of
the fermionic and gauge actions moves the staggered quarks closer to the
continuum limit where they respond correctly to QCD topology.


title: Chiral Perturbation Theory on the Lattice and its Applications

abstract:
  Chiral perturbation theory (CPT), the low-energy effective theory of QCD, can
be used to describe QCD observables in the low-energy region in a
model-independent way. At any given order in the chiral expansion, CPT
introduces a finite number of parameters that encode the short-distance physics
and that must be determined from experiment or numerical lattice QCD
simulations. In this thesis, we calculate a number of hadronic observables in
the quenched and partially quenched versions of CPT:
  Chiral corrections to B^(*) --> D^(*) at zero recoil are investigated in
quenched CPT. We study in detail the charge radii of the meson and baryon
octets, electromagnetic properties of the baryon decuplet, and the baryon
decuplet to octet electromagnetic transitions in both, quenched and partially
quenched CPT. We further show how effects due to the finite size of the lattice
can be accounted for in heavy meson CPT and calculate, as explicit examples,
neutral B meson mixing and the heavy-light meson decay constants. We also
demonstrate how one can account for effects due to finite lattice spacing in
the low-energy theories, considering as an example electromagnetic meson and
baryon properties.
  The results of our calculations are crucial to extrapolate quenched and
partially quenched lattice data from the heavier light quark masses used on the
lattice to the physical values.


title:
QCD thermodynamics from an imaginary mu_B: results on the four flavor
  lattice model

abstract:
  We study four flavor QCD at nonzero temperature and density by analytic
continuation from an imaginary chemical potential. The explored region is T =
0.95 T_c < T < 3.5 T_c, and the baryochemical potentials range from 0 to
approx. 500 MeV. Observables include the number density, the order parameter
for chiral symmetry, and the pressure, which is calculated via an integral
method at fixed temperature and quark mass. The simulations are carried out on
a 16^3 X 4 lattice, and the mass dependence of the results is estimated by
exploiting the Maxwell relations. In the hadronic region we confirm that the
results are consistent with a simple resonance hadron gas model, and we
estimate the critical density by combining the results for the number density
with those for the critical line. In the hot phase, above the endpoint of the
Roberge-Weiss transition T_E approx 1.1 T_c the results are consistent with a
free lattice model with a fixed effective number of flavor slightly different
from four. We confirm that confinement and chiral symmetry are coincident by a
further analysis of the critical line, and we discuss the interrelation between
thermodynamics and critical behavior. We comment on the strength and weakness
of the method, and propose further developments.


title: Sea quark effects in B_K from N_f=2 clover-improved Wilson fermions

abstract:
  We report calculations of the parameter B_K appearing in the Delta S=2
neutral kaon mixing matrix element, whose uncertainty limits the power of
unitarity triangle constraints for testing the standard model or looking for
new physics. We use two flavours of dynamical clover-improved Wilson lattice
fermions and look for dependence on the dynamical quark mass at fixed lattice
spacing. We see some evidence for dynamical quark effects and in particular B_K
decreases as the sea quark masses are reduced towards the up/down quark mass.