title:
D_s spectrum and leptonic decays with Fermilab heavy quarks and improved
  staggered light quarks

abstract:
  We present preliminary results for the D_s meson spectrum and decay constants
in unquenched lattice QCD. Simulations are carried out with 2+1 dynamical
quarks using gauge configurations generated by the MILC collaboration. We use
the ``asqtad'' a^2 improved staggered action for the light quarks, and the
clover heavy quark action with the Fermilab interpretation. We compare our
spectrum results with the newly discovered 0+ and 1+ states in the D_s system.


title:
Phase Fluctuation of Fermion Determinant in Lattice QCD at Finite
  Density

abstract:
  Once the quark chemical potential $\mu$ is introduced in finite density QCD,
the fermion determinant appeared in the path integral measure becomes complex.
In order to investigate the phase effect of SU(3) lattice QCD (2-flavors), we
calculated the fluctuation of the phase of $\det\Delta(\mu)$ on a $8^3\times4$
lattice at $\mu = 0.1$ and 0.2. Then we calculated the chiral condensate and
Polyakov line in the no phase and reweighted cases. There is little difference
between these two cases at $\mu = 0.1$ and 0.2. We consider a possible reason
for this result below $\mu \le 0.27$ in terms of $Z_3$ symmetry.


title:
Recent progress in calculating weak matrix elements using staggered
  fermions

abstract:
  We present a chronological review of the progress in calculating weak matrix
elements using staggered fermions. We review the perturbative calculation of
one-loop matching formula including both current-current diagrams and penguin
diagrams using improved staggered fermions. We also present preliminary results
of weak matrix elements relevant to CP violation calculated using the improved
(HYP (II)) staggered fermions. Since the complete set of matching coefficients
at the one-loop level became available recently, we have constructed lattice
operators with all the $g^2$ corrections included. The main results include
both $\Delta I = 3/2$ and $\Delta I = 1/2$ contributions.


title:
Solution of the Dirac equation in lattice QCD using a domain
  decomposition method

abstract:
  Efficient algorithms for the solution of partial differential equations on
parallel computers are often based on domain decomposition methods. Schwarz
preconditioners combined with standard Krylov space solvers are widely used in
this context, and such a combination is shown here to perform very well in the
case of the Wilson--Dirac equation in lattice QCD. In particular, with respect
to even-odd preconditioned solvers, the communication overhead is significantly
reduced, which allows the computational work to be distributed over a large
number of processors with only small parallelization losses.


title: On the phase diagram of quenched QCD with Wilson fermions

abstract:
  In this talk, I reported on recent work on the Aoki phase diagram for
quenched QCD with two flavors of Wilson fermions. Part of this work was done in
collaboration with Yigal Shamir, and a shorter account of this part appeared
recently. In this write-up, I will therefore limit myself to reporting on work
done with Steve Sharpe and Robert Singleton, Jr, which has not been published
yet. We discuss the symmetries of quenched QCD, paying careful attention to
non-perturbative issues. This allows us to derive an effective lagrangian which
agrees with standard quenched chiral perturbation theory, but which can also be
used to address questions of a non-perturbative nature.


title: Lattice measurement of the couplings g_infinity and g_Bstar_B_pi

abstract:
  We present the results of a quenched lattice QCD study of the coupling g_hat,
in the static heavy quark limit. After combining this with our previous results
obtained by using propagating heavy quarks with a mass around the physical
charm quark, we are able to interpolate to the b-quark sector. Our results are
g_hat_infinity = 0.48 +/- 0.03 +/- 0.11, g_hat_b = 0.58 +/- 0.06 +/- 0.10, and
g_Bstar_ B_p = 47 +/- 5 +/- 8.


title: Lattice QCD at finite T and \mu

abstract:
  Recent results of lattice QCD at finite temperature and density are reviewed.
At vanishing density the transition temperature, the equation of state and
hadron properties are discussed both for the pure gauge theory and for
dynamical staggered, Wilson and overlap fermions. The second part deals with
finite density. There are recent results for full QCD at finite temperature and
moderate density, while at larger densities QCD-like models are studied.


title: Simulation of Wilson fermion at finite isospin density

abstract:
  For QCD with Wilson fermions at isospin chemical potential we study the
finite phase transition on an $8^3\times4$ lattice at $\kappa=0.15$. We use two
gauge actions: Wilson action and DBW2 action. Both actions give the same
results. The phase diagram is qualitatively similar to the one obtained for QCD
at small baryon chemical potential. We also calculate the number density for
various isospin chemical potentials.


title: The pion electromagnetic form factor

abstract:
  A ratio of lattice correlation functions is identified from which the pion
form factor can be obtained directly. Preliminary results from quenched Wilson
simulations are presented.


title: Lattice regularized chiral perturbation theory

abstract:
  Chiral perturbation theory can be defined and regularized on a spacetime
lattice. A few motivations are discussed here, and an explicit lattice
Lagrangian is reviewed. A particular aspect of the connection between lattice
chiral perturbation theory and lattice QCD is explored through a study of the
Wess-Zumino-Witten term.


title: Dynamical Domain Wall Fermions

abstract:
  We report on an exploratory study of N_f=2 dynamical domain wall fermions and
the DBW2 gauge action at weak coupling. Details of improved simulation
algorithms and preliminary results for the hadron spectrum and renormalised
light and strange quark masses will be presented.


title: Description and comparison of Fat7-bar and HYP fat links

abstract:
  We study various methods of constructing fat links based upon the HYP (by
Hasenfratz & Knechtli) and Fat7-bar (by W. Lee) algorithms. We present the
minimum plaquette distribution for these fat links. This enables us to
determine which algorithm is most effective at reducing the spread of plaquette
values - a strong indicator of improved statistics for spectrum and static
potential measurements, among other quantities.


title: Center Dominance in SU(2) Gauge-Higgs Theory

abstract:
  We study the SU(2) gauge-Higgs system in D=4 dimensions, and analyze the
influence of the fundamental-representation Higgs field on the vortex content
of the gauge field. It is shown that center projected Polyakov lines, at low
temperature, are finite in the infinite volume limit, which means that the
center vortex distribution is consistent with color screening. In addition we
confirm and further investigate the presence of a "Kertesz-line" in the
strong-coupling region of the phase diagram, which we relate to the percolation
properties of center vortices. It is shown that this Kertesz-line separates the
gauge-Higgs phase diagram into two regions: a confinement-like region, in which
center vortices percolate, and a Higgs region, in which they do not. The free
energy of the gauge-Higgs system, however, is analytic across the Kertesz line.


title: B_K from Two-flavor Dynamical Domain Wall Fermions

abstract:
  We report preliminary results from an ongoing calculation of $B_K$ for
$N_f=2$ dynamical QCD with domain wall fermions. Simulations have been done
with three dynamical quark masses on $16^3 \times 32$ volumes with $L_s = 12$,
where the lattice spacing is $a^{-1} = 1.81(6)$ GeV. Using measurements on
$\sim 70$ lattices for each dynamical mass and extrapolating $\mdyn=\mval$ to
the kaon point, we find $B_K^{\rm \bar{MS}}(\mu=2{\rm GeV}) = 0.503(20)$.


title: Quarkonium at finite temperature

abstract:
  I discuss quarkonium spectral functions at finite temperature reconstructed
using the Maximum Entropy Method. I show in particular that the J/psi survives
in the deconfined phase up to 1.5Tc


title: Non-Perturbative Renormalization and the Fermilab Action

abstract:
  We discuss the application of the regularization independent (RI) scheme of
Rome/Southampton to determine the normalization of heavy quark operators
non-perturbatively using the Fermilab action.


title: Vector and chiral gauge theories on the lattice

abstract:
  We combine a pair of independent Weyl fermions to compose a Dirac fermion on
the four-dimensional Euclidean lattice. The obtained Dirac operator is
antihermitian and does not reproduce anomaly under the usual chiral
transformation. To simulate the correct chiral anomaly, we modify the chiral
transformation. We also show that chiral gauge theories can be constructed
nonperturbatively with exact gauge invariance. The formulation is based on a
doubler-free lattice derivative, which is a simple matrix defined as a discrete
Fourier transform of momentum with antiperiodic boundary conditions. Long-range
fermion hopping interactions are truncated using the Lanczos factor.


title: The Chiral Condensate of Strongly Coupled QCD in the 't Hooft Limit

abstract:
  Using the recently proposed generalization to an arbitrary number of colors
of the strong coupling approach to lattice gauge
theories\cite{Grignani:2003uv}, we compute the chiral condensate of massless
QCD in the 't Hooft limit.


title: Heavy Quarks and Lattice QCD

abstract:
  This paper is a review of heavy quarks in lattice gauge theory, focusing on
methodology. It includes a status report on some of the calculations that are
relevant to heavy-quark spectroscopy and to flavor physics.


title:
Lattice calculation of the lowest order hadronic contribution to the
  muon anomalous magnetic moment: an update with Kogut-Susskind fermions

abstract:
  I present a preliminary calculation of the hadronic vacuum polarization for
2+1 flavors of improved Kogut-Susskind quarks by utilizing a set of gauge
configurations recently generated by the MILC collaboration. The polarization
function $\Pi(q^2)$ is then used to calculate the lowest order (in
$\alpha_{QED}$) hadronic contribution to the muon anomalous magnetic moment.


title: Pion Mass Dependence of Nucleon Magnetic Moments

abstract:
  The relevance of the pion mass, provenient from a term which explicitely
breaks chiral symmetry in the Lagrangian, for nucleon magnetic moment in the
frame of the Skyrmion model in two different versions: the usual Skyrme model
and a modified one which includes a coupling to a light scalar meson field, the
sigma $\sigma (\simeq 500-600$ MeV). The results are compared to other
calculations. Our main motivation comes from usual extrapolations for values of
low energy QCD observables obtained in lattices with large values of pion/quark
masses toward realistic value of $m_{\pi}$. which do not allow it. We do a
comparison with results from the Cloudy Bag Model and a chiral hadronic model
from chiral perturbation theory. There are several resulting extrapolations
from the region of large pion mass to the realistic value depending on the
considered model for low energy QCD.


title: Monte Carlo Hamiltonian: Inverse Potential

abstract:
  The Monte Carlo Hamiltonian method developed recently allows to investigate
ground state and low-lying excited states of a quantum system, using Monte
Carlo algorithm with importance sampling. However, conventional MC algorithm
has some difficulties when applying to inverse potentials. We propose to use
effective potential and extrapolation method to solve the problem. We present
examples from the hydrogen system.


title:
Staggered versus overlap fermions: a study in the Schwinger model with
  $N_f=0,1,2$

abstract:
  We study the scalar condensate and the topological susceptibility for a
continuous range of quark masses in the Schwinger model with $N_f=0,1,2$
dynamical flavors, using both the overlap and the staggered discretization. At
finite lattice spacing the differences between the two formulations become
rather dramatic near the chiral limit, but they get severely reduced, at the
coupling considered, after a few smearing steps.


title: I=2 $\pi\pi$ scattering using G-parity boundary condition

abstract:
  To make the $\pi\pi$ state with non-zero relative momentum as the leading
exponential, we impose anti-periodic boundary condition on the pion, which is
implemented by imposing G-parity or H-parity on the quark fields at the
boundary. With this, we calculate the I=2 $\pi\pi$ phase shift from lattice
simulation by using L\"uscher's formula.


title: Further Improvements to Staggered Quarks

abstract:
  The improved staggered quark action has enabled breakthrough calculations of
QCD with three light dynamical quarks. The largest remaining $a^2$ scaling
violations come from "taste-changing" interactions, which are significantly
reduced over naive quarks because of carefully chosen smearing of the gauge
links. Here we examine further improvements to the quark action and show that
additional smearing of the links can reduce the taste-changing errors by
another factor of two, whilst retaining a fully $a^2$-improved action. The
taste-changing errors can be understood within a perturbative calculation of
the four-quark operators that appear at one-loop. We also discuss unquenching
techniques with such a highly improved action.


title:
Triviality of hierarchical O(N) spin model in four dimensions with large
  N

abstract:
  The renormalization group transformation for the hierarchical O(N) spin model
in four dimensions is studied by means of characteristic functions of
single-site measures, and convergence of the critical trajectory to the
Gaussian fixed point is shown for a sufficiently large N. In the strong
coupling regime, the trajectory is controlled by the help of the exactly solved
O(\infty) trajectory, while, in the weak coupling regime, convergence to the
Gaussian fixed point is shown by power decay of the effective coupling
constant.


title:
Electromagnetic fluxes, monopoles, and the order of the 4d compact U(1)
  phase transition

abstract:
  We consider the 4d compact U(1) gauge theory with extended action
  S=-beta sum_P cos theta_P -gamma sum_P cos 2 theta_P
  We give a full characterization of the phase diagram of this model using the
notion of flux. The relation with the usual monopole picture is discussed. In
analogy with the XY model we consider the helicity modulus \cite{Jose:1977gm}
for this theory, and show that it is an order parameter. Analyzing the
finite-size effects of the helicity modulus we conclude that the transition is
first-order. The value of this order parameter is related to the renormalized
coupling beta_R. We measure beta^c_R at the transition point and give a
counterexample to its conjectured universal value \cite{Cardy:jg}.


title: The helicity modulus in gauge field theories

abstract:
  We consider the 4d compact U(1) theory with Wilson action and characterize
its phase diagram using the notion of electromagnetic flux, instead of the more
usual magnetic monopole. Taking inspiration from the flux picture, we consider
the helicity modulus (h.m.) for this theory, and show that it is an order
parameter for the confinement deconfinement phase transition. We extend the
definition of the h.m. to an Abelian projected Yang-Mills theory, and discuss
its behavior in SU(2).


title: Twisted-mass lattice QCD with mass non-degenerate quarks

abstract:
  The maximally twisted lattice QCD action of an $SU_f(2)$ doublet of mass
degenerate Wilson quarks gives rise to a real positive fermion determinant and
it is invariant under the product of standard parity times the change of sign
of the coefficient of the Wilson term. The existence of this spurionic symmetry
implies that O($a$) improvement is either automatic or achieved through simple
linear combinations of quantities taken with opposite external three-momenta.
We show that in the case of maximal twist all these nice results can be
extended to the more interesting case of a mass non-degenerate quark pair.


title: A doubler-free lattice theory for QCD based on geometric fermions

abstract:
  We present doubler-free gauge-invariant lattice vector gauge action for some
real representations of Wilson gauge fields on an octet of fermions. It is
based on a geometric representation of the Dirac equation as an evolution
equation on the three-dimensional exterior bundle /(R^3) for a single bispinor
and of the bundle (/\x/)(R^3) for an octet. We find doubler-free lattice Dirac
operators for above bundles. A gauge-invariant connection with Wilson lattice
gauge fields is possible for some real representations of the gauge group. The
QCD action of SU(3) is of this type.
  Application in lattice QCD seems useful: We don't have to waste time and
memory for doublers as well as for correction terms to suppress them.


title: Dynamical overlap fermions, results with hybrid Monte-Carlo algorithm

abstract:
  We present first, exploratory results of a hybrid Monte-Carlo algorithm for
dynamical, n_f=2, four-dimensional QCD with overlap fermions. As expected, the
computational requirements are typically two orders of magnitude larger for the
dynamical overlap formalism than for the more conventional (Wilson or
staggered) formulations.


title: Recent development and perspectives of machines for lattice QCD

abstract:
  I highlight recent progress in cluster computer technology and assess status
and prospects of cluster computers for lattice QCD with respect to the
development of QCDOC and apeNEXT. Taking the LatFor test case, I specify a
512-processor QCD-cluster better than 1$/Mflops.


title:
Axial Correlation Functions in the epsilon-Regime: a Numerical Study
  with Overlap Fermions

abstract:
  We present simulation results employing overlap fermions for the axial
correlation functions in the epsilon-regime of chiral perturbation theory. In
this regime, finite size effects and topology play a dominant role. Their
description by quenched chiral perturbation theory is compared to our numerical
results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm
are necessary to interpret the numerical data obtained in distinct topological
sectors in terms of the epsilon-expansion. Such lattices are, however, still
substantially smaller than the ones needed in standard chiral perturbation
theory. However, we also observe severe difficulties at very low values of the
quark mass, in particular in the topologically trivial sector.


title: Application of DWF to heavy-light mesons

abstract:
  We consider application of domain wall fermions to quarks with relatively
heavy masses, aiming at precision calculations of charmed meson properties.
Preliminary results for a few basic quantities are presented.


title:
The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on
  anisotropic lattices

abstract:
  The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is
examined to extract the Hamiltonian limit, using standard path integral Monte
Carlo (PIMC) methods. We examine the mean plaquette and string tension and
compare them to results obtained within the Hamiltonian framework of Kogut and
Susskind. The results are a significant improvement upon previous Hamiltonian
estimates, despite the extrapolation procedure necessary to extract
observables. We conclude that the PIMC method is a reliable method of obtaining
results for the Hamiltonian version of the theory. Our results also clearly
demonstrate the universality between the Hamiltonian and Euclidean formulations
of lattice gauge theory. It is particularly important to take into account the
renormalization of both the anisotropy, and the Euclidean coupling $ \beta_E $,
in obtaining these results.


title:
The Study of Chiral Restoration using the Quark-Gluon Mixed Condensate
  g<\bar{q} \sigma G q> in Lattice QCD at Finite Temperature

abstract:
  The quark-gluon mixed condensate g<\bar{q} \sigma G q> is studied using
SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. Using
the lattices as \beta = 6.0 with 16^3 * N_t (N_t=16,12,10,8,6,4), \beta = 6.1
with 20^3 * N_t (N_t=20,12,10,8,6) and \beta = 6.2 with 24^3 * N_t
(N_t=24,16,12,10,8) in high statistics of 100-1000 gauge configurations, we
perform accurate measurement of the thermal effects on g<\bar{q} \sigma G q> as
well as <\bar{q}q> in the chiral limit. We find that the thermal effects on
both the condensates are very weak except for the vicinity of T_c, while both
the condensates suddenly vanish around T_c \simeq 280 MeV, which indicates
strong chiral restoration near 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, which means that these two different condensates
obey the same critical behavior. This nontrivial similarity between them would
impose constraints on the chiral structure of the QCD vacuum near T_c.


title:
Static potential, force, and flux-tube profile in 4D compact U(1)
  lattice gauge theory with the multi-level algorithm

abstract:
  The long range properties of four-dimensional compact U(1) lattice gauge
theory with the Wilson action in the confinement phase is studied by using the
multi-level algorithm. The static potential, force and flux-tube profile
between two static charges are successfully measured from the correlation
function involving the Polyakov loop. The universality of the coefficient of
the 1/r correction to the static potential, known as the Luescher term, and the
transversal width of the flux-tube profile as a function of its length are
investigated. While the result supports the presence of the 1/r correction, the
width of the flux tube shows an almost constant behavior at a large distance.


title:
Structure functions and form factors close to the chiral limit from
  lattice QCD

abstract:
  Results for nucleon matrix elements (arising from moments of structure
functions) and form factors from a mixture of runs using Wilson, clover and
overlap fermions (both quenched and unquenched) are presented and compared in
an effort to explore the size of the chiral `regime', lattice spacing errors
and quenching artefacts. While no run covers this whole range of effects the
partial results indicate a picture of small lattice spacing errors, small
quenching effects and only reaching the chiral regime at rather light quark
masses.


title: Analytic Smearing of SU(3) Link Variables in Lattice QCD

abstract:
  An analytic method of smearing link variables in lattice QCD is proposed and
tested. The differentiability of the smearing scheme with respect to the link
variables permits the use of modern Monte Carlo updating methods based on
molecular dynamics evolution for gauge-field actions constructed using such
smeared links. In examining the smeared mean plaquette and the static
quark-antiquark potential, no degradation in effectiveness is observed as
compared to link smearing methods currently in use, although an increased
sensitivity to the smearing parameter is found.


title: Finite Density Lattice Gauge Theories with Positive Fermion Determinants

abstract:
  We perform simulations of (3-colour) QCD with 2 quark flavours at a finite
chemical potential $\mu_I$ for isospin($I_3$), and of 2-colour QCD at a finite
chemical potential $\mu$ for quark number. At zero temperature, QCD at finite
$\mu_I$ has a mean-field phase transition at $\mu_I=m_\pi$ to a superfluid
state with a charged pion condensate which spontaneously breaks $I_3$. We study
the finite temperature transition as a function of $\mu_I$. For $\mu_I <
m_\pi$, where this is closely related to the transition at finite $\mu$, this
appears to be a crossover independent of quark mass, with no sign of the
proposed critical endpoint. For $\mu_I > m_\pi$ this becomes a true phase
transition where the pion condensate evaporates. For $\mu_I$ just above $m_\pi$
the transition seems to be second order, while for larger $\mu_I$ it appears to
become first order. At zero temperature, 2-colour QCD also possesses a
superfluid state with a diquark condensate. We study its spectrum of Goldstone
and pseudo-Goldstone bosons associated with chiral and quark-number symmetry
breaking.


title:
Improved gauge action on an anisotropic lattice II - Anisotropy
  parameter in the medium coupling region -

abstract:
  The quantum correction of the anisotropy parameter, $\eta$, is calculated for
$\xi=2$ and 3 in the $\beta$ region where numerical simulations such as hadron
spectroscopy are currently carried out, for the improved actions composed of
plaquette and rectangular 6-link loops. The $\beta$ dependences of $\eta$ for
the renormalization group improved actions are quite different from those of
the standard and Symanzik actions. In Iwasaki and DBW2 actions, $\eta$ stays
almost constant in a wide range of $\beta$, which also differs from the
one-loop perturbative result, while in the case of Symanzik action, it
increases as $\beta$ decreases, which is qualitatively similar to the
perturbative result, but the slope is steeper. In the calculation of the $\eta$
parameter close to and in the confined phase, we have applied the link
integration method to suppress the fluctuation of the gauge fields. Some
technical details are summarized.


title:
A Lattice Formulation of Super Yang-Mills Theories with Exact
  Supersymmetry

abstract:
  We construct super Yang-Mills theories with extended supersymmetry on
hypercubic lattices of various dimensions keeping one or two supercharges
exactly. Gauge fields are represented by ordinary unitary link variables, and
the exact supercharges are nilpotent up to gauge transformations. Among the
models, we show that the desired continuum theories are obtained without any
fine tuning of parameters for the cases ${\cal N}=2, 4, 8$ in two-dimensions.


title: Connecting short to long scales in the confining vacuum

abstract:
  We study approximate decimations in SU(N) LGT that connect the short to long
distance regimes. Simple `bond-moving' decimations turn out to provide both
upper and lower bounds on the exact partition function. This leads to a
representation of the exact partition function in terms of successive
decimations whose effective couplings flows are related to those of the easily
computable bond-moving decimations. The implications for a derivation of
confinement from first principles are discussed.


title: The pion mass in finite volume

abstract:
  We determine the relative pion mass shift $M_\pi(L)/M_\pi-1$ due to the
finite spatial extent $L$ of the box by means of two-flavor chiral perturbation
theory and the one-particle L\"uscher formula. We use as input the expression
for the infinite volume $\pi\pi$ forward scattering amplitude up to
next-to-next-to-leading order and can therefore control the convergence of the
chiral series. A comparison to the full leading order chiral expression for the
pion mass in finite volume allows us to check the size of subleading terms in
the large-$L$ expansion.


title: Lattice calculation of gluon screening masses

abstract:
  We study SU(3) gluon electric and magnetic masses at finite temperatures
using quenched lattice QCD on a $20^2 \times 32 \times 6$ lattice. We focus on
temperature regions between $T=T_c$ and $6T_c$, which are realized in BNL
Relativistic Heavy Ion Collider and CERN Large Hadron Collider experiments.
Stochastic quantization with a gauge-fixing term is employed to calculate gluon
propagators. The temperature dependence of the electric mass is found to be
consistent with the hard-thermal-loop perturbation, and the magnetic mass has
finite values in the temperature region of interest. Both screening masses have
little gauge parameter dependence. The behavior of the gluon propagators is
very different in confinement/deconfinement physics. The short distance
magnetic part behaves like a confined propagator even in the deconfinement
phase. A simulation with a larger lattice, $32^2 \times 48 \times 6 $, shows
that the magnetic mass has a stronger finite size effect than the electric
mass.


title:
Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov
  Subspace Methods

abstract:
  We investigate optimal choices for the (outer) iteration method to use when
solving linear systems with Neuberger's overlap operator in QCD. Different
formulations for this operator give rise to different iterative solvers, which
are optimal for the respective formulation. We compare these methods in theory
and practice to find the overall optimal one.For the first time, we apply the
so-called SUMR method of Jagels and Reichel to the shifted unitary version of
Neuberger's operator, and show that this method is in a sense the optimal
choice for propagator computations. When solving the ``squared'' equations in a
dynamical simulation with two degenerate flavours, it turns out that the CG
method should be used.


title:
Matter degrees of freedom and string breaking in Abelian projected
  quenched SU(2) QCD

abstract:
  In the Abelian projection the Yang--Mills theory contains Abelian gauge
fields (diagonal degrees of freedom) and the Abelian matter fields
(off-diagonal degrees) described by a complicated action. The matter fields are
essential for the breaking of the adjoint string. We obtain numerically the
effective action of the Abelian gauge and the Abelian matter fields in quenched
SU(2) QCD and show that the Abelian matter fields provide an essential
contribution to the total action even in the infrared region. We also observe
the breaking of an Abelian analog of the adjoint string using Abelian
operators. We show that the adjoint string tension is dominated by the Abelian
and the monopole contributions similarly to the case of the fundamental
particles. We conclude that the adjoint string breaking can successfully be
described in the Abelian projection formalism.


abstract:
  A quick review of the features of FermiQCD, a C++ library for fast
development of parallel Lattice QCD applications. FermiQCD is fully Object
Oriented and is based on MPI but, it required no previsius knowledge of
parallel programming. It includes parallel algorithms for Wilson, Clover,
Staggered, Asqtad and Domain Wall fermions. Optimizations are based on M.
Luescher's SSE2 macros.


title: Impact of the finite volume effects on the chiral behavior of fK and BK

abstract:
  We discuss the finite volume corrections to fK and BK by using the one-loop
chiral perturbation theory in full, quenched, and partially quenched QCD. We
show that the finite volume corrections to these quantities dominate the
physical (infinite volume) chiral logarithms.


title:
Center Vortex Model for the Infrared Sector of SU(3) Yang-Mills Theory -
  Confinement and Deconfinement

abstract:
  The center vortex model for the infrared sector of Yang-Mills theory,
previously studied for the SU(2) gauge group, is extended to SU(3). This model
is based on the assumption that vortex world-surfaces can be viewed as random
surfaces in Euclidean space-time. The confining properties are investigated,
with a particular emphasis on the finite-temperature deconfining phase
transition. The model predicts a very weak first order transition, in agreement
with SU(3) lattice Yang-Mills theory, and also reproduces a consistent behavior
of the spatial string tension in the deconfined phase. The geometrical
structure of the center vortices is studied, including vortex branchings, which
are a new property of the SU(3) case.


title:
Nonperturbative renormalisation of composite operators with overlap
  quarks

abstract:
  We compute non-perturbatively the renormalisation constants of composite
operators on a $16^3 \times 32 $ lattice with lattice spacing $a$ = 0.093 fm
for the overlap fermion action by using the regularisation independent (RI)
scheme. The quenched gauge configurations are generated by tadpole improved
plaquette plus rectangle action. We test the perturbative continuum relation
$Z_A = Z_V$ and $ Z_S=Z_P$ and find that they agree well above $\mu$ = 1.6 GeV.
We also perform a Renormalisation Group analysis at the next-to-next-to-leading
order and convert the renormalisation constants to the $\bar{MS}$ scheme.


title:
Discretization and Continuum Limit of Quantum Gravity on a
  Four-Dimensional Space-Time Lattice

abstract:
  The Regge Calculus is a powerful method to approximate a continuous manifold
by a simplicial lattice, keeping the connectivities of the underlying lattice
fixed and taking the edge lengths as degrees of freedom. The Discrete Regge
Model limits the choice of the link lengths to a finite number. We examine the
phase structure of Standard Regge Calculus in four dimensions and compare our
Monte Carlo results with those of the $Z_2$-Regge Model as well as with another
formulation of lattice gravity derived from group theoretical considerations.
Within all of the three models of quantum gravity we find an extension of the
well-defined phase to negative gravitational couplings and a new phase
transition. We calculate two-point functions between geometrical quantities at
the corresponding critical point and estimate the masses of the respective
interaction particles. A main concern in lattice field theories is the
existence of a continuum limit which requires the existence of a continuous
phase transition. The recently conjectured second-order transition of the
four-dimensional Regge skeleton at negative gravity coupling could be such a
candidate. We examine this regime with Monte Carlo simulations and critically
discuss its behavior.


title: Chiral perturbation theory for lattice QCD with a twisted mass term

abstract:
  Quantum Chromodynamics on a lattice with Wilson fermions and a chirally
twisted mass term for two degenerate quark flavours is considered in the
framework of chiral perturbation theory. The pion mass and decay constant are
calculated in next-to-leading order including terms linear in the lattice
spacing $a$.


title:
The photon propagator in compact QED_{2+1}: the effect of wrapping Dirac
  strings

abstract:
  We discuss the influence of closed Dirac strings on the photon propagator in
the Landau gauge emerging from a study of the compact U(1) gauge model in 2+1
dimensions. This gauge also minimizes the total length of the Dirac strings.
Closed Dirac strings are stable against local gauge-fixing algorithms only due
to the torus boundary conditions of the lattice. We demonstrate that these
left-over Dirac strings are responsible for the previously observed unphysical
behavior of the propagator of space-like photons (D_T) in the deconfinement
(high temperature) phase. We show how one can monitor the number N_3 of thermal
Dirac strings which allows to separate the propagator measurements into N_3
sectors. The propagator in N_3 \neq 0 sectors is characterized by a non--zero
mass and an anomalous dimension similarly to the confinement phase. Both mass
squared and anomalous dimension are found to be proportional to N_3.
Consequently, in the N_3=0 sector the unphysical behavior of the D_T photon
propagator is cured and the deviation from the free massless propagator
disappears.


title: Minimalist's Linux Cluster

abstract:
  Using barebone PC components and NIC's, we construct a linux cluster which
has 2-dimensional mesh structure. This cluster has smaller footprint, is less
expensive, and use less power compared to conventional linux cluster. Here, we
report our experience in building such a machine and discuss our current
lattice project on the machine.


title: Two Particle States in an Asymmetric Box

abstract:
  The exact two-particle energy eigenstates in an 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. 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: Teleparallel gravity on the lattice

abstract:
  We consider quantum gravity model with the squared curvature action. We
construct lattice discretization of the model (both on hypercubic and
simplicial lattices) starting from its teleparallel equivalent. The resulting
lattice models have the actions that are bounded from below while Einstein
equations (without matter) appear in their classical limit.


title: Supersymmetry on the lattice: where do predictions and results stand?

abstract:
  I summarize recent results in lattice supersymmetry with special attention to
N=1 Super Yang-Mills (SYM) theory.


title: Chiral extrapolation and physical insights

abstract:
  It has recently been established that finite-range regularisation in chiral
effective field theory enables the accurate extrapolation of modern lattice QCD
results to the chiral regime. We review some of the highlights of
extrapolations of quenched lattice QCD results, including spectroscopy and
magnetic moments. The $\Delta$ resonance displays peculiar chiral features in
the quenched theory which can be exploited to demonstrate the presence of
significant chiral corrections.


title: Actions for dynamical fermion simulations: are we ready to go?

abstract:
  A critical review, playing devil's advocate, on present dynamical fermion
simulations is given.


title: An Introduction to Lattice Chiral Fermions

abstract:
  This write-up starts by introducing lattice chirality to people possessing a
fairly modern mathematical background, but little prior knowledge about modern
physics. I then proceed to present two new and speculative ideas.


title:
On practical problems to compute the ghost propagator in SU(2) lattice
  gauge theory

abstract:
  In SU(2) lattice pure gauge theory we study numerically the dependence of the
ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau)
gauge. We find that the effect of Gribov copies is essential in the scaling
window region, however, it tends to decrease with increasing beta. On the other
hand, we find that at larger beta-values very strong fluctuations appear which
can make problematic the calculation of the ghost propagator.


title: Lattice Sigma Models with Exact Supersymmetry

abstract:
  We show how to construct lattice sigma models in one, two and four dimensions
which exhibit an exact fermionic symmetry. These models are discretized and
{\it twisted} versions of conventional supersymmetric sigma models with N=2
supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built
from the original supercharges. The lattice theories possess local actions and
in many cases admit a Wilson term to suppress doubles. In the two and four
dimensional theorie s we show that these lattice theories are invariant under
additional discrete symmetries. We argue that the presence of these exact
symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry
in the continuum limit. As a concrete example we show preliminary numerical
results from a simulation of the O(3) supersymmetric sigma model in two
dimensions.


title:
SO(3) vs. SU(2) Yang-Mills theory on the lattice: an investigation at
  non-zero temperature

abstract:
  The adjoint SU(2) lattice gauge theory in 3+1 dimensions with the Wilson
plaquette action modified by a Z(2) monopole suppression term is reinvestigated
with special emphasis on the existence of a finite-temperature phase transition
decoupling from the well-known bulk transitions.


title: Lattice simulations of 2-colour QCD with Wilson fermions

abstract:
  We report on the status of our simulations of two-colour QCD with two
flavours of Wilson quarks, at nonzero chemical potential and diquark source.
Preliminary results are presented for the static quark potential, gluon
propagator, and meson and diquark spectrum.


title: Baryon operators and spectroscopy in lattice QCD

abstract:
  The construction of the operators and correlators required to determine the
excited baryon spectrum is presented, with the aim of exploring the spatial and
spin structure of the states while minimizing the number of propagator
inversions. The method used to construct operators that transform irreducibly
under the symmetries of the lattice is detailed, and the properties of example
operators are studied using domain-wall fermion valence propagators computed on
MILC asqtad dynamical lattices.


title: Two Nucleons on a Lattice

abstract:
  The two-nucleon sector is near an infrared fixed point of QCD and as a result
the S-wave scattering lengths are unnaturally large compared to the effective
ranges and shape parameters. It is usually assumed that a lattice QCD
simulation of the two-nucleon sector will require a lattice that is much larger
than the scattering lengths in order to extract quantitative information. In
this paper we point out that this does not have to be the case: lattice QCD
simulations on much smaller lattices will produce rigorous results for nuclear
physics.


title:
Effective String Picture for Confining Gauge Theories at Finite
  Temperature

abstract:
  We study the ``effective string picture'' of confinement, deriving
theoretical predictions for the interquark potential at finite temperature. At
low temperatures, the leading string correction to the linear confining
potential between a heavy quark-antiquark pair is the "L\"uscher term''.
Assuming a Nambu-Goto effective string action, subleading contributions can be
worked out in an analytical way. We also discuss the contribution given by a
possible ``boundary term'' in the effective action, and compare these
predictions with high precision results from simulations of lattice Z(2) gauge
theory in three dimensions, obtained with an algorithm that exploits the
duality of the Z(2) gauge model with the Ising spin model.


title: Study of QCD thermodynamics at finite density by Taylor expansion

abstract:
  We discuss the phase structure and the equation of state for QCD at non-zero
temperature and density. Derivatives of $\ln Z$ with respect to quark chemical
potential $\mu_q$ up to fourth order are calculated for 2-flavor QCD, enabling
estimates of the pressure, quark number density and associated susceptibilities
as functions of $\mu_q$ via a Taylor series expansion. Also, the phase
transition line for 2 and 3-flavor QCD and the critical endpoint in the $(T,
\mu_q)$ plane are investigated in the low density regime.


title: Excited B mesons from the lattice

abstract:
  We determine the energies of the excited states of a heavy-light meson
$Q\bar{q}$, with a static heavy quark and light quark with mass approximately
that of the strange quark from both quenched lattices and with dynamical
fermions. We are able to explore the energies of orbital excitations up to L=3,
the spin-orbit splitting up to L=2 and the first radial excitation. These $b
\bar{s}$ mesons will be very narrow if their mass is less than 5775 MeV -- the
$BK$ threshold. We investigate this in detail and present evidence that the
scalar meson (L=1) will be very narrow and that as many as 6 $b \bar{s}$
excited states will have energies close to the $BK$ threshold and should also
be relatively narrow.


title: Mesonic Form Factors

abstract:
  We have started a program to compute the electromagnetic form factors of
mesons. We discuss the techniques used to compute the pion form factor and
present preliminary results computed with domain wall valence fermions on MILC
asqtad lattices, as well as Wilson fermions on quenched lattices. These methods
can easily be extended to rho-to-gamma-pi transition form factors.


title: Anisotropic lattices for precision computations in heavy flavor physics

abstract:
  We study the anisotropic lattice QCD for precision computations of
heavy-light matrix elements. Our previous study in which the lattices are
calibrated with a few percent accuracy has already given results comparable to
the existing calculations. This suggests that even higher precision may be
achieved by a more precise calibration of anisotropic lattices. We describe our
strategy to tune the gauge and quark parameters with accuracies much less than
1 % in the quenched approximation.


title: Numerical study of staggered fermion on anisotropic lattices

abstract:
  We study calibration procedures of the staggered quarks on anisotropic
lattices in the quenched approximation and in $N_f = 2$ dynamical simulations.
For the calibration conditions we adopt the hadronic radii $r_0$ and the meson
masses in the temporal and spatial directions. On the quenched lattice, we
calibrate the quark field and compare the result with the result determined
using the meson dispersion relation. In dynamical simulations, we determine the
anisotropy parameters $\gamma_G$ and $\gamma_F$ simultaneously within 1%
accuracy at renormalized anisotropy $\xi = a_s/a_t = 4$.


title:
Non-perturbative calculation of $Z_V$ and $Z_A$ in domain-wall QCD on a
  finite box

abstract:
  We report on a non-perturbative evaluation of the renormalization factors for
the vector and axial-vector currents, $Z_V$ and $Z_A$, in the quenched
domain-wall QCD (DWQCD) with plaquette and renormalization group improved gauge
actions. We take the Dirichlet boundary condition for both gauge and
domain-wall fermion fields on the finite box, and introduce the flavor-chiral
Ward-Takahashi identities to calculate the renormalization factors. As a test
of the method, we numerically confirm the expected relation that $Z_V \simeq
Z_A$ in DWQCD. Employing two different box sizes for the numerical simulations
at several values of the gauge coupling constant $g^2$ and the domain-wall
height $M$, we extrapolate $Z_V$ to the infinite volume to remove $a/L$ errors.
We finally give the interpolation formula of $Z_V$ in the infinite volume as a
function of $g^2$ and $M$.


title: Low-energy couplings of QCD from topological zero-mode wave functions

abstract:
  By matching 1/m^2 divergences in finite-volume two-point correlation
functions of the scalar or pseudoscalar densities with those obtained in chiral
perturbation theory, we derive a relation between the Dirac operator zero-mode
eigenfunctions at fixed non-trivial topology and the low-energy constants of
QCD. We investigate the feasibility of using this relation to extract the pion
decay constant, by computing the zero-mode correlation functions on the lattice
in the quenched approximation and comparing them with the corresponding
expressions in quenched chiral perturbation theory.


title: Scaling test for Wilson twisted mass QCD

abstract:
  We present a first scaling test of twisted mass QCD with pure Wilson quarks
for a twisting angle of pi/2. We have computed the vector meson mass and the
pseudoscalar decay constant for different values of beta at fixed value of r_0
m_PS. The results obtained in the quenched approximation are compared with data
for pure Wilson and non-perturbatively O(a) improved Wilson computations. We
show that our results from Wilson twisted mass QCD show clearly reduced lattice
spacing errors, consistent with O(a) improvement and without the need of any
improvement terms added. These results thus provide numerical evidence of the
prediction in ref. [1].


title: Transverse Structure of Nucleon Parton Distributions from Lattice QCD

abstract:
  This work presents the first calculation in lattice QCD of three moments of
spin-averaged and spin-polarized generalized parton distributions in the
proton. It is shown that the slope of the associated generalized form factors
decreases significantly as the moment increases, indicating that the transverse
size of the light-cone quark distribution decreases as the momentum fraction of
the struck parton increases.


title: Heavy quark free energies and the renormalized Polyakov loop in full QCD

abstract:
  We study the renormalized free energy of a heavy quark anti-quark pair in the
different colour channels in full QCD at finite temperature. Similarities and
differences to the quenched case are discussed and the temperature dependence
as well as their short distance behavior are analyzed. The asymptotic large
distance behavior of the free energy is used to define the non-perturbatively
renormalized Polyakov loop which is well behaved in the continuum limit.


title: Effective heavy-light meson energies in small-volume quenched QCD

abstract:
  We study effective energies of heavy-light meson correlation functions in
lattice QCD and a small volume of (0.2 fm)^4 to non-perturbatively calculate
their dependence on the heavy quark mass in the continuum limit. Our quenched
results obtained here constitute an essential intermediate step of a first
fully non-perturbative computation of the b-quark's mass in the static
approximation that has recently been presented as an application of a new
proposal to non-perturbatively renormalize the Heavy Quark Effective Theory.
The renormalization constant and the improvement coefficients relating the
renormalized current and subtracted quark mass are determined in the relevant
parameter region at weak couplings, which allows to perform the numerical
simulations at several, precisely fixed values of the renormalization group
invariant heavy quark mass in a range from 3 GeV to 15 GeV.


title:
One-Loop Matching of the Heavy-Light A_0 and V_0 Currents with NRQCD
  Heavy and Improved Naive Light Quarks

abstract:
  One-loop matching of heavy-light currents is carried out for a highly
improved lattice action, including the effects of dimension 4 O(1/M) and O(a)
operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive
action for light quarks, and the Symanzik improved glue action. As part of the
matching procedure we also present results for the NRQCD self energy and for
massless Asqtad quark wavefunction renormalization with improved glue.


title: Spontaneous violation of CP symmetry in the strong interactions

abstract:
  Some time ago Dashen pointed out that spontaneous CP violation can occur in
the strong interactions. I show how a simple effective Lagrangian exposes the
remarkably large domain of quark mass parameters for which this occurs. I close
with some warnings for lattice simulations.


title:
Excitations of the static quark-antiquark system in several gauge
  theories

abstract:
  The spectrum of gluons in the presence of a static quark-antiquark pair is
studied using Monte Carlo simulations on anisotropic space-time lattices. For
very small quark-antiquark separations R, the level orderings and approximate
degeneracies disagree with the expectations from an effective string theory. As
the quark-antiquark separation R increases, a dramatic rearrangement of the
energies occurs, and above 2 fm, all of the levels studied show behavior
consistent with an effective string description. The energy spacings are nearly
pi/R, but a tantalizing fine structure remains. In addition to 4-dimensional
SU(3) gauge theory, results from 3-dimensional SU(2) and compact U(1) gauge
theories are also presented.


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

abstract:
  We study expectation values related to the dynamical lattice spacing that
occurs in the recent supersymmetric 2d lattice Yang-Mills constructions of
Cohen et al. [hep-lat/0307012]. For the purposes of this preliminary analysis,
we restrict our attention to the bosonic part of that theory. That is, we
compute observables in the fully quenched ensemble, equivalent to
non-supersymmetric 2d lattice Yang-Mills with a dynamical lattice spacing and
adjoint scalars. Our numerical simulations indicate difficulties with the
proposed continuum limit. We find that expectation values tend to those of the
undeformed ``daughter theory,'' in spite of the deformation suggested by Cohen
et al. In an effort to understand these results, we examine the zero action
configurations, with and without the deformation. Based on these
considerations, we are able to interpret the simulation results in terms of
entropic effects.


title: General chiral gauge theories

abstract:
  Only requiring that Dirac operators decribing massless fermions on the
lattice decompose into Weyl operators we arrive at a large class of them. After
deriving general relations from spectral representations we study correlation
functions of Weyl fermions for any value of the index, stressing the related
conditions for basis transformations and getting the precise behaviors under
gauge and CP transformations. Using the detailed structure of the chiral
projections we also obtain a form of the correlation functions with a
determinant in the general case.


title:
The Deconfinement Phase Transition of Sp(2) and Sp(3) Yang-Mills
  Theories in 2+1 and 3+1 Dimensions

abstract:
  Some time ago, Svetitsky and Yaffe have argued that -- if the deconfinement
phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is
second order -- it should be in the universality class of a d-dimensional spin
model symmetric under the center of G. For d=3 these arguments have been
confirmed numerically only in the SU(2) case with center Z(2), simply because
all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order
phase transitions. The symplectic groups Sp(N) also have the center Z(2) and
provide another extension of SU(2) = Sp(1) to general N. Using lattice
simulations, we find that the deconfinement phase transition of Sp(2)
Yang-Mills theory is first order in 3+1 dimensions, while in 2+1 dimensions
stronger fluctuations induce a second order transition. In agreement with the
Svetitsky-Yaffe conjecture, for (2+1)-d Sp(2) Yang-Mills theory we find the
universal critical behavior of the 2-d Ising model. For Sp(3) Yang-Mills theory
the transition is first order both in 2+1 and in 3+1 dimensions. This suggests
that the size of the gauge group -- and not the center symmetry -- determines
the order of the deconfinement phase transition.


title:
Pion structure from improved lattice QCD: form factor and charge radius
  at low masses

abstract:
  The charge form factor of the pion is calculated in lattice QCD. The
non-perturbatively improved Sheikholeslami-Wohlert action is used together with
the $\mathcal{O}(a)$ improved vector current. Other choices for the current are
examined. The form factor is extracted for pion masses from 970 MeV down to 360
MeV and for momentum transfers $Q^2 \leq 2 \mathrm{GeV}^2$. The mean square
charge radius is extracted, compared to previous determinations and its
extrapolation to lower masses discussed.


title:
A note on the power divergence in lattice calculations of $\Delta I =
  1/2$ $K\to\pi\pi$ amplitudes at $M_{K}=M_{\pi}$

abstract:
  In this note, we clarify a point concerning the power divergence in lattice
calculations of $\Delta I = 1/2$ $K\to\pi\pi$ decay amplitudes. There have been
worries that this divergence might show up in the Minkowski amplitudes at
$M_{K}=M_{\pi}$ with all the mesons at rest. Here we demonstrate, via an
explicit calculation in leading-order Chiral Perturbation Theory, that the
power divergence is absent at the above kinematic point, as predicted by CPS
symmetry.


abstract:
  A simplified test of universality in Lattice QCD is performed by analytically
evaluating the continuous Euclidean time limits of various lattice fermion
determinants, both with and without a Wilson term to lift the fermion doubling
on the Euclidean time axis, and comparing them with each other and with the
zeta-regularised fermion determinant in the continuous time--lattice space
setting. The determinant relations expected from universality considerations
are found to be violated by a certain gauge field-dependent factor, i.e. we
uncover a "universality anomaly". The physical significance, or lack thereof,
of this factor is a delicate question which remains to be settled.


title:
The Calculation of Critical Parameters in SU(2) Gauge Theory with
  Kouvel-Fisher Method

abstract:
  We calculate the critical coupling $4/g_c^2$ and critical exponent $\beta$
for the order parameter in SU(2) lattice gauge theory by applying of the finite
size scaling technique and the method proposed by Kouvel and Fisher for
analysis of experimental data. In contrast to the standard finite size scaling
approach, this method allows to determine simultaneously both $g_c^2/4$ and
$\beta$ as two parameters of the linear fit to the Monte-Carlo data.


title: A Finite Baryon Density Algorithm

abstract:
  I will review the progress toward a finite baryon density algorithm in the
canonical ensemble approach which entails particle number projection from the
fermion determinant. These include an efficient Pad\'{e}-Z$_2$ stochastic
estimator of the $Tr \log$ of the fermion matrix and a Noisy Monte Carlo update
to accommodate unbiased estimate of the probability. Finally, I will propose a
Hybrid Noisy Monte Carlo algorithm to reduce the large fluctuation in the
estimated $Tr \log$ due to the gauge field which should improve the acceptance
rate. Other application such as treating $u$ and $d$ as two separate flavors is
discussed.


title: Large N QCD -- Continuum reduction

abstract:
  Numerical evidence combined with Eguchi-Kawai reduction indicate that there
are no finite volumes effects in the large N limit of QCD as long as the linear
extent of the four-torus is bigger than a critical size. This is referred to as
continuum reduction. Since fermions in the fundamental representation are
naturally quenched in the large N limit, as long as we only have a finite
number of flavors, continuum reduction provides us with the exciting
possibility to numerically solve large N QCD using chiral fermions and present
day computers.


title:
Calculation of Finite Size Effects on the Nucleon Mass in Unquenched QCD
  using Chiral Perturbation Theory

abstract:
  The finite size effects on nucleon masses are calculated in relativistic
chiral perturbation theory. Results are compared with two-flavor lattice
results.


title:
The nucleon mass in N_f=2 lattice QCD: finite size effects from chiral
  perturbation theory

abstract:
  In the framework of relativistic SU(2)_f baryon chiral perturbation theory we
calculate the volume dependence of the nucleon mass up to and including O(p^4).
Since the parameters in the resulting finite size formulae are fixed from the
pion mass dependence of the large volume nucleon masses and from phenomenology,
we obtain a parameter-free prediction of the finite size effects. We present
mass data from the recent N_f=2 simulations of the UKQCD and QCDSF
collaborations and compare these data as well as published mass values from the
dynamical simulations of the CP-PACS and JLQCD collaborations with the
theoretical expectations. Remarkable agreement between the lattice data and the
predictions of chiral perturbation theory in a finite volume is found.


title:
Detailed Lattice-QCD Study for the Three-Quark Potential and Y-type
  Flux-Tube Formation

abstract:
  We study the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$
and the excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ using SU(3) lattice
Q CD. From the accurate and thorough calculation for more than 300 different
patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm
g.s.}$ is found to be well described by the Coulomb plus Y-type linear
potential, i.e., Y-ansatz, within 1%-level deviation. With lattice QCD, we
calculate also the excited-state potential in the 3Q system, and find the
gluonic excitation energy, $V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$, to be
about 1 GeV. This large gluonic-excitation energy would play an essential role
to the success of the quark model for the low-lying hadrons in terms of the
absence of the gluonic mode.


title:
Vacuum Polarisation and Hadronic Contribution to muon g-2 from Lattice
  QCD

abstract:
  We compute the vacuum polarisation on the lattice in quenched QCD using
non-perturbatively improved Wilson fermions. Above Q^2 of about 2 GeV^2 the
results are very close to the predictions of perturbative QCD. Below this scale
we see signs of non-perturbative effects which we can describe by the use of
dispersion relations. We use our results to estimate the light quark
contribution to the muon's anomalous magnetic moment. We find the result
446(23) x 10^{-10}, where the error only includes statistical uncertainties.
Finally we make some comments on the applicability of the Operator Product
Expansion to our data.


title: Negative-Parity Baryons in Quenched Anisotropic Lattice QCD

abstract:
  We study negative-parity baryon spectra in quenched anisotropic lattice QCD.
The negative-parity baryons are measured as the parity partner of the
ground-state baryons. In addition to the flavor octet and decuplet baryons, we
pay much attention to the flavor-singlet negative-parity baryon as a
three-quark state and compare it with the Lambda(1405) baryon. Numerical
results of the flavor octet and decuplet negative-parity baryon masses are
close to experimental values of lowest-lying negative-parity baryons, while the
flavor-singlet baryon is much heavier than Lambda(1405). This indicates that
the Lambda(1405) would be a multi-quark state such as the N-Kbar molecule
rather than the flavor-singlet 3 quark state.


title: The Yang-Mills Spectrum from a 2-level Algorithm

abstract:
  We investigate in detail a 2-level algorithm for the computation of 2-point
functions of fuzzy Wilson loops in lattice gauge theory. Its performance and
the optimization of its parameters are described in the context of 2+1D SU(2)
gluodynamics. In realistic calculations of glueball masses, it is found that
the reduction in CPU time for given error bars on the correlator at
time-separation ~0.2fm, where a mass-plateau sets in, varies between 1.5 and 7
for the lightest glueballs in the non-trivial symmetry channels; only for the
lightest glueball is the 2-level algorithm not helpful. For the heavier states,
or for larger time-separations, the gain increases as expected exponentially in
(mt). We present further physics applications in 2+1 and 3+1 dimensions and for
different gauge groups that confirm these conclusions.


title: Topological Charge Evolution in the Markov-Chain of QCD

abstract:
  The topological charge is studied on lattices of large physical volume and
fine lattice spacing. We illustrate how a parity transformation on the SU(3)
link-variables of lattice gauge configurations reverses the sign of the
topological charge and leaves the action invariant. Random applications of the
parity transformation are proposed to traverse from one topological charge sign
to the other. The transformation provides an improved unbiased estimator of the
ensemble average and is essential in improving the ergodicity of the Markov
chain process.


title: Propagators and running coupling from SU(2) lattice gauge theory

abstract:
  We perform numerical studies of the running coupling constant alpha_R(p^2)
and of the gluon and ghost propagators for pure SU(2) lattice gauge theory in
the minimal Landau gauge. Different definitions of the gauge fields and
different gauge-fixing procedures are used respectively for gaining better
control over the approach to the continuum limit and for a better understanding
of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex
renormalization constant is finite in the continuum limit, confirming earlier
results by all-order perturbation theory. In the low momentum regime, the gluon
form factor is suppressed while the ghost form factor is divergent.
Correspondingly, the ghost propagator diverges faster than 1/p^2 and the gluon
propagator appears to be finite. Precision data for the running coupling
alpha_R(p^2) are obtained. These data are consistent with an IR fixed point
given by lim_{p \to 0} alpha_R(p^2) = 5(1).


title: Behavior of Charmonium Systems after Deconfinement

abstract:
  We present a study of charmonia in hot gluonic plasma, for temperatures upto
three times the deconfinement transition temperature Tc. q \bar{q} systems with
quark masses close to the charm mass and different spin-parity quantum numbers
were studied on very fine isotropic lattices. The analysis of temporal
correlators, and spectral functions constructed from them, shows that the J/psi
and eta_c survive up to quite high temperatures, with little observable change
up to 1.5 Tc, and then gradually weakening and disappearing by 3 Tc. For the
scalar and axial vector channels, serious modifications are induced by the hot
medium already close to Tc, possibly dissociating the mesons by 1.1 Tc.


title: Density of States Method at Finite Isospin Density

abstract:
  The density of states method is applied for lattice QCD at a finite isospin
density. The advantage of this method is that one can easily obtain results for
various values of parameters (quark mass, coupling constant and the number of
flavors). We compare results for the chiral condensate and the quark number
density with those from the R-algorithm and find that they are in good
agreement. By calculating the chiral condensate we obtain information on the
phase structure for various quark flavors and isospin chemical potentials. We
also show results for the chiral condensate at two different quark masses and
at two different isospin densities which are not easily obtainable in the
conventional Monte Carlo method.


title:
A new scheme for the Klein-Gordon and Dirac fields on the lattice with
  axial anomaly

abstract:
  Using the method of finite differences a scheme is proposed to solve exactly
the Klein-Gordon and Dirac free field equations, in a (1+1)-dimensional
lattice. The hamiltonian of the Dirac field is translational invariant,
hermitian, avoids fermion doubling, and, for the massless case, preserves
global chiral symmetry. Coupling the fermion field to the electromagnetic
vector potential we construct a gauge invariant vector current leading to the
correct axial anomaly.


title: Properties of Thermal Glueballs

abstract:
  We study the properties of the 0++ glueball at finite temperature using SU(3)
quenched lattice QCD. We find a significant thermal effects near T_c. We
perform the \chi^2 fit analyses adopting two Ansaetze for the spectral
function, i.e., the conventional narrow-peak Ansatz and an advanced
Breit-Wigner Ansatz. The latter is an extension of the former, taking account
of the appearance of the thermal width at T>0. We also perform the MEM
analysis. These analyses indicate that the thermal effect on the glueball is a
significant thermal-width broadening \Gamma(T_c) \sim 300 MeV together with a
modest reduction in the peak center \Delta\omega_0(T_c) \sim 100 MeV.


title:
A relativistic invariant scheme for the quantum Klein-Gordon and Dirac
  fields on the lattice

abstract:
  We explore the connection between the symmetry transformations and
conservation laws for the Klein-Gordon and Dirac fields on the lattice. The
generators of the space time translations and Lorentz boost (defined on the
lattice) are constants of motion and satisfy the standard commutation
relations.


title:
Representations of classical groups on the lattice and its application
  to the field theory on discrete space-time

abstract:
  We explore the mathematical consequences of the assumption of a discrete
space-time. The fundamental laws of physics have to be translated into the
language of discrete mathematics. We find integral transformations that leave
the lattice of any dimension invariant and apply these transformations to field
equations.


title: Primordial function and ambiguity in its determination

abstract:
  We study the possibility to reconstruct the primordial function for some
periodic function. The procedure includes an analytical continuation of a
discrete function for Fourier coefficients computation, that introduces an
ambiguity. To establish conditions under which no ambiguity appears, the
modification of Carlson theorem is suggested. In a case when no subsidiary
condition is imposed, ambiguity in the definition of primordial function does
not go beyond the functions which belong to space $\Omega^{\prime}$.


title: A realistic interpretation of lattice gauge theories

abstract:
  Following recent assumptions to unify quantum mechanics and general
relativity, the structure of spacetime is suppose to be a consequence of the
relations among some fundamental objects, and its concept can be formulated
without the reference to the intuition. As physical consequences the continuous
laws should be translated in to difference equations and the lattice field
theories should be interpreted as a realistic model.


title: Discrete Differential Geometry and Lattice Field Theory

abstract:
  We develope a difference calculus analogous to the differential geometry by
translating the forms and exterior derivatives to similar expressions with
difference operators, and apply the results to fields theory on the lattice
[Ref. 1]. Our approach has the advantage with respect to other attempts [Ref.
2-6] that the Lorentz invariance is automatically preserved as it can be seen
explicitely in the Maxwell, Klein-Gordon and Dirac equations on the lattice.


title: Y-type Flux-Tube Formation in Baryons

abstract:
  For more than 300 different patterns of the 3Q systems, the ground-state 3Q
potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated using SU(3) lattice QCD with
$12^3\times 24$ at $\beta=5.7$ and $16^3\times 32$ at $\beta=5.8, 6.0$ at the
quenched level. As a result of the detailed analyses, we find that the
ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is well described with so-called
Y-ansatz as $V_{\rm 3Q}=-A_{\rm 3Q}\sum_{i<j}\frac1{|{\bf r}_i-{\bf r}_j|}
+\sigma_{\rm 3Q} L_{\rm min}+C_{\rm 3Q}$, with the accuracy better than 1%.
Here, $L_{\rm min}$ denotes the minimal value of total flux-tube length. We
also studythe excited-state potential $V_{\rm 3Q}^{\rm e.s.}$ using lattice QCD
with $16^3\times 32$ at $\beta=5.8, 6.0$ for more than 100 patterns of the 3Q
systems. The energy gap between $V_{\rm 3Q}^{\rm g.s.}$ and $V_{\rm 3Q}^{\rm
e.s.}$, which physically means the gluonic excitation energy, is found to be
about 1 GeV in the typical hadronic scale. Finally, we suggest a possible
scenario which connects the success of the quark model to QCD.


title:
Connecting Lattice QCD with Chiral Perturbation Theory at Strong
  Coupling

abstract:
  We study the difficulties associated with detecting chiral singularities
predicted by chiral perturbation theory (ChPT) in lattice QCD. We focus on the
physics of the remnant O(2) chiral symmetry of staggered fermions in the strong
coupling limit using the recently discovered directed path algorithm. Since it
is easier to look for power-like singularities as compared to logarithmic ones,
our calculations are performed at a fixed finite temperature in the chirally
broken phase. We show that the behavior of the chiral condensate, the pion mass
and the pion decay constant, for small masses, are all consistent with the
predictions of ChPT.
  However, the values of the quark masses that we need to demonstrate this are
much smaller than those being used in dynamical QCD simulations. We also need
to use higher order terms in the chiral expansion to fit our data.


title:
Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge
  Theories

abstract:
  We show that the confining property of the one-gluon propagator, in Coulomb
gauge, is linked to the unbroken realization of a remnant gauge symmetry which
exists in this gauge. An order parameter for the remnant gauge symmetry is
introduced, and its behavior is investigated in a variety of models via
numerical simulations. We find that the color-Coulomb potential, associated
with the gluon propagator, grows linearly with distance both in the confined
and - surprisingly - in the high-temperature deconfined phase of pure
Yang-Mills theory. We also find a remnant symmetry-breaking transition in SU(2)
gauge-Higgs theory which completely isolates the Higgs from the
(pseudo)confinement region of the phase diagram. This transition exists despite
the absence, pointed out long ago by Fradkin and Shenker, of a genuine
thermodynamic phase transition separating the two regions.


title: A partially quenched analysis of the eta-eta' system in N_f=2 QCD

abstract:
  We report on a first, comprehensive partially quenched study of the eta-eta'
problem, based on SESAM configurations on a 16^3x32 lattice at beta=5.6 QCD
with two (mass degenerate) active sea quark flavours. By means of the spectral
approximation of the two-loop (hairpin) diagrams, we find clear plateau
formation in the effective masses which enables us both to determine the
eta-eta' mass matrix and the alpha-parameter in the effective chiral Lagrangian
for the flavour singlet sector, alpha=0.028 +- 0.013.


title: Computing the eta and eta' Mesons in Lattice QCD

abstract:
  It has been known for a long time that the large experimental singlet-octet
mass gap in the pseudoscalar meson mass spectrum originates from the anomaly of
the axial vector current, i.e. from nonperturbative effects and the nontrivial
topological structure of the QCD vacuum. In the N_colour -> infinity limit of
the theory, this connection elucidates in the famous Witten-Veneziano relation
between the eta'-mass and the topological susceptibility of the quenched QCD
vacuum.While lattice QCD has by now produced impressive high precision results
on the flavour nonsinglet hadron spectrum, the determination of the
pseudoscalar singlet mesons from direct correlator studies is markedly lagging
behind, due to the computational complexity in handling observables that
include OZI-rule violating diagrams, like the eta' propagator. In this article,
we report on some recent progress in dealing with the numerical bottleneck
problem.


title:
Discrete reflection groups and induced representations of Poincare group
  on the lattice

abstract:
  We continue the program, presented in previous Symposia, of discretizing
physical models. In particular we calculate the integral Lorentz
transformations with the help of discrete reflection groups, and use them for
the covariance of Klein-Gordon and Dirac wave equation on the lattice. Finally
we define the unitary representation of Poincar group on discrete momentum and
configuration space, induced by integral representations of its closed
subgroup.


title: Least-Squared Optimized Polynomials for Smeared Link Actions

abstract:
  We introduce a numerical method for generating the approximating polynomials
used in fermionic calculations with smeared link actions. We investigate the
stability of the algorithm and determine the optimal weight function and the
optimal type of discretization. The achievable order of polynomial
approximation reaches several thousands allowing fermionic calculations using
the Hypercubic Smeared Link action even with physical quark masses.


title:
Induced representations of Poincare group on the lattice: spin 1/2 and 1
  case

abstract:
  Following standard methods we explore the construction of the discrete
Poincare group, the semidirect product of discrete translations and integral
Lorentz transformations, using the Wigner-Mackey construction restricted to the
momentum and position space on the lattice. The orbit condition, irreducibility
and assimptotic limit are discussed.


title:
Numerical study of staggered quark action on quenched anisotropic
  lattices

abstract:
  The staggered quark action on anisotropic lattices is studied. We carry out
numerical simulations in the quenched approximation at three values of lattice
spacing ($a_{\sigma}^{-1}=1-2$ GeV) with the anisotropy $\xi=
a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are the spatial and
temporal lattice spacings, respectively. The bare anisotropy $\gamma_F$ in the
quark action is numerically tuned through the ratio of meson masses in the fine
and coarse directions, and through the dispersion relation of a meson, so that
the renormalized fermionic anisotropy coincides with that of the gauge field.
The discrepancy between these two calibration schemes provides an estimate of
the finite lattice artifact, which is found to be sizable in the range of
cutoff explored in this work. We also compute the meson masses using
correlators with the wall source at the tuned anisotropy parameter. The flavor
symmetry breaking effect smoothly decreases as $\beta$ increases. The effect of
uncertainty in $\gamma_F$ on the meson masses are examined. We also discuss a
perspective on dynamical simulations.


title: Charmonium correlators at finite temperature in quenched lattice QCD

abstract:
  We study charmonium correlators at finite temperature using quenched lattice
QCD simulations. Two analysis procedures are applied to extract information on
the spectral function: the maximum entropy method, and the $\chi^2$ fit
analyses including the constrained curve fitting. We focus on the low energy
structure of the spectral function by applying the smearing technique. We first
discuss the applicability of these methods to the finite temperatures by
analyzing the data at T=0 with restricted numbers of degrees of freedom. Then
we apply these methods to the correlators at $T>0$. We find no indication of
mass shift and finite width for the charmonium states at $T\simeq 0.9T_c$. The
results at $T\simeq 1.1 T_c$ imply that bound-state-like structures may survive
even above $T_c$.


title: Improving meson two-point functions in lattice QCD

abstract:
  We describe and test a method to compute Euclidean meson two-point functions
in lattice QCD. The contribution from the low-lying eigenmodes of the Dirac
operator is averaged over all positions of the quark sources. The contribution
from the higher modes is estimated in the traditional way with one or a few
source points per lattice. In some channels, we observe a significant
improvement in the two-point functions for small quark masses.


title:
Remarks on the multi-parameter reweighting method for the study of
  lattice QCD at non-zero temperature and density

abstract:
  We comment on the reweighting method for the study of finite density lattice
QCD. We discuss the applicable parameter range of the reweighting method for
models which have more than one simulation parameter. The applicability range
is determined by the fluctuations of the modification factor of the Boltzmann
weight. In some models having a first order phase transition, the fluctuations
are minimized along the phase transition line if we assume that the pressure in
the hot and the cold phase is balanced at the first order phase transition
point. This suggests that the reweighting method with two parameters is
applicable in a wide range for the purpose of tracing out the phase transition
line in the parameter space. To confirm the usefulness of the reweighting
method for 2 flavor QCD, the fluctuations of the reweighting factor are
measured by numerical simulations for the cases of reweighting in the quark
mass and chemical potential directions. The relation with the phase transition
line is discussed. Moreover, the sign problem caused by the complex phase
fluctuations is studied.


title:
Exact solutions of the Dirac equation and induced representations of the
  Poincare group on the lattice

abstract:
  We deduce the structure of the Dirac field on the lattice from the discrete
version of differential geometry and from the representation of the integral
Lorentz transformations. The analysis of the induced representations of the
Poincare group on the lattice reveals that they are reducible, a result that
can be considered a group theoretical approach to the problem of fermion
doubling.


title:
Finite Temperature QCD with Two Flavors of Non-perturbatively Improved
  Wilson Fermions

abstract:
  We study QCD with two flavors of non-perturbatively improved Wilson fermions
at finite temperature on the $16^3 8$ lattice. We determine the transition
temperature at lattice spacings as small as $a \sim 0.12$ fm, and study string
breaking below the finite temperature transition. We find that the static
potential can be fitted by a two-state ansatz, including a string state and a
two-meson state. We investigate the role of Abelian monopoles at finite
temperature.


title: Discretisation effects in the topological susceptibility in lattice QCD

abstract:
  We study the topological susceptibility, chi, in QCD with two quark flavours
using lattice field configurations that have been produced with an
O(a)-improved clover quark action. We find clear evidence for the expected
suppression at small quark mass, m_q, and examine the variation of $\chi$ with
this mass and the lattice spacing, a. A joint continuum and chiral
extrapolation yields good agreement with theoretical expectations as (a, m_q)
-> 0. A moderate increase in autocorrelation is observed on the more chiral
ensembles, but within large statistical errors. Finite volume effects are
negligible for Leutwyler-Smilga parameter x_LS > 10, and no evidence for a
nearby phase transition is observed.


title:
Equation of state at finite temperature and chemical potential, lattice
  QCD results

abstract:
  We present an N_t=4 lattice study for the equation of state of 2+1 flavour
staggered, dynamical QCD at finite temperature and chemical potential. We use
the overlap improving multi-parameter reweighting technique to extend the
equation of state for non-vanishing chemical potentials. The results are
obtained on the line of constant physics and our physical parameters extend in
temperature and baryon chemical potential upto \approx 500-600 MeV.


title:
Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact
  Supersymmetry

abstract:
  We construct super Yang-Mills theories with ${\cal N}=2, 4$ supersymmetries
on the two-dimensional square lattice keeping one or two supercharges exactly.
Along the same line as the previous paper \cite{sugino}, the construction is
based on topological field theory formulation. In order to resolve the problem
of degenerate classical vacua encountered in the previous paper, we consider
two kinds of modifications of the action. For one of them, any supersymmetry
breaking terms do not need to be introduced, and the formulations exactly
realize some of supersymmetries at the lattice level. Our lattice actions flow
to the desired continuum theories without any fine-tuning of parameters.


title: Numerical Portrait of a Relativistic BCS Gapped Superfluid

abstract:
  We present results of numerical simulations of the 3+1 dimensional Nambu -
Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the
introduction of a chemical potential mu not equal to 0. The triviality of the
model with a number of dimensions d>=4 is dealt with by fitting low energy
constants, calculated analytically in the large number of colors (Hartree)
limit, to phenomenological values. Non-perturbative measurements of local order
parameters for superfluidity and their related susceptibilities show that, in
contrast to the 2+1 dimensional model, the ground-state at high chemical
potential and low temperature is that of a traditional BCS superfluid. This
conclusion is supported by the direct observation of a gap in the dispersion
relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15%
the size of the vacuum fermion mass. We also present results of an initial
investigation of the stability of the BCS phase against thermal fluctuations.
Finally, we discuss the effect of splitting the Fermi surfaces of the pairing
partners by the introduction of a non-zero isospin chemical potential.


title:
Representations of the discrete inhomogeneous Lorentz group and Dirac
  wave equation on the lattice

abstract:
  We propose the fundamental and two dimensional representation of the Lorentz
groups on a (3+1)-dimensional hypercubic lattice, from which representations of
higher dimensions can be constructed. For the unitary representation of the
discrete translation group we use the kernel of the Fourier transform. From the
Dirac representation of the Lorentz group (including reflections) we derive in
a natural way the wave equation on the lattice for spin 1/2 particles. Finally
the induced representation of the discrete inhomogeneous Lorentz group is
constructed by standard methods and its connection with the continuous case is
discussed.


title: The deconfining phase transition in full QCD with two dynamical flavors

abstract:
  We investigate the deconfining phase transition in SU(3) pure gauge theory
and in full QCD with two flavors of staggered fermions. The phase transition is
detected by measuring the free energy in presence of an abelian monopole
background field. In the pure gauge case our finite size scaling analysis is in
agreement with the well known presence of a weak first order phase transition.
In the case of 2 flavors full QCD we find, using the standard pure gauge and
staggered fermion actions, that the phase transition is consistent with weak
first order, contrary to the expectation of a crossover for not too large quark
masses and in agreement with results obtained by the Pisa group.


title: Lattice QCD at finite density

abstract:
  QCD at finite density presents specific challenges to lattice gauge theory.
Nonetheless, a region of the QCD phase diagram up to moderately large baryon
chemical potentials has been successfully explored on the lattice and new
results and idea are continuously emerging.
  I will outline the lattice formulation of QCD, introduce the calculational
schemes currently used to treat a nonzero baryon density, and mention lattice
methods alternative to MonteCarlo, including the strong coupling expansion
which might give access to the the superconducting phase of QCD. The results
for the critical line, and the different phases will be discussed highlighting
the strength of the different methods, as well as the possible comparisons with
phenomenological models.


title: The QCD equation of state at finite T/\mu on the lattice

abstract:
  We present N_t=4 lattice results for the equation of state of 2+1 flavour
staggered, dynamical QCD at finite temperature and chemical potential. We use
the overlap improving multi-parameter reweighting technique to extend the
equation of state for non-vanishing chemical potentials. The results are
obtained along the line of constant physics. Our physical parameters extend in
temperature and baryon chemical potential upto \approx 500-600 MeV.


title: Finite T/\mu lattice QCD and the critical point

abstract:
  We present results on lattice QCD at finite temperature (T) and chemical
potential (\mu). We apply the overlap-improving multi-parameter reweighting
technique for n_f=4 and 2+1 staggered QCD. We use semi-realistic masses on
L_t=4 lattices. The critical endpoint (E) of 2+1 flavour QCD on the \mu-T plane
is located. Our results are based on {\cal{O}}(10^3-10^4) configurations.


title: Real and imaginary chemical potential in 2-color QCD

abstract:
  In this paper we study the finite temperature SU(2) gauge theory with
staggered fermions for non-zero imaginary and real chemical potential. The
method of analytical continuation of Monte Carlo results from imaginary to real
chemical potential is tested by comparison with simulations performed {\em
directly} for real chemical potential. We discuss the applicability of the
method in the different regions of the phase diagram in the temperature --
imaginary chemical potential plane.


title:
A numerical solution to the local cohomology problem in U(1) chiral
  gauge theories

abstract:
  We consider a numerical method to solve the local cohomology problem related
to the gauge anomaly cancellation in U(1) chiral gauge theories. In the
cohomological analysis of the chiral anomaly, it is required to carry out the
differentiation and the integration of the anomaly with respect to the
continuous parameter for the interpolation of the admissible gauge fields. In
our numerical approach, the differentiation is evaluated explicitly through the
rational approximation of the overlap Dirac operator with Zolotarev
optimization. The integration is performed with a Gaussian Quadrature formula,
which turns out to show rather good convergence. The Poincare lemma is
reformulated for the finite lattice and is implemented numerically. We compute
the current associated with the cohomologically trivial part of the chiral
anomaly in two-dimensions and check its locality properties.


title:
Baryonic Flux in Quenched and Two-Flavor Dynamical QCD after Abelian
  projection

abstract:
  We study the distribution of color electric flux of the three-quark system in
quenched and full QCD (with N_f = 2 flavors of dynamical quarks) at zero and
finite temperature. To reduce ultra-violet fluctuations, the calculations are
done in the abelian projected theory fixed to the maximally abelian gauge. In
the confined phase we find clear evidence for a Y--shape flux tube surrounded
and formed by the solenoidal monopole current, in accordance with the dual
superconductor picture of confinement. In the deconfined, high temperature
phase monopoles cease to condense, and the distribution of the color electric
field becomes Coulomb--like.


title:
Profiles of the broken string in two-flavor QCD below and above the
  finite temperature transition

abstract:
  We study the Abelian flux tube profile of mesonic and the baryonic
configurations of static quarks below and above the finite-temperature
transition in $N_f=2$ full QCD. To reduce effects of ultra-violet fluctuations
we measure Abelian distributions of the action density, the color-electric
field and the monopole current after fixing to the maximally Abelian gauge.
Changing the distance $R$ between quarks for fixed $T/T_c<1$, one can see a
clear signal of string breaking for large $R$. The electric field becomes
Coulomb-like and the circulating monopole current disappears. We study also the
temperature dependence of the flux profile for fixed $R \approx 0.7$ fm. The
disappearance of the squeezed flux is observed clearly above $T_c$. Similar
behaviors are observed both in the mesonic and the baryonic systems.


title: Topology of SU(N) gauge theories at T=0 and T=Tc

abstract:
  We calculate the topological charge density of SU(N) lattice gauge fields for
values of N up to N=8. Our T=0 topological susceptibility appears to approach a
finite non-zero limit at N=infinity that is consistent with earlier
extrapolations from smaller values of N. Near the deconfining temperature Tc we
are able to investigate separately the confined and deconfined phases, since
the transition is quite strongly first order. We find that the topological
susceptibility of the confined phase is always very similar to that at T=0. By
contrast, in the deconfined phase at larger N there are no topological
fluctuations except for rare, isolated and small instantons. This shows that as
N->infinity the large-T suppression of large instantons and the large-N
suppression of small instantons overlap, even at T=Tc, so as to suppress all
topological fluctuations in the deconfined phase. In the confined phase by
contrast, the size distribution is much the same at all T, becoming more peaked
as N grows, suggesting that D(rho) is proportional to a delta function at
N=infinity, centered on rho close to 1/Tc.


title: Electromagnetic Form Factors with FLIC fermions

abstract:
  The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of
nonperturbative O(a) improvement and allows efficient access to the light
quark-mass regime. FLIC fermions enable the construction of the
nonperturbatively O(a)-improved conserved vector current without the
difficulties associated with the fine tuning of the improvement coefficients.
  The simulations are performed with an O(a^2) mean-field improved
plaquette-plus-rectangle gluon action on a 20^3 x 40 lattice with a lattice
spacing of 0.128 fm, enabling the first simulation of baryon form factors at
light quark masses on a large volume lattice.
  Magnetic moments, electric charge radii and magnetic radii are extracted from
these form factors, and show interesting chiral nonanalytic behavior in the
light quark mass regime.


title:
Perturbative Determination of Mass Dependent $O(a)$ Improvement
  Coefficients for the Vector and Axial Vector Currents with a Relativistic
  Heavy Quark Action

abstract:
  We carry out a perturbative determination of mass dependent renormalization
factors and $O(a)$ improvement coefficients for the vector and axial vector
currents with a relativistic heavy quark action, which we have designed to
control $m_Qa$ errors by extending the on-shell $O(a)$ improvement program to
the case of $m_Q \gg \Lambda_{\rm QCD}$ with $m_Q$ the heavy quark mass. We
discuss what kind of improvement operators are required for the heavy-heavy and
the heavy-light cases under the condition that the Euclidean rotational
symmetry is not retained anymore because of the $m_Qa$ corrections. Our
calculation is performed employing the ordinary perturbation theory with the
fictitious gluon mass as an infrared regulator. We show that all the
improvement coefficients are determined free from infrared divergences. Results
of the renormalization factors and the improvement coefficients are presented
as a function of $m_Q a$ for various improved gauge actions as well as the
plaquette action.


title: Lattice QCD at non-zero chemical potential and the resonance gas model

abstract:
  We present results from lattice calculations on the thermodynamics of QCD at
non-zero temperature and baryon chemical potential and discuss the role of
resonances for the occurrence of the transition to the quark-gluon plasma in
hot and dense matter. Properties of a hadronic resonance gas are compared to
lattice results on the equation of state at zero as well as non-zero baryon
chemical potential. Furthermore, it is shown that the quark mass dependence of
the transition temperature can be understood in terms of lines of constant
energy density in a resonance gas.


title: QCD String formation and the Casimir Energy

abstract:
  Three distinct scales are identified in the excitation spectrum of the gluon
field around a static quark-antiquark pair as the color source separation R is
varied. The spectrum, with string-like excitations on the largest length scales
of 2-3 fm, provides clues in its rich fine structure for developing an
effective bosonic string description. New results are reported from the
three-dimensional Z(2) and SU(2) gauge models, providing further insight into
the mechanism of bosonic string formation. The precocious onset of string-like
behavior in the Casimir energy of the static quark-antiquark ground state is
observed below R=1 fm where most of the string eigenmodes do not exist and the
few stable excitations above the ground state are displaced. We find no firm
theoretical foundation for the widely held view of discovering string formation
from high precision ground state properties below the 1 fm scale.


title:
Renormalization Constants of Quark Operators for the Non-Perturbatively
  Improved Wilson Action

abstract:
  We present the results of an extensive lattice calculation of the
renormalization constants of bilinear and four-quark operators for the
non-perturbatively O(a)-improved Wilson action. The results are obtained in the
quenched approximation at four values of the lattice coupling by using the
non-perturbative RI/MOM renormalization method. Several sources of systematic
uncertainties, including discretization errors and final volume effects, are
examined. The contribution of the Goldstone pole, which in some cases may
affect the extrapolation of the renormalization constants to the chiral limit,
is non-perturbatively subtracted. The scale independent renormalization
constants of bilinear quark operators have been also computed by using the
lattice chiral Ward identities approach and compared with those obtained with
the RI-MOM method. For those renormalization constants the non-perturbative
estimates of which have been already presented in the literature we find an
agreement which is typically at the level of 1%.


title: Nf=1 QCD simulation with improved gauge action at finite temperature

abstract:
  We study the deconfinement transition of $N_f=1$ QCD by the hybrid Monte
Carlo algorithm with Wilson fermions. We calculate the Polyakov loop, its
susceptibility and Binder cumulant and use the $\chi^2$ method to locate the
phase transition point. Our results are similar to the previous results
obtained by the multiboson algorithm.


title:
Low-energy couplings of QCD from current correlators near the chiral
  limit

abstract:
  We investigate a new numerical procedure to compute fermionic correlation
functions at very small quark masses. Large statistical fluctuations, due to
the presence of local ``bumps'' in the wave functions associated with the
low-lying eigenmodes of the Dirac operator, are reduced by an exact low-mode
averaging. To demonstrate the feasibility of the technique, we compute the
two-point correlator of the left-handed vector current with Neuberger fermions
in the quenched approximation, for lattices with a linear extent of L~1.5 fm, a
lattice spacing a~0.09 fm, and quark masses down to the epsilon-regime. By
matching the results with the corresponding (quenched) chiral perturbation
theory expressions, an estimate of (quenched) low-energy constants can be
obtained. We find agreement between the quenched values of F extrapolated from
the p-regime and extracted in the epsilon-regime.


title:
Chiral perturbation theory for partially quenched twisted mass lattice
  QCD

abstract:
  Partially quenched Quantum Chromodynamics with Wilson fermions on a lattice
is considered in the framework of chiral perturbation theory. Two degenerate
quark flavours are associated with a chirally twisted mass term. The pion
masses and decay constants are calculated in next-to-leading order including
terms linear in the lattice spacing $a$.


title: An additional symmetry in the Weinberg - Salam model

abstract:
  An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the
Standard Model has been found recently. It has a singular nature and is
connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A
lattice regularization of the Standard Model was constructed that possesses
this symmetry. In this paper we report our results on the numerical simulation
of its Electroweak sector.