title: Hadronic decays from the lattice

abstract:
  We discuss strategies to determine hadronic decay couplings from lattice
studies. As an application, we explore the decay of a vector meson to two
pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working
with quark masses that do not allow a physical decay, we show how the
transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and
from the annihilation component of $\pi \pi \to \pi \pi$. We explore the decay
amplitude for two different pion momenta and find consistent results. The
coupling strength we find is in agreement with experiment. We also find
evidence for a shift in the $\rho$ mass caused by mixing with two pion states.


title:
Simulating the Schroedinger functional with two pseudo-fermions:
  algorithmic study and the running mass

abstract:
  We present an algorithmic study for the simulation of two massless flavors of
O(a) improved Wilson quarks with Schroedinger functional boundary conditions.
The algorithm used is Hybrid Monte Carlo with two pseudo-fermion fields as
proposed by M. Hasenbusch. A gain in CPU cost of a factor two is reached when
compared to one pseudo-fermion field due to the larger possible step-size. This
study is integrated in the ALPHA project for the computation of the running of
the renormalized quark mass. We include an update on these physics results.


title: I=2 pion scattering length with the parametrized fixed point action

abstract:
  We report on the pion-pion scattering length in the I=2 channel using the
parametrized fixed point action. Pion masses of 320 MeV were reached in this
quenched calculation of the scattering length.


title:
The Factorization Method for Monte Carlo Simulations of Systems With a
  Complex Action

abstract:
  We propose a method for Monte Carlo simulations of systems with a complex
action. The method has the advantages of being in principle applicable to any
such system and provides a solution to the overlap problem. In some cases, like
in the IKKT matrix model, a finite size scaling extrapolation can provide
results for systems whose size would make it prohibitive to simulate directly.


title: The equation of state for two flavor QCD at finite density

abstract:
  We discuss the equation of state for QCD at non-zero temperature and density.
We present results of a simulation for QCD with 2 flavors of p4-improved
staggered fermions. Derivatives of $\ln {\cal Z}$ with respect to quark
chemical potential $\mu_q$ up to fourth order are calculated, enabling
estimates of the pressure, quark number density and associated susceptibilities
as functions of $\mu_q$ via a Taylor series expansion. We also discuss the
radius of convergence of the expansion as a function of temperature. It is
found that the fluctuations in the quark number density increase in the
vicinity of the phase transition temperature and the susceptibilities start to
develop a pronounced peak as $\mu_q$ is increased. This suggests the presence
of a critical endpoint in the $(T, \mu_q)$ plane.


title: Accelerating Hasenbusch's acceleration of Hybrid Monte Carlo

abstract:
  Hasenbusch has proposed splitting the pseudo-fermionic action into two parts,
in order to speed-up Hybrid Monte Carlo simulations of QCD. We have tested a
different splitting, also using clover-improved Wilson fermions. An additional
speed-up between 5 and 20% over the original proposal was achieved in
production runs.


title: Baryonic Operators for Lattice Simulations

abstract:
  The construction of baryonic operators for determining the N* excitation
spectrum is discussed. The operators are designed with one eye towards
maximizing overlaps with the low-lying states of interest, and the other eye
towards minimizing the number of sources needed in computing the required quark
propagators. Issues related to spin identification are outlined. Although we
focus on tri-quark baryon operators, the construction method is applicable to
both mesons and penta-quark operators.


title: Static quarks with improved statistical precision

abstract:
  We present a numerical study for different discretisations of the static
action, concerning cut-off effects and the growth of statistical errors with
Euclidean time. An error reduction by an order of magnitude can be obtained
with respect to the Eichten-Hill action, for time separations beyond 1.3 fm,
keeping discretization errors small. The best actions lead to a big improvement
on the precision of the quark mass Mb and F_Bs in the static approximation.


title:
The mass of the charm quark from unquenched lattice QCD at fixed lattice
  spacing

abstract:
  We determine the mass of the charm quark ($m_c$) from lattice QCD with two
flavors of dynamical quarks with a mass around the strange quark. We compare
this to a determination in quenched QCD which has the same lattice spacing (0.1
fm). We investigate different formulations of the quark mass, based on the
Vector Ward Identity, PCAC relation and the FNAL heavy quark formalism. Based
on these preliminary results we find no effects due to sea quarks with a mass
around strange.


title: Classical issues in electroweak baryogenesis

abstract:
  In one scenario of baryogenesis, the matter-antimatter asymmetry was
generated in the early universe during a cold electroweak transition. We model
this transition by changing the sign of the effective mass-squared parameter of
the Higgs field from positive to negative. The resulting `tachyonic'
instability leads to a rapid growth of occupation numbers, such that a
classical approximation can be made in computing subsequent developments in
real time.
  We solve the classical equations of motion in the SU(2)-Higgs model under the
influence of effective CP-violation. The resulting baryon asymmetry follows
from the generated Chern-Simons number using the anomaly equation. The
`classical' difficulties with lattice implementations of these observables are
avoided here because the fields are smooth on the lattice scale.


title: Meson Correlation Functions in the epsilon-Regime

abstract:
  We present a numerical pilot study of the meson correlation functions in the
epsilon-regime of chiral perturbation theory. Based on simulations with overlap
fermions we measured the axial and pseudo-scalar correlation functions, and we
discuss the implications for the leading low energy constants in the chiral
Lagrangian.


title: The RHMC Algorithm for 2 Flavours of Dynamical Staggered Fermions

abstract:
  We describe an implementation of the Rational Hybrid Monte Carlo (RHMC)
algorithm for dynamical computations with two flavours of staggered quarks. We
discuss several variants of the method, the performance and possible sources of
error for each of them, and we compare the performance and results to the
inexact R algorithm.


title: Volume dependence of light hadron masses in full lattice QCD

abstract:
  The aim of the GRAL project is to simulate full QCD with standard Wilson
fermions at light quark masses on small to medium-sized lattices and to obtain
infinite-volume results by extrapolation. In order to establish the functional
form of the volume dependence we study systematically the finite-size effects
in the light hadron spectrum. We give an update on the status of the GRAL
project and show that our simulation data for the light hadron masses depend
exponentially on the lattice size.


title: Progress in automated perturbation theory for heavy quark physics

abstract:
  We review our perturbative techniques for improved heavy quark actions. A new
procedure for computing improvement coefficients is suggested, where the
continuum limit of a lattice-regularized theory provides the matching
conditions.We also use a gauge-invariant infrared regulator that is well suited
to higher-order calculations in lattice gauge theory. We report on preliminary
tests of our method, as well as a possible way to reduce systematic errors in
these calculations.


title: Improved bilinears in unquenched lattice QCD

abstract:
  We summarize the extent to which one can use Ward identities to
non-perturbatively improve flavor singlet and non-singlet bilinears with three
flavors of non-degenerate dynamical Wilson-like fermions.


title: Pion and kaon physics with improved staggered quarks

abstract:
  We compute pseudoscalar meson masses and decay constants using staggered
quarks on lattices with three flavors of sea quarks and lattice spacings
$\approx 0.12$ fm and $\approx 0.09$ fm. We fit partially quenched results to
``staggered chiral perturbation theory'' formulae, thereby taking into account
the effects of taste-symmetry violations. Chiral logarithms are observed. From
the fits we calculate $f_\pi$ and $f_K$, extract Gasser-Leutwyler parameters of
the chiral Lagrangian, and (modulo rather large perturbative errors) find the
light and strange quark masses.


title: New advances in numerical simulations of theta-vacuum systems

abstract:
  We proposed two different methods for simulating theta-vacuum systems. Both
can be affected by systematic effects but these errors can be controlled by
comparing the results of the two unrelated methods. This has been done for some
analytically soluble models and here the same procedure is successfully applied
to the interesting case of CP^9 in the scaling region.


title: Pentaquark hadrons from lattice QCD

abstract:
  We study spin 1/2 isoscalar and isovector candidates in both parity channels
for the recently discovered \Theta^+(1540) pentaquark particle in quenched
lattice QCD. Our analysis takes into account all possible uncertainties, such
as statistical, finite size and quenching errors when performing the chiral and
continuum extrapolations and we have indications that our signal is separated
from scattering states. The lowest mass that we find in the I^P=0^- channel is
in complete agreement with the experimental value of the \Theta^+ mass. On the
other hand, the lowest mass state in the opposite parity I^P=0^+ channel is
much higher. Our findings suggests that the parity of the \Theta^+ is negative.


title: Mass spectrum of N* and source optimization

abstract:
  We have computed correlation functions for nucleons and extracted the masses
for positive- and negative-parities. Use of group theory plays an important
role in obtaining sources that have good overlap to higher spin states and
minimum contamination from unwanted states. In the simulation three distinct
sources and corresponding sinks that transform according to the $G_1$
irreducible representations are tested and used to form matrices of correlation
functions. Diagonalizations give us clear mass splittings between low-lying
states and excited states for both parities.


title: Progress Calculating Decay Constants with NRQCD and AsqTad Actions

abstract:
  We combine a light AsqTad antiquark with a nonrelativistic heavy quark to
compute the decay constants of heavy-light pseudoscalar mesons using the
ensemble of 3-flavor gauge field configurations generated by the MILC
collaboration. Preliminary results for $f_{B_s}$ and $f_{D_s}$ are given and
status of the chiral extrapolation to $f_B$ is reported. We also touch upon
results of the perturbative calculation which matches matrix elements in the
effective theory to the full theory at 1-loop order.


title: Lattice Theories with Nonlinearly Realized Chiral Symmetry

abstract:
  We present the lattice formulation of effective Lagrangians in which chiral
symmetry is realized nonlinearly on the fermion fields. In this framework both
the Wilson term removing unphysical doubler fermions and the fermion mass term
do not break chiral symmetry. Our lattice formulation allows us to address
non-perturbative questions in effective theories of baryons interacting with
pions and in models involving constitutent quarks interacting with pions and
gluons. With the presented methods, a system containing a non-zero density of
static baryons interacting with pions can be studied on the lattice without
encountering a complex action problem. This might lead to new insights into the
phase diagram of strongly interacting matter at non-zero chemical potential.


title: Quark mass dependence of pseudoscalar masses and decay constants

abstract:
  The dependence of pseudo-scalar masses and decay constants on the sea and
valence quark masses is investigated in the pseudo-Goldstone boson sector of
QCD with two light quark flavours. The sea quark masses are at present in the
range ${1/3}m_s \leq m_{ud} \leq {2/3}m_s$ whereas the valence quark masses
satisfy ${1/2}m_{sea} \leq m_{val} \leq 2m_{sea}$. The values of the
Gasser-Leutwyler low energy constants $L_4$, $L_5$, $L_6$ and $L_8$ are
estimated. The computation is done with the Wilson-quark lattice action at
gauge coupling $\beta=5.1$ on $16^4$ lattices. ${\cal O}(a)$ effects are taken
into account by applying chiral perturbation theory for the Wilson lattice
action as proposed by Rupak and Shoresh.


title: Quantum chaos and regularity in $\Phi^4$ theory

abstract:
  We check the eigenvalue spectrum of the $\Phi^{4}_{1+1}$ Hamiltonian against
Poisson or Wigner behavior predicted from random matrix theory. We discuss
random matrix theory as a tool to discriminate the validity of a model
Hamiltonian compared to an analytically solvable Hamiltonian or experimental
data.


title: Hardware and software status of QCDOC

abstract:
  QCDOC is a massively parallel supercomputer whose processing nodes are based
on an application-specific integrated circuit (ASIC). This ASIC was
custom-designed so that crucial lattice QCD kernels achieve an overall
sustained performance of 50% on machines with several 10,000 nodes. This strong
scalability, together with low power consumption and a price/performance ratio
of $1 per sustained MFlops, enable QCDOC to attack the most demanding lattice
QCD problems. The first ASICs became available in June of 2003, and the testing
performed so far has shown all systems functioning according to specification.
We review the hardware and software status of QCDOC and present performance
figures obtained in real hardware as well as in simulation.


title: Theory and Phenomenology of the Polyakov loop in QCD Thermodynamics

abstract:
  A synthesis of Polyakov loop models of the deconfinement transition and
quasiparticle models of gluon plasma thermodynamics leads to a class of models
in which gluons move in a non-trivial Polyakov loop background. These models
are successful candidates for explaining both critical behavior and the
equation of state for the SU(3) gauge theory at finite temperature. Two
sensitive lattice probes which can discriminate between models are the Polyakov
loop P and e-3p.


title: Chiral and Critical Behavior in Strong Coupling QCD

abstract:
  We use a cluster algorithm to study the critical behavior of strongly coupled
lattice QCD in the chiral limit. We show that the finite temperature chiral
phase transition belongs to the O(2) universality class as expected. When we
compute the finite size effects of the chiral susceptibility in the low
temperature phase close to the transition, we find clear evidence for chiral
singularities predicted by chiral perturbation theory (ChPT). On the other hand
it is difficult to reconcile the quark mass dependence of various quantities
near the chiral limit with ChPT.


title: Recent Developments in Lattice Supersymmetry

abstract:
  I discuss a new approach to constructing lattices for gauge theories with
extended supersymmetry. The lattice theories themselves respect certain
supersymmetries, which in many cases allows the target theory to be obtained in
the continuum limit without fine-tuning.


title: Four-momentum boosted Fermion fields

abstract:
  A formulation of the fermion action is discussed which includes an explicit
four momentum boost on the field prior to discretisation. This is used to shift
the zero of lattice momentum to lie near one of the on-shell quark poles. The
positive pole is selected if we wish to describe a valence quark, and negative
pole for a valence anti-quark. Like NRQCD, the typical lattice momenta involved
in hadronic correlation functions can be kept small: of order $O(a \Lambda_{\rm
QCD})$, rather than $O(a m_Q)$ even when describing heavy quarks. If we expand
around the particle pole, the anti-particle correlator will be poorly described
for large $a m_Q$. However, in that case the anti-particle will be far off
shell and will only affect unphysical, renormalization factors. The formulation
produces the correct continuum limit, and preliminary results have been
obtained (for an unimproved action) of both the one-loop self energy and a
non-perturbative correlation function.


title: Analytic estimates of quenched penguins

abstract:
  When we embed the strong penguin operator Q_6 in the quenched theory, it does
not remain a singlet under right-handed chiral transformations. As a
consequence, more low-energy constants associated with this operator appear
than in the unquenched theory. We give analytic estimates of the leading
constants. The results suggest that the effects of quenching on this operator
are large.


title: MEM Analysis of Glueball Correlators at T>0

abstract:
  Maximum Entropy Method (MEM) is applied to glueball correlators at finite
temperature constructed by using 5,500-9,900 gauge field configurations
generated in SU(3) quenched lattice QCD with the lattice parameter beta =
2N_c/g^2 = 6.25 and the renormalized anisotropy a_s/a_t = 4. The results
support the thermal width broadening of the 0++ glueball near the critical
temperature.


title: Positivity and Fermionic Dense Matter

abstract:
  Euclidean dense matter generically suffers from the fermion sign problem.
However, we argue that the sign problem is absent if one considers only
low-energy degrees of freedom. Specifically, the low energy effective theory of
dense QCD has positive Euclidean path integral measure, which allows one to
establish rigorous inequalities showing that the color-flavor locked (CFL)
phase is the true vacuum of three flavor, massless QCD. We then describe a
method for simulating dense QCD on the lattice. We also discuss applications to
electronic systems in condensed matter, such as generalized Hubbard models.


title:
Lattice Study of the Massive Schwinger Model with a $\theta$ term under
  L\"uscher's "Admissibility" condition

abstract:
  We present a numerical study of the massive two-flavor QED in two dimensions
with the gauge action proposed by L\"uscher, which allows only ``admissible''
gauge fields. We find that the admissibility condition does not allow any
topology changes by the local updation in Hybrid Monte Carlo algorithm so that
the configurations in each topological sector can be generated separately. By
developing a new method to sum over different topological sectors, we
investigate $\theta$ vacuum effects. Combining with domain-wall fermion action,
we obtain the fermion mass dependence and $\theta$ dependence of the meson
masses, which are consistent with the analytic results by mass perturbation in
the continuum theory.


title: Calculating weak matrix elements using HYP staggered fermions

abstract:
  We present preliminary results of weak matrix elements relevant to CP
violation calculated using the 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: Searching for KvBLL calorons in SU(3) lattice gauge field ensembles

abstract:
  We discuss Kraan - van Baal - Lee - Lu (KvBLL) solutions of the classical
Yang-Mills equations with temperature in the context of SU(3) lattice gauge
theory. We present discretized lattice versions of KvBLL solutions and other
dyonic structures, obtained by cooling in order to understand their variety and
signature. An analysis of the zero modes of the lattice Dirac operator for
different fermionic boundary conditions gives clear evidence for a KvBLL-like
background of finite T lattice subensembles with Q = +/-1. Using APE-smearing
we are able to study the topological charge density q(x) of the configurations
and to corroborate this interpretation.


title: Semileptonic decays of $D$ mesons in unquenched lattice QCD

abstract:
  We present our preliminary results for semileptonic form factors of $D$
mesons in unquenched lattice QCD. Simulations are carried out with $n_f=2+1$
dynamical quarks using gauge configurations generated by the MILC
collaboration. For the valence quarks, we adopt an improved staggered light
quark action and the clover heavy quark action. Our results for $D \to K$ and
$D \to \pi$ form factors at $q^2=0$ are in agreement with the experimental
values.


title:
Preliminary results in unquenched Numerical Stochastic Perturbation
  Theory

abstract:
  Introducing fermionic loops contributions in Numerical Stochastic
Perturbation Theory was mainly motivated by the proposal to compute 2-3 loops
for renormalization constants (and improvement coefficients). This is feasible
because the computational overhead of unquenching NSPT is by far lower than for
non perturbative simulations. We report on first, preliminary results for the
quark propagator (basically the third loop for the critical mass) and discuss
the status of the computation of other quantities.


title: The phase diagram of N_f=3 QCD for small baryon densities

abstract:
  We demonstrate how to locate the critical endpoint of the QCD phase
transition by means of simulations at imaginary \mu. For the three flavor
theory, we present numerical results for the pseudo-critical line as a function
of chemical potential and bare quark mass, as well as the bare quark mass
dependence of the endpoint.


title: SU(2) Glueballs, diquarks and mesons in dense matter

abstract:
  We present preliminary results from a high statistics study of 2-color QCD at
low temperature and non-zero baryon density. The simulations are carried out on
a 6^3*12 lattice and use a standard hybrid molecular dynamics algorithm for
staggered fermions for two values of quark mass. Observables include glueball
correlators evaluated via a multi-step smearing procedure as well as scalar and
vector mesons and diquarks.


title: Four loop stochastic perturbation theory in 3d SU(3)

abstract:
  Dimensional reduction is a key issue in finite temperature field theory. For
example, when following the QCD Free Energy from low to high scales across the
critical temperature, ultrasoft degrees of freedom can be captured by a 3d
SU(3) pure gauge theory. For such a theory a complete perturbative matching
requires four loop computations, which we undertook by means of Numerical
Stochastic Perturbation Theory. We report on the computation of the pure gauge
plaquette in 3d, and in particular on the extraction of the logarithmic
divergence at order g^8, which had already been computed in the continuum.


title: Tackling the infrared problem of thermal QCD

abstract:
  Perturbative calculations of corrections to the behavior of an ideal gas of
quarks and gluons, the limit that is formally realized at infinite temperature,
are obstructed by severe infrared divergences. The limits to computability that
the infrared problem poses can be overcome in the framework of dimensionally
reduced effective theories. Here, we give details on the evaluation of the
highest perturbative coefficient needed for this setup, in the continuum.


title: Nucleon axial charge and structure functions with domain wall fermions

abstract:
  We report the current status of RBCK calculations on nucleon structure with
both quenched and unquenched lattice QCD. The combination of domain wall
fermions and DBW2 gauge action works well for isovector vector and axial
charges, and moments of structure functions <x>_q, d_1, and <1>_{\delta q}.


title: QCD Critical Region and Quark Gluon Plasma from an Imaginary mu_B

abstract:
  We discuss the imaginary chemical potential approach to the study of QCD at
nonzero temperature and density, present results for the four flavor model in
the different phases and show that this method is ideally suited for a
comparison between lattice data and phenomenological models.


title: Baryons and confining strings

abstract:
  The subleading term of the heavy quark potential (the analogue of the Luscher
term) is computed in a string model for the case of three quarks. It turns out
to be positive in 2+1 dimensions, making the potential non-concave as a
function of the scale for fixed geometry. The results are compared to numerical
simulations of the lattice gauge theory.


title: Where is the chiral critical point in 3-flavor QCD?

abstract:
  We determine the location of the second order endpoint of the line of first
order chiral phase transition in 3-flavor QCD at vanishing chemical potential.
Using Ferrenberg-Swendsen reweighting for two values of the quark mass we
determine the dependence of the transition line on the chemical potential and
locate the chiral critical point. For both quantities we find a significant
quark mass dependence.


title: Excited States in Staggered Meson Propagators

abstract:
  We report on preliminary results from multi-particle fits to meson
propagators with three flavors of light dynamical quarks. We are able to
measure excited states in propagators with pion quantum numbers, which we
interpret as the pion 2S state, and is evidence of locality of the action. In
the a_0 (0^{++}) propagators we find evidence for excited states which are
probably the expected decay channels, pi+eta and K+Kbar.


title:
The Phase Diagram of High Temperature QCD with Three Flavors of Improved
  Staggered Quarks

abstract:
  We report on progress in our study of high temperature QCD with three flavors
of improved staggered quarks. Simulations are being carried out with three
degenerate quarks with masses less than or equal to the strange quark mass,
$m_s$, and with degenerate up and down quarks with masses in the range $0.1 m_s
\leq m_{u,d}\leq 0.6 m_s$, and the strange quark mass fixed near its physical
value. For the quark masses studied to date we find rapid crossovers, which
sharpen as the quark mass is reduced, rather than bona fide phase transitions.


title: Hybrid and Exotic Mesons from FLIC Fermions

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


title:
Dirac-Kaehler fermion with noncommutative differential forms on a
  lattice

abstract:
  Noncommutativity between a differential form and a function allows us to
define differential operator satisfying Leibniz's rule on a lattice. We propose
a new associative Clifford product defined on the lattice by introducing the
noncommutative differential forms. We show that this Clifford product naturally
leads to the Dirac-K\"ahler fermion on the lattice.


title: Heavy quark free energies, potentials and the renormalized Polyakov loop

abstract:
  We discuss the renormalized free energy of a heavy quark anti-quark pair in
the color singlet channel for quenched and full QCD at finite temperature. The
temperature and mass dependence, as well as its short distance behavior is
analyzed. Using the free energies we calculate the heavy quark potential and
entropy in quenched QCD. 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. String breaking is studied in the
color singlet channel in 2-flavor QCD.


title: Improving Dynamical Domain-Wall Fermion Simulations

abstract:
  We report on studies of the chiral properties of dynamical domain wall
fermions combined with the DBW2 gauge action for different gauge couplings and
fermion masses. For quenched theories, the DBW2 action gives a residual chiral
symmetry breaking much smaller than what was found with more traditional
choices for the gauge action. Our goal is to investigate the possibilities
which this and further improvements provide for the study of QCD thermodynamics
and other simulations at stronger couplings.


title: Taste breaking in staggered fermions from random matrix theory

abstract:
  We discuss the construction of a chiral random matrix model for staggered
fermions. This model includes $O(a^2)$ corrections to the continuum limit of
staggered fermions and is related to the zero momentum limit of the Lee-Sharpe
Lagrangian for staggered fermions. The naive construction based on a specific
expansion in lattice spacing ($a$) of the Dirac matrix produces the term which
gives the dominant contribution to the observed taste splitting in the pion
masses. A more careful analysis can include extra terms which are also
consistent with the symmetries of staggered fermions. Lastly I will mention
possible uses of the model including studies of topology and fractional powers
of the fermion determinant.


title:
Thermal Effects on the Condensates of Chiral Order Parameters, the Quark
  Condensate and the Quark Gluon Mixed Condensate, and Chiral Restoration from
  Lattice QCD

abstract:
  We study the quark-gluon mixed condensate g<\bar{q} \sigma G q> using the
SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We
perform the first but accurate measurement of the thermal effects on the mixed
condensate in lattice QCD at \beta = 6.0 with 16^3 * Nt (Nt=16,12,10,8,6,4),
\beta = 6.1 with 20^3 * Nt (Nt=20,12,10,8,6), and \beta = 6.2 with 24^3 * Nt
(Nt=24,16,12,10,8). At each temperature, the lattice calculation is carried out
with high statistics using more than 100 gauge configurations. In particular,
about 1000 gauge configurations are used near the critical temperature T_c. The
chiral extrapolation is done from the lattice result with the current-quark
mass of m_q = 21,36,52 MeV. While the thermal effects on both of the mixed
condensate and the quark condensate are very weak except for the vicinity of
T_c, both the condensates suddenly vanish around T_c \simeq 280 MeV, which
indicates strong chiral restoration near T_c. To compare the thermal effects on
the two condensates, we analyze the ratio m_0^2 = g<\bar{q} \sigma G q>/
<\bar{q}q>, and find that m_0^2 is almost independent of the temperature, even
in the very vicinity of T_c. This means that these two different condensates
obey the same critical behavior, and this nontrivial similarity between them
would impose constraints on the chiral structure of the QCD vacuum near T_c.


title: 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.


title: Pion parton distribution functions from lattice QCD

abstract:
  We report on recent results for the pion matrix element of the twist-2
operator corresponding to the average momentum of non-singlet quark densities.
For the first time finite volume effects of this matrix element are
investigated and come out to be surprisingly large. We use standard Wilson and
non-perturbatively improved clover actions in order to control better the
extrapolation to the continuum limit. Moreover, we compute, fully
non-perturbatively, the renormalization group invariant matrix element, which
allows a comparison with experimental results in a broad range of energy
scales. Finally, we discuss the remaining uncertainties, the extrapolation to
the chiral limit and the quenched approximation.


title: Computational Aspects of Lattice QCD

abstract:
  Monte Carlo simulations applied to the lattice formulation of quantum
chromodynamics (QCD) enable a study of the theory from first principles, in a
nonperturbative way. After over two decades of developments in the methodology
for this study and with present-day computers in the teraflops range,
lattice-QCD simulations are now able to provide quantitative predictions with
errors of a few percent. This means that these simulations will soon become the
main source of theoretical results for comparison with experiments in physics
of the strong interactions. It is therefore an important moment for the
beginning of Brazilian participation in the field.


title: Matrix elements of DI=3/2 K-->pi pi decays

abstract:
  We present a numerical computation of matrix elements of DI=3/2 K-->pi pi
decays by using Wilson fermions. In order to extrapolate to the physical point
we work at unphysical kinematics and we resort to Chiral Perturbation Theory at
the next-to-leading order. In particular we explain the case of the electroweak
penguins O_{7,8} which can contribute significantly in the theoretical
prediction of epsilon'/epsilon. The study is done at beta=6.0 on a 24^3x64
lattice.


title:
Studying the role of the 't Hooft interaction in QCD, by means of
  lattice simulations

abstract:
  We report on a recent investigation on the dynamics of light quarks, at
intermediate and low energy. By measuring some appropriate correlation
functions on the lattice, it is possible to probe the Dirac and flavor
structure of the non-perturbative quark-quark interaction and look directly for
signatures of the 't Hooft Lagrangian. Results obtained with chiral fermions
strongly support the instanton picture and the phenomenological parameters of
the Instanton Liquid Model


title: Dynamics of Phase Transitions by Hysteresis Methods I

abstract:
  In studies of the QCD deconfining phase transition or crossover by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. Motivated by this, we look at
hysteresis methods to study the dynamics of phase transitions. Our systems are
temperature driven through the phase transition using updating procedures in
the Glauber universality class. Hysteresis calculations are presented for a
number of observables, including the (internal) energy, properties of
Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d
Potts models, which provide a rich collection of phase transitions with a
number of rigorously known properties. Comparing with equilibrium
configurations we find a scenario where the dynamics of the transition leads to
a spinodal decomposition which dominates the statistical properties of the
configurations. One may expect an enhancement of low energy gluon production
due to spinodal decomposition of the Polyakov loops, if such a scenario is
realized by nature.


title: HQET with chiral symmetry on the lattice

abstract:
  We show that by combining the static heavy quark action with the Neuberger
action for the light quark, the renormalisation of the heavy-light bilinear and
four-quark operators, computed on the lattice, becomes highly simplified: all
the heavy-light bilinears get renormalised by a single multiplicative constant,
whereas the renormalisation of the complete set of parity even dB=2 four-quark
operators involves only four independent constants. The relevant (matching)
constants are computed at NLO in perturbation theory and are presented here.


title:
Quark bilinear step scaling functions and their continuum limit
  extrapolation

abstract:
  Some new results on nonperturbative renormalisation of quark bilinears in
quenched QCD with Schroedinger Functional techniques are presented. Special
emphasis is put on a study of the universality of the continuum limit for step
scaling functions computed with different levels of O(a) improvement.


title:
Chiral Perturbation Theory and Finite Size Effects on the Nucleon Mass
  in unquenched QCD

abstract:
  We calculate finite size effects on nucleon masses in chiral perturbation
theory. We confront the theoretical predictions with N_f=2 lattice results and
discuss chiral extrapolation formulae.


title: $B_K$ from twisted mass QCD

abstract:
  We present some preliminary results for $B_K$ at $\beta=6.0$, using the
twisted mass QCD formalism for the computation of bare matrix elements of the
$\Delta S=2$ operator. The main advantage of the method is that mixing with
other $d=6$ operators under renormalisation is avoided. Moreover the operator
renormalisation is performed in the Schr\"odinger functional (SF) framework,
using earlier results of our collaboration for the corresponding step scaling
function.


title:
Nonperturbative Renormalization for Domain Wall Fermions and the Chiral
  Condensate

abstract:
  We study the chiral condensate, $<\bar\psi\psi>$, and various quark bilinear
vertex functions for domain wall fermions at different lattice scales, with
both the Wilson and DBW2 gauge actions, in both quenched and dynamical fermion
simulations. We use the vertex functions to calculate renormalization factors
within a non-perturbative scheme.


title: Quantum Markov Process on a Lattice

abstract:
  We develop a systematic description of Weyl and Fano operators on a lattice
phase space. Introducing the so-called ghost variable even on an odd lattice,
odd and even lattices can be treated in a symmetric way. The Wigner function is
defined using these operators on the quantum phase space, which can be
interpreted as a spin phase space. If we extend the space with a dichotomic
variable, a positive distribution function can be defined on the new space. It
is shown that there exits a quantum Markov process on the extended space which
describes the time evolution of the distribution function.


title:
Light hadron spectrum in three-flavor QCD with O(a)-improved Wilson
  quark action

abstract:
  We report on a calculation of the light hadron spectrum and quark masses in
three-flavor dynamical QCD using the non-perturbatively O(a)-improved Wilson
quark action and a renormalization-group improved gauge action. Simulations are
carried out on a 16^3 \times 32 lattice at \beta=1.9, where a^{-1} \simeq 2GeV,
with 6 ud quark masses corresponding to m_{pi}/m_{rho} \simeq 0.64-0.77 and 2 s
quark masses close to the physical value. We observe that the inclusion of
dynamical strange quark brings the lattice QCD meson spectrum to good agreement
with experiment. Dynamical strange quarks also lead to a reduction of the uds
quark masses by about 15%.


title: Improvement and Analytic Techniques in Hamiltonian Lattice Gauge Theory

abstract:
  This thesis is concerned with two topics in Hamiltonian lattice gauge theory:
improvement and the application of analytic techniques. On the topic of
improvement, we develop a direct method for improving lattice Hamiltonians for
gluons, in which linear combinations of gauge invariant lattice operators are
chosen to cancel the lowest order discretisation errors. On the topic of
analytic methods, we extend the techniques that have been used in 2+1
dimensional SU(2) variational calculations for many years, to the general case
of SU(N). For this purpose a number of group integrals are calculated in terms
of Toeplitz determinants. As generating functions these group integrals allow
the calculation of all matrix elements appearing in variational glueball mass
calculations in 2+1 dimensions. Making use of these analytic techniques,
glueball masses in various symmetry sectors are calculated with N as large as
25 allowing extrapolations to infinite N to be performed. We finish with a
feasibility study of applying analytic Hamiltonian techniques in 3+1
dimensional calculations.


title: Continuum limit of proton decay matrix elements in quenched lattice QCD

abstract:
  We present a lattice QCD calculation of the parameters \alpha and \beta which
are necessary in the theoretical estimation of the proton lifetime in grand
unified theories (GUTs) using chiral lagrangian approach. The simulation is
carried out using the Wilson quark action at three gauge coupling constants in
the quenched approximation. We obtain
|\alpha(2GeV)|=0.0091(08)(^{+10}_{-19})GeV^3 and
|\beta(2GeV)|=0.0098(08)(^{+10}_{-20})GeV^3 in the continuum limit where the
first error is statistical and the second one is due to scale setting.


title:
Lattice Extraction of $\epsilon^\prime/\epsilon$ using (PQ) Chiral
  Perturbation Theory

abstract:
  Results at NLO in (PQ)ChPT for extracting $\epsilon^\prime/\epsilon$ from
lattice data are discussed.


title:
Study of finite volume effects in the non-perturbative determination of
  $\csw$ with the SF method in full three-flavor lattice QCD

abstract:
  The non-perturbative $\csw$ determined by the Schr\"{o}dinger functional (SF)
method with the RG-improved gauge action in dynamical $N_f=3$ QCD shows a
finite volume effect when the numerical simulations are carried out at a
constant lattice size $L/a$. We remove the unwanted finite volume effect by
keeping physical lattice extent $L$ at a constant. The details of the method
and the result obtained for non-perturbative $\csw$ with a constant $L$ are
reported.


title:
Gluon and ghost propagators from the viewpoint of general principles of
  quantized gauge field theories

abstract:
  We discuss the possible form of gluon and ghost propagators in the infrared
region of Yang-Mills theory in the covariant gauge from the viewpoint of
general principles of quantized gauge field theories.


title:
Application of Maximum Entropy Method to Lattice Field Theory with a
  Topological Term

abstract:
  In Monte Carlo simulation, lattice field theory with a $\theta$ term suffers
from the sign problem.
  This problem can be circumvented by Fourier-transforming the topological
charge distribution $P(Q)$. Although this strategy works well for small lattice
volume, effect of errors of
  $P(Q)$ becomes serious with increasing volume and prevents one from studying
the phase structure. This is called flattening. As an alternative approach, we
apply the maximum entropy method (MEM) to the Gaussian $P(Q)$. It is found that
the flattening could be much improved by use of the MEM.


title:
Finite temperature phase transition in full QCD with $N_f=2$ flavors of
  clover fermions at $N_t=8$ and 10

abstract:
  We present results for QCD with $N_f=2$ flavors of dynamical quarks using
nonperturbatively improved Wilson fermions at finite temperature on $16^3
\times 8$ and $24^3 \times 10$ lattices. We determine the transition
temperature in the range of quark masses $0.6 \lesssim m_\pi/m_\rho \leq 0.8$.
After fixing the Maximal Abelian gauge we investigate the contribution of
Abelian monopoles to the Polyakov loop, Polyakov loop susceptibility and
confirm Abelian and monopole dominance in full QCD.


title: Topological susceptibility from the overlap

abstract:
  The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic
actions constrains the renormalization of the lattice operators; in particular,
the topological susceptibility does not require any renormalization, when using
a fermionic estimator to define the topological charge. Therefore, the overlap
formalism appears as an appealing candidate to study the continuum limit of the
topological susceptibility while keeping the systematic errors under
theoretical control. We present results for the SU(3) pure gauge theory using
the index of the overlap Dirac operator to study the topology of the gauge
configurations. The topological charge is obtained from the zero modes of the
overlap and using a new algorithm for the spectral flow analysis. A detailed
comparison with cooling techniques is presented. Particular care is taken in
assessing the systematic errors. Relatively high statistics (500 to 1000
independent configurations) yield an extrapolated continuum limit with errors
that are comparable with other methods. Our current value from the overlap is
$\chi^{1/4} = 188 \pm 12 \pm 5 \MeV$.


title: QCD at zero baryon density

abstract:
  While the grand canonical partition function Z_{GC}(mu) with chemical
potential mu explicitly breaks the Z_3 symmetry with the Dirac determinant, the
canonical partition function at fixed baryon number Z_C(B) is manifestly
Z_3-symmetric. We compare Z_{GC}(mu=0) and Z_C(B=0) formally and by numerical
simulations, in particular with respect to properties of the deconfinement
transition. Differences between the two ensembles, for physical observables
characterising the phase transition, vanish with increasing lattice size. We
show numerically that the free energy density is the same for both ensembles in
the thermodynamic limit.


title:
Effective string picture for confinement at finite temperature:
  theoretical predictions and high precision numerical results

abstract:
  The effective string picture of confinement is used to derive theoretical
predictions for the interquark potential at finite temperature. At short
distances, the leading string correction to the linear confining potential
between a heavy quark-antiquark pair is the "L\"uscher term''. We assume a
Nambu--Goto effective string action, and work out subleading contributions in
an analytical way. We discuss the contribution given by a possible ``boundary
term'' in the effective action, comparing these predictions with results from
simulations of lattice $Z_2$ gauge theory in three dimensions, obtained with an
algorithm which exploits the duality of the $Z_2$ gauge model with the Ising
spin model.


title:
Improving the locality of the overlap Dirac operator via approximate
  solutions of the Ginsparg-Wilson relation

abstract:
  We determine the free field hypercubic Dirac operator which is optimally
close to satisfying the Ginsparg-Wilson relation. Inserting this operator into
the overlap formula, we show that the analytic locality bound on the resulting
overlap Dirac operator is substantially stronger than in the standard case.
This improvement generally persists in gauge backgrounds when the plaquette
variables are all close to unity.


title: Benchmarking computer platforms for lattice QCD applications

abstract:
  We define a benchmark suite for lattice QCD and report on benchmark results
from several computer platforms. The platforms considered are apeNEXT, CRAY
T3E, Hitachi SR8000, IBM p690, PC-Clusters, and QCDOC.


title: Non perturbative renormalization in coordinate space

abstract:
  We present an exploratory study of a gauge-invariant non-perturbative
renormalization technique. The renormalization conditions are imposed on
correlation functions of composite operators in coordinate space on the
lattice. Numerical results for bilinears obtained with overlap and
O(a)-improved Wilson fermions are presented. The measurement of the quark
condensate is also discussed.


title: Hadronic matrix elements of proton decay on the lattice

abstract:
  We report on our on-going project to calculate proton decay matrix elements
using domain-wall fermions on the lattice. By summarizing the history of the
proton decay calculation on the lattice, we reveal the systematic errors of
those calculations. Then we discuss our approach to tackle those uncertainties
and show our preliminary results on the matrix elements.


title: Nucleon Decay with Domain-Wall Fermions

abstract:
  We report on our on-going project to calculate the nucleon decay matrix
elements with domain-wall fermions. Operator mixing is discussed employing a
non-perturbative renormalization. Bare matrix elements of all the possible
decay modes induced by the dimension-six operators are calculated with the
direct method, which are compared with the indirect calculation using chiral
perturbation theory.


title: Deconfinement transition in 2+1-dimensional SU(4) lattice gauge theory

abstract:
  A missing piece is added to the Svetitsky-Yaffe conjecture. The spin model in
the same universality class as the (2+1)d SU(4) theory, the 2d Ashkin-Teller
model, has a line of continuously varying critical exponents. The exponents
measured in the gauge theory correspond best to the Potts point on the
Ashkin-Teller line.


title: Dynamical FLIC Fermions

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


title:
I=2 pion-pion scattering phase shift in the continuum limit calculated
  with two-flavor full QCD

abstract:
  We present a calculation of the scattering phase shift for the I=2 S-wave
pion-pion system in the continuum limit with two-flavor full QCD. Calculations
are made at three lattice spacings, using the finite volume method of L\"uscher
in the center of mass frame, and its extension to the laboratory frame.


title: Maximum Entropy Method Approach to $\theta$ Term

abstract:
  In Monte Carlo simulations of lattice field theory with a $\theta$ term, one
confronts the complex weight problem, or the sign problem. This is circumvented
by performing the Fourier transform of the topological charge distribution
$P(Q)$. This procedure, however, causes flattening phenomenon of the free
energy $f(\theta)$, which makes study of the phase structure unfeasible.
  In order to treat this problem, we apply the maximum entropy method (MEM) to
a Gaussian form of $P(Q)$, which serves as a good example to test whether the
MEM can be applied effectively to the $\theta$ term. We study the case with
flattening as well as that without flattening. In the latter case, the results
of the MEM agree with those obtained from the direct application of the Fourier
transform. For the former, the MEM gives a smoother $f(\theta)$ than that of
the Fourier transform. Among various default models investigated, the images
which yield the least error do not show flattening, although some others cannot
be excluded given the uncertainty related to statistical error.


title: Chirally improving Wilson fermions

abstract:
  It is possible to improve the chiral behaviour and the approach to the
continuum limit of correlation functions in lattice QCD with standard and
twisted Wilson fermions by taking arithmetic averages of correlators computed
in theories regularized with Wilson terms of opposite sign. To avoid the
problem of the spurious zero-modes of the Wilson--Dirac operator, twisted-mass
lattice QCD should be used for the actual computation of the correlators taking
part in the averages. A particularly useful choice for the twisting angle is
$\pm\pi/2$ where many physical quantities (e.g. masses and zero-momentum matrix
elements) are automatically improved with no need of averaging.


title:
Higher orders of the high-temperature expansion for the Ising model in
  three dimensions

abstract:
  The new algorithm of the finite lattice method is applied to generate the
high-temperature expansion series of the simple cubic Ising model to
$\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic
susceptibility and to $\beta^{29}$ for the second moment correlation length.
The series are analyzed to give the precise value of the critical point and the
critical exponents of the model.


title: Phase structure of lattice QCD for general number of flavors

abstract:
  We investigate the phase structure of lattice QCD for the general number of
flavors in the parameter space of gauge coupling constant and quark mass,
employing the one-plaquette gauge action and the standard Wilson quark action.
Performing a series of simulations for the number of flavors $N_F=6$--360 with
degenerate-mass quarks, we find that when $N_F \ge 7$ there is a line of a bulk
first order phase transition between the confined phase and a deconfined phase
at a finite current quark mass in the strong coupling region and the
intermediate coupling region. The massless quark line exists only in the
deconfined phase. Based on these numerical results in the strong coupling limit
and in the intermediate coupling region, we propose the following phase
structure, depending on the number of flavors whose masses are less than
$\Lambda_d$ which is the physical scale characterizing the phase transition in
the weak coupling region: When $N_F \ge 17$, there is only a trivial IR fixed
point and therefore the theory in the continuum limit is free. On the other
hand, when $16 \ge N_F \ge 7$, there is a non-trivial IR fixed point and
therefore the theory is non-trivial with anomalous dimensions, however, without
quark confinement. Theories which satisfy both quark confinement and
spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F
\le 6$.


title:
A perturbative determination of O($a$) boundary improvement coefficients
  for the Schr\"odinger Functional coupling at 1-loop with improved gauge
  actions

abstract:
  We perturbatively determine O($a$) boundary improvement coefficients at
1-loop for the Schr\"odinger Functional coupling with improved gauge actions.
These coefficients are required to implement the 1-loop O($a$) improvement in
full QCD simulations for the coupling with the improved gauge actions. To this
order, lattice artifacts of the step scaling function (SSF) for each improved
gauge action are also investigated. Furthermore, we investigate the effect of
the 1-loop O($a$) improvement to the SSF in numerical simulations of the pure
SU(3) gauge theory.


title:
A Perturbative Determination of Mass Dependent $O(a)$ Improvement
  Coefficients in a Relativistic Heavy Quark Action

abstract:
  We present the results for a perturbative determination of mass dependent
improvement coefficients $\nu$, $r_s$, $c_E$ and $c_B$ in 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 $m_Q \gg \Lambda_{\rm QCD}$,
where $m_Q$ is the heavy quark mass. The parameters $\nu$ and $r_s$ are
determined from the quark propagator and $c_E$ and $c_B$ are from the on-shell
quark-quark scattering amplitude. We show that all the parameters, together
with the quark wave function and the mass renormalization factors, are
determined free from infrared divergences once their tree level values are
properly tuned. Results of these parameters are shown as a function of $m_Q a$
for various improved gauge actions.


title: Heavy hadrons on an anisotropic lattice

abstract:
  Results from simulations of quarkonia and heavy-light mesons on an
anisotropic lattice are presented. The improved quark action and
action-parameter tuning used in this study are discussed.


title:
Non-perturbative propagators and dimension 2 condensate in Yang-Mills
  theory

abstract:
  We have found ultraviolet asymptotic slutions of the Schwinger-Dyson equation
for the gluon and ghost propagators which have simultaneously the perturbative
logarithmic correction and the non-perturbative $1/p^2$ power correction. By
including the perturbative corrections, the power correction reproduces exactly
the leading OPE result suggesting the existence of dimension two condensate.


title:
Solving the Schwinger-Dyson Equations for Gluodynamics in the Maximal
  Abelian Gauge

abstract:
  We derive the Schwinger-Dyson equations for the SU(2) Yang-Mills theory in
the maximal Abelian gauge and solve them in the infrared asymptotic region. We
find that the infrared asymptotic solutions for the gluon and ghost propagators
are consistent with the hypothesis of Abelian dominance.


title: Infrared Features of the Lattice Landau Gauge QCD

abstract:
  The infrared properties of lattice Landau gauge QCD of SU(3) are studied by
measuring gluon propagator, ghost propagator, QCD running coupling and
Kugo-Ojima parameter of $\beta=6.0, 16^4,24^4,32^4$ and $\beta=6.4, 32^4,48^4$
lattices. We study Gribov copy problem by parallel tempering (PT) gauge fixing
of $\beta=2.2, 16^4$ SU(2) configurations. Rather unexpected features of the
unique gauge(fundamental modular gauge, FMG) are observed in relation of
physical values vs the optimizing function.


title:
Infrared Features of Lattice Landau Gauge QCD and the Gribov Copy
  Problem

abstract:
  Infrared features of gluon propagator, ghost propagator, QCD running coupling
and the Kugo-Ojima parameter in lattice Landau gauge QCD are presented. The
framework of PMS analysis suggests that there appear infrared, intermediate and
ultraviolet regions specified by $\Lambda_{\bar{MS}}$, $\beta_0$ and $\beta_1$.
The propagators and the running coupling of $q>1GeV$ are fitted by the
$\widetilde{MOM}$ scheme using the factorization scale as the scale parameter.
The running coupling data of $q<14GeV$ are fitted by the contour improved
perturbation method. The Gribov copy problem is studied in SU(2), $\beta= 2.2$
samples by comparing the data gauge fixed by the parallel tempering method and
the data gauge fixed by the straightforward gauge fixing. The Gribov noise
effect turned out to be about 2%.


title: Chiral Dirac fermions on the lattice using Geometric Discretisation

abstract:
  A new approach to the problem of doubling is presented with the Dirac-Kahler
(DK) theory as a starting point and using Geometric Discretisation providing us
with a new way of extracting the Dirac field in the discrete setting of a
hyper-cubic complex.


title: I=2 Pion Scattering Length from Two-Pion Wave Function

abstract:
  We present a preliminary report on a calculation of scattering length for I=2
$S$-wave two-pion system directly from the two-pion wave function. Results are
compared with those calculated from the time dependence of two-pion four-point
functions. Calculations are made with an RG-improved action for gluons and
improved Wilson action for quarks at $a^{-1}=1.207(12)$ GeV on $20^3 \times 48$
and $24^3 \times 48$ lattices.


title: Exploring two non-perturbative definitions of $c_A$

abstract:
  We present two determinations of the coefficient $c_A$ in quenched QCD,
needed to build the $O(a)$ improved axial current. The first condition used is
the requirement that the PCAC quark mass, as a function of $x_0$, stays flat
for a non-trivial spatial phase for the fermions in the Schr\"odinger
functional. The second condition is that the PCAC relation for the ground-state
and the first excited state at finite L give the same quark mass. Our results
confirm previous findings that in the quenched theory the intrinsic $O(a)$
ambiguity of $c_A$ gets relevant around $\beta\simeq6.0$.


title: Features of SU(N) Gauge Theories

abstract:
  We review recent lattice results for the large $N$ limit of SU(N) gauge
theories. In particular, we focus on glueball masses, topology and its relation
to chiral symmetry breaking (relevant for phenomenology), on the tension of
strings connecting sources in higher representations of the gauge group
(relevant for models of confinement and as a comparative ground for theories
beyond the Standard Model) and on the finite temperature deconfinement phase
transition (relevant for RHIC-like experiments). In the final part we present
open challenges for the future.


title: Large cutoff effects of dynamical Wilson fermions

abstract:
  We present and discuss results for cutoff effects in the PCAC masses and the
mass dependence of r_0 for full QCD and various fermion actions. Our discussion
of how one computes mass dependences - here of r_0 - is also relevant for
comparisons with chiral perturbation theory.


title: Adventures in Coulomb Gauge

abstract:
  We study the phase structure of SU(2) gauge theories at zero and high
temperature, with and without scalar matter fields, in terms of the
symmetric/broken realization of the remnant gauge symmetry which exists after
fixing to Coulomb gauge. The symmetric realization is associated with a
linearly rising color Coulomb potential (which we compute numerically), and is
a necessary but not sufficient condition for confinement.


title: Pion electromagnetic form-factor with domain wall fermions

abstract:
  Motivated by recent measurements at J-Lab, the pion electromagnetic
form-factor is investigated with quenched domain wall fermions and a
renormalization group improved gauge action called DBW2. We see that quark mass
dependence of the form-factor with finite momentum transfers is rather small.


title: Calculation of CP Violation in Non-leptonic Kaon Decay on the Lattice

abstract:
  We give a progress report of our lattice calculation of direct and indirect
CP violation in kaon decays, parametrized as $\epsilon'/\epsilon$ and $B_K$,
which require non-perturbative calculation of the matrix elements of the
Standard Model effective Hamiltonian.


title:
Calcutation of kaon matrix elements in quenched domain-wall QCD with
  DBW2 gauge action

abstract:
  We give a progress report of our new $a^{-1}\approx 3$ GeV quenched
calculation of kaon matrix elements with domain-wall fermion and DBW2 gauge
action. Our smaller lattice spacing allows us to address the effect of charmed
quark on the lattice. We show preliminary results of $B_K$ renormalized
non-perturbatively and $K\to\pi$ matrix elements.


title:
Structure of the baryonic flux tube in N_{f}=2 lattice QCD at finite
  temperature

abstract:
  We study the flux tube profile in the baryonic system in full QCD at finite
temperature on $N_{t}=8$ lattice. We fix the maximally Abelian gauge and
measure the monopole and the photon parts of the Abelian action density, the
color electric field and the monopole current on both sides of the finite
temperature transition. We demonstrate the disappearance of the flux tube in
the high temperature phase.


title: Excited nucleon spectrum from lattice QCD with maximum entropy method

abstract:
  We study excited states of the nucleon in quenched lattice QCD with the
spectral analysis using the maximum entropy method. Our simulations are
performed on three lattice sizes $16^3\times 32$, $24^3\times 32$ and
$32^3\times 32$, at $\beta=6.0$ to address the finite volume issue. We find a
significant finite volume effect on the mass of the Roper resonance for light
quark masses. After removing this systematic error, its mass becomes
considerably reduced toward the direction to solve the level order puzzle
between the Roper resonance $N'(1440)$ and the negative-parity nucleon
$N^*(1535)$.


title:
Light meson correlation functions near the deconfining transition on
  anisotropic lattices

abstract:
  We study the light hadron correlators near the deconfining transition by
extracting the spectral function on quenched anisotropic lattices. We adopt the
method successfully applied to the charmonium systems: the use of the smeared
operators and the analysis method which is composed of the maximum entropy
method and the $\chi^2$ fitting assuming several forms. The numerical
simulations are performed on lattices of $a_s^{-1} \simeq 2$ GeV and
$a_s/a_t=4$, with the clover quark around the strange quark mass. Towards
applications to the plasma phase, we check the reliability of our procedure by
examining how the results for the correlators below $T_c$ ($N_t=32$) changes
under variation of input parameters such as the smearing function.


title: Large Mass and Chemical Potential Model: A Laboratory for QCD?

abstract:
  We use a model based on the hopping parameter expansion to study QCD at large
$\mu$. We find interesting behavior in the region expected to show flavor-color
locking.


title: Excitations of torelon

abstract:
  The excitations of gluonic flux tube in a periodic lattice are examined.
Monte Carlo simulations from an anisotropic lattice are presented and the
comparison with effective string models is discussed.


title:
Non-perturbative renormalization of moments of parton distribution
  functions

abstract:
  We compute non-perturbatively the evolution of the twist-2 operators
corresponding to the average momentum of non-singlet quark densities. The
calculation is based on a finite-size technique, using the Schr\"odinger
Functional, in quenched QCD. We find that a careful choice of the boundary
conditions, is essential, for such operators, to render possible the
computation. As a by-product we apply the non-perturbatively computed
renormalization constants to available data of bare matrix elements between
nucleon states.


title:
D-Theory: Field Quantization by Dimensional Reduction of Discrete
  Variables

abstract:
  D-theory is an alternative non-perturbative approach to quantum field theory
formulated in terms of discrete quantized variables instead of classical
fields. Classical scalar fields are replaced by generalized quantum spins and
classical gauge fields are replaced by quantum links. The classical fields of a
d-dimensional quantum field theory reappear as low-energy effective degrees of
freedom of the discrete variables, provided the (d+1)-dimensional D-theory is
massless. When the extent of the extra Euclidean dimension becomes small in
units of the correlation length, an ordinary d-dimensional quantum field theory
emerges by dimensional reduction. The D-theory formulation of scalar field
theories with various global symmetries and of gauge theories with various
gauge groups is constructed explicitly and the mechanism of dimensional
reduction is investigated.


title: The pion form factor from first principles

abstract:
  We calculate the electromagnetic form factor of the pion in quenched lattice
QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is
used together with the ${\mathcal O}(a)$ improved current. We calculate form
factor for pion masses down to $m_\pi = 360 MeV$. We compare the mean square
radius for the pion extracted from our form factors to the value obtained from
the 'Bethe Salpeter amplitude'. Using (quenched) chiral perturbation theory, we
extrapolate our results towards the physical pion mass.


title: A global optimization method for Landau gauge fixing in Lattice QCD

abstract:
  An algorithm for gauge fixing to the minimal Landau gauge in lattice QCD is
described. The method, a combination of an evolutionary algorithm with a
steepest descent method, is able to solve the problem of the nonperturbative
gauge fixing. The performance of the combined algorithm is investigated on
$8^4$, $\beta = 5.7$, and $16^4$, $\beta = 6.0$, lattice SU(3) gauge
configurations.


title:
Non-perturbative renormalization of vector and axial vector currents in
  quenched QCD for a renormalization group improved gauge action

abstract:
  Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents
are determined non-perturbatively in quenched QCD for an RG-improved gauge
action and a tadpole-improved clover quark action using the Schr\"odinger
functional method. Meson decay constants $f_\rho$ and $f_\pi$ show much better
scaling when $Z_V$ and $Z_A$ estimated for infinite physical volume are used
instead of $Z$-factors from tadpole-improved one-loop perturbation theory.


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: Chiral Structure in Baryon Magnetic Moments

abstract:
  We highlight recent advances in finite-range regularised chiral effective
field theory. Application to baryon magnetic moments show an unambiguous signal
of quenched chiral physics in FLIC fermion simulations.


title:
Numerical study of the equation of state for two flavor QCD at finite
  density

abstract:
  We discuss the equation of state for 2 flavor 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, enabling estimates of the pressure,
quark number density and associated susceptibilities as functions of $\mu_q$
via a Taylor series expansion. It is found that the fluctuations in the quark
number density increase in the vicinity of the phase transition temperature and
the susceptibilities start to develop a pronounced peak as $\mu_q$ is
increased. This suggests the presence of a critical endpoint in the $(T,
\mu_q)$ plane.


title: Lattice QCD in the epsilon-regime and random matrix theory

abstract:
  In the epsilon-regime of QCD the main features of the spectrum of the
low-lying eigenvalues of the (euclidean) Dirac operator are expected to be
described by a certain universality class of random matrix models. In
particular, the latter predict the joint statistical distribution of the
individual eigenvalues in any topological sector of the theory. We compare some
of these predictions with high-precision numerical data obtained from lattice
QCD for a range of lattice spacings and volumes. While no complete matching is
observed, the results agree with theoretical expectations at volumes larger
than about 5 fm^4.


title: Dimensional reduction and a Z(3) symmetric model

abstract:
  We present first results from a numerical investigation of a Z(3) symmetric
model based on dimensional reduction.


title: Free Meson Spectral Functions on the Lattice

abstract:
  We present results from an analytic calculation of thermal meson spectral
functions in the infinite temperature (free field) limit. We compare spectral
functions for various lattice fermion formulations used at present in studies
of in-medium properties of hadrons based on the maximum entropy method (MEM).
In particular, we will present a new calculation of spectral functions
performed with extended quark sources.


title:
One-loop calculation of mass dependent ${\cal O}(a)$ improvement
  coefficients for the relativistic heavy quarks on the lattice

abstract:
  We carry out the one-loop calculation of mass dependent ${\cal O}(a)$
improvement coefficients in the relativistic heavy quark action recently
proposed, employing the ordinary perturbation theory with the fictitious gluon
mass as an infrared regulator. We also determine renormalization factors and
improvement coefficients for the axial-vector current at the one-loop level. It
is shown that the improvement coefficients are infrared finite at the one-loop
level if and only if the improvement coefficients in the action are properly
tuned at the tree level.


title: Energy spectrum of a Heavy-Light meson

abstract:
  The energies of different angular momentum states of a heavy-light meson were
measured on a lattice by Michael and Peisa in Phys. Rev. D 58, 34506 (1998). We
have now repeated this study using a larger, quenched lattice to check that
there the finite size effects are under control. Also the effect of quenching
is studied by using dynamical fermion configurations. In the latter case the
lattice spacing a is smaller, which allows one to make an estimate of a -> 0
corrections. The new measurements confirm the earlier calculated energy
spectrum.
  From some theoretical considerations it is expected that, for high angular
momentum states, the multiplets should be inverted compared with the Coulomb
spectrum, i.e. L- should lie higher than L+ (see H. J. Schnitzer Phys. Lett. B
226, 171 (1989)). This happens when a pure scalar confining potential is
present. Here the notation L+(-) means that the light quark spin couples to
angular momentum L giving the total j=L+/- 1/2. Experimentally this inversion
is not seen for P-wave mesons, and lattice measurements now suggest that there
is no inversion in the D-wave either. Indeed we find that the spin-orbit
splitting is very small for both values L=1 and 2. This almost exact
cancellation need not be a coincidence, and could probably be understood by
using straightforward symmetry arguments (P.R. Page, T. Goldman and J.N.
Ginocchio, Phys. Rev. Lett. 86, 204 (2001)).


title: Extraction of parton distributions from lattice QCD

abstract:
  We review the calculation of moments of both the polarized and unpolarized
parton distribution functions of the nucleon in lattice QCD, and in particular
their extrapolation to the physical region. We also discuss the reconstruction
of the x dependence of the valence quark distributions in the nucleon from a
finite number of lattice moments.


title: The Factorization Method for Simulating Systems With a Complex Action

abstract:
  We propose a method for Monte Carlo simulations of systems with a complex
action. The method has the advantages of being in principle applicable to any
such system and provides a solution to the overlap problem. We apply it in
random matrix theory of finite density QCD where we compare with analytic
results. In this model we find non--commutativity of the limits $\mu\to 0$ and
$N\to\infty$ which could be of relevance in QCD at finite density.


title: String effects in SU(2) lattice gauge theory

abstract:
  We discuss the effective string picture for the confining regime of lattice
gauge theories at zero and finite temperature. We present results of extensive
Monte Carlo simulations - performed with the Luscher and Weisz algorithm - for
SU(2) Yang-Mills theory in 2+1 dimensions. We also address the issue of "string
universality" by comparing our results with those obtained in other lattice
gauge theories.


title:
Preliminary results from a simulation of quenched QCD with overlap
  fermions on a large lattice

abstract:
  We simulate quenched QCD with the overlap Dirac operator. We work with the
Wilson gauge action at beta=6 on an 18^3x64 lattice. We calculate quark
propagators for a single source point and quark mass ranging from am_q=0.03 to
0.75. We present here preliminary results based on the propagators for 60 gauge
field configurations.


title: A study of colour field distributions in the baryon

abstract:
  The distributions of chromo-electric and chromo-magnetic field associated
with flux tubes in the baryon are studied in SU(3) lattice QCD. Maximal Abelian
projection is used to reduce the statistical fluctuations. For a fixed source
geometry, many different string configurations are possible. We investigated
whether the string configuration, that is the choice of operator, biases the
observed flux distribution.


title: Heavy quark masses from finite volume effects

abstract:
  I discuss the results of a new calculation of the charm and bottom quark
masses in the quenched approximation and in the continuum limit of lattice QCD.
The work has been done by the APE group at the ``Tor Vergata'' University
making use of the step scaling method, previously introduced to deal with two
scale problems, that allows to take the continuum limit of the lattice data. We
have computed the RGI quark masses and then we have connected the results to
the MSbar scheme. The continuum numbers are m_b^{RGI} = 6.73(16) GeV for the
b-quark and m_c^{RGI} = 1.681(36) GeV for the c-quark, corresponding
respectively to m_b^{MSbar}(m_b^{MSbar}) = 4.33(10) GeV and
m_c^{MSbar}(m_c^{MSbar}) = 1.319(28) GeV. The latter result, in agreement with
current estimates, is for us a check of the method.


title: Heavy-light decay constants from the step scaling method

abstract:
  We discuss results for the heavy-light decay constants in the continuum limit
of quenched lattice QCD from finite size scaling techniques. We disentangle the
simultaneous presence of the different energy scales characterizing heavy-light
physics by first performing simulations at the unphysical volume L_0=0.4 fm,
and then evolving the results towards the infinite volume. We find f_{Bs}=
192(6)(4) MeV and f_{Ds}=240(5)(5) MeV. The approach has been developed by the
APE group at the University of Rome ``Tor Vergata''.


title: Hadronic transitions from the lattice

abstract:
  I discuss strategies to determine hadronic decay couplings from lattice
studies.
  As a check of the methods, I explore the decay of a vector meson to two
pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working
with quark masses that do not allow a physical decay, I show how the transition
rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the
annihilation component of $\pi \pi \to \pi \pi$. I explore the decay amplitude
for two different pion momenta and find consistent results. The coupling
strength found is in agreement with experiment. I also find evidence for a
shift in the $\rho$ mass caused by mixing with two pion states.
  I also present results for the decay of a hybrid meson, for the case of heavy
valence quarks.


title: Dynamics of Monopoles and Flux Tubes in Two-Flavor Dynamical QCD

abstract:
  We investigate the confining properties of the QCD vacuum with $N_f=2$
flavors of dynamical quarks, and compare the results with the properties of the
quenched theory. We use non-perturbatively $\mathcal{O}(a)$ improved Wilson
fermions to keep cut-off effects small. We focus on color magnetic monopoles.
Among the quantities we study are the monopole density and the monopole
screening length, the static potential and the profile of the color electric
flux tube. We furthermore derive the low-energy effective monopole action.
Marked differences between the quenched and dynamical vacuum are found.


title: Unphysical Operators in Partially Quenched QCD

abstract:
  We point out that the chiral Lagrangian describing pseudo-Goldstone bosons in
partially quenched QCD has one more four-derivative operator than that for
unquenched QCD with three flavors. The new operator can be chosen to vanish in
the unquenched sector of the partially quenched theory. Its contributions begin
at next-to-leading order in the chiral expansion. At this order it contributes
only to unphysical scattering processes, and we work out some examples. Its
contributions to pseudo-Goldstone properties begin at next-to-next-to-leading
order, and we determine their form. We also determine all the zero and two
derivative operators in the $O(p^6)$ partially quenched chiral Lagrangian,
finding three more than in unquenched QCD, and use these to give the general
form of the analytic next-to-next-to-leading order contributions to the
pseudo-Goldstone mass and decay constant. We discuss the general implications
of such additional operators for the utility of partially quenched simulations


title: Glueball Matrix Elements on Anisotropic Lattices

abstract:
  The glueball-to-vacuum matrix elements of local gluonic operators in scalar,
tensor, and pseudoscalar channels are investigated numerically on several
anisotropic lattices with the spatial lattice spacing in the range 0.1fm --
0.2fm. These matrix elements are needed to predict the glueball branching
ratios in $J/\psi$ radiative decays which will help to identify the glueball
states in experiments. Two types of improved local gluonic operators are
constructed for a self-consistent check, and the finite volume effects are also
studied. The lattice spacing dependence of our results is very small and the
continuum limits are reliably extrapolated.


title: Lattice study of exotic S=+1 baryon

abstract:
  We propose S=+1 baryon interpolating operators, which are based on an exotic
description of the antidecuplet baryon like diquark-diqaurk-antiquark. By using
one of the new operators, the mass spectrum of the spin-1/2 pentaquark states
is calculated in quenched lattice QCD at $\beta=6/g^2=6.2$ on a $32^3\times48$
lattice. It is found that the $J^P$ assignment of the lowest $\Theta(uudd \bar
s)$ state is most likely $(1/2)^-$. We also calculate the mass of the charm
analog of the $\Theta$ and find that the $\Theta_c(uudd \bar c)$ state lies
much higher than the $DN$ threshold, in contrast to several model predictions.


title: Lattice QCD on Earth Simulator

abstract:
  We report on coding and performance of our polynomial hybrid Monte Carlo
program on the Earth Simulator. At present the entire program achieves 25--40%
efficiency. An analysis of overheads shows that a tuning of inter-node
communications is required for further improvement.


title: A More Improved Lattice Action for Heavy Quarks

abstract:
  We extend the Fermilab formalism for heavy quarks to develop a more improved
action. We give results of matching calculations of the improvement couplings
at tree level. Finally, we estimate the discretization errors associated with
the new action.


title:
Consistency of lattice definitions of U(1) flux in Abelian projected
  SU(2) gauge theory

abstract:
  We reexamine the dual Abrikosov vortex under the requirement that the lattice
averages of the fields satisfy exact Maxwell equations [ME]. The electric ME
accounts for the total flux and the magnetic ME determines the shape of the
confining string. This leads to unique and consistent definitions of flux and
electric and magnetic currents at finite lattice spacing. The resulting
modification of the standard DeGrand-Toussaint construction gives a magnetic
current comprised of smeared monopoles.


title: A New Method for Simulating QCD at Finite Density

abstract:
  We propose a new method for simulating QCD at finite density, where
interesting phases such as the color superconductivity phase is conjectured to
appear. The method is based on a general factorization property of distribution
functions of observables, and it is therefore applicable to any system with a
complex action. The so-called overlap problem is completely eliminated by the
use of constrained simulations. We test this method in a Random Matrix Theory
for finite density QCD, where we are able to reproduce the exact results for
the quark number density. The achieved system size is large enough to extract
the thermodynamic limit. Our results provide a clear understanding of how the
expected first order phase transition is induced by the imaginary part of the
action. We also discuss the noncommutativity of the zero chemical potential
limit and the thermodynamic limit, which is relevant to recent Monte Carlo
studies at small chemical potential.


title: Lattice Superstring and Noncommutative Geometry

abstract:
  Recent developments in superstring theory and noncommutative geometry are
deeply related to the idea of Eguchi-Kawai reduction in large N gauge theories
which dates back to early 80s. After a general review on this subject including
revived interests in solving planar QCD, we present some results in the
superstring matrix model suggesting the dynamical generation of 4d space-time
due to the collapse of the eigenvalue distribution. We then discuss interesting
dynamical properties of field theories in noncommutative geometry, which have
been revealed by Monte Carlo simulations of twisted reduced models. We conclude
with a comment on the recent proposal for a lattice construction of
supersymmetric gauge theories based on reduced models.


title: An Approach to Higher Dimensional Theories Based on Lattice Gauge Theory

abstract:
  A higher dimensional lattice space can be decomposed into a number of
four-dimensional lattices called as layers. The higher dimensional gauge theory
on the lattice can be interpreted as four-dimensional gauge theories on the
multi-layer with interactions between neighboring layers. We propose the new
possibility to realize the continuum limit of a five-dimensional theory based
on the property of the phase diagram.


title: Confinement of Color: Recent Progress

abstract:
  Recent progress done in Pisa on the subject is presented. It is shown that
dual superconductivity of the vacuum or absence of it is an intrinsic property
of QCD vacuum, independent of the choice of the abelian projection. The order
of the deconfining phase transition in $N_f=2$ QCD is studied as a key to
understand the mechanism of confinement.


title: What is the order of the deconfining phase transition?

abstract:
  The techniques are discussed by which the order of the deconfining phase
transition is investigated on the lattice. QCD with $N_f=2$ is a special case,
which can provide information on the mechanism of confinement.


title: Confinement of Color: A Review

abstract:
  The status of our understanding of the mechanisms of color confinement is
reviewed, in particular the results of numerical simulations on the lattice.


title: Classical simulations and particle production in heavy-ion collisions

abstract:
  The classical approximation may be applied to a number of problems in
non-equilibrium field theory. The principles and limits of classical real-time
lattice simulations are presented, with particular emphasis on the definition
of particle numbers and energies and on applications to the earliest stages of
heavy-ion collisions.


title:
Consistent Definitions of Flux and Electric and Magnetic Current in
  Abelian Projected SU(2) Lattice Gauge Theory

abstract:
  Through the use of a lattice U(1) Ward-Takahashi identity, one can find a
precise definition of flux and electric four-current that does not rely on the
continuum limit. The magnetic four-current defined for example by the
DeGrand-Toussaint construction introduces order a^2 errors in the field
distributions. We advocate using a single definition of flux in order to be
consistent with both the electric and magnetic Maxwell's equations at any
lattice spacing. In a U(1) theory the monopoles are slightly smeared by this
choice, i.e. are no longer associated with a single lattice cube. In Abelian
projected SU(2) the consistent definition suggests further modifications. For
simulations in the scaling window, we do not foresee large changes in the
standard analysis of the dual Abrikosov vortex in the maximal Abelian gauge
because the order a^2 corrections have small fluctuations and tend to cancel
out. However in other gauges, the consequences of our definitions could lead to
large effects which may help in understanding the choice of gauge. We also
examine the effect of truncating all monopoles except for the dominant cluster
on the profile of the dual Abrikosov vortex.


title:
Large scale simulations of lattice gauge theory: key NSF project of
  China and recent developments

abstract:
  In a recent funded Key Project of National Science Foundation of China, we
have planned to do large scale simulations of lattice Quantum Chromodynamics,
using the parallel supercomputing facilities in mainland China. Here I briefly
review our plan and progress in recent years.


title: Vacuum polarisation and the muon g-2 in lattice QCD

abstract:
  We measure the hadronic contribution to the vacuum polarisation tensor, and
use it to estimate the hadronic contribution to (g-2)_mu, the muon anomalous
magnetic moment.


title:
Quark spectra and light hadron phenomenology from overlap fermions with
  improved gauge field action

abstract:
  We present first results from a simulation of quenched overlap fermions with
improved gauge field action. Among the quantities we study are the spectral
properties of the overlap operator, the chiral condensate and topological
charge, quark and hadron masses, and selected nucleon matrix elements. To make
contact with continuum physics, we compute the renormalization constants of
quark bilinear operators in perturbation theory and beyond.


title: Full QCD Algorithms towards the Chiral Limit

abstract:
  I discuss the behaviour of algorithms for dynamical fermions as the sea-quark
mass decreases. I focus on the Hybrid-Monte-Carlo (HMC) algorithm applied to
two degenerate flavours of Wilson fermions. First, I briefly review the
performance obtained in large scale HMC simulations. Then I discuss a modified
pseudo-fermion action for the HMC simulation that has been introduced three
years ago. I summarize recent results obtained with this pseudo-fermion action
by the QCDSF and the ALPHA collaborations. I comment on alternatives to the
HMC, like the Multiboson algorithm and variants of it.


title: On Dirac sheet configurations of SU(2) lattice fields

abstract:
  Finite temperature Euclidean SU(2) lattice gauge fields close to the
deconfinement phase transition are subjected to cooling. We find relatively
stable or absolutely stable configurations with an action below the
one-instanton action $S_{inst}=2\pi^2$ both in the deconfinement and the
confinement phases. In this paper we attempt an interpretation of these lowest
action configurations. Their action is purely magnetic and amounts to
$S/S_{inst} \approx N_t/N_s$, where $N_t$ ($N_s$) is the timelike (spacelike)
lattice size, while the topological charge vanishes. In the confined phase part
of the corresponding lattice configurations turns out to be absolutely stable
with respect to the cooling process in which case Abelian projection reveals a
homogeneous, purely Abelian magnetic field closed over the "boundary" in one of
the spatial directions. Referring to the dyonic structure established for the
confinement phase near $T_c$ and based on the observation made for this phase
that such events below the instanton action $S_{inst}$ emerge from
dyon-antidyon annihilation, the question of stability (metastability) is
discussed for both phases. The hypothetically different dyonic structure of the
deconfinement phase, inaccessible by cooling, could explain the metastability.


title: A Novel Ansatz for the Energy-Momentum Tensor on the Lattice

abstract:
  The comparison of structural analogies between the energy-momentum tensors in
general relativity and in a gauge theory of Yang-Mills type is tentatively
extended to lattice physics. These considerations are guiding to a new lattice
model for the symmetric energy-momentum tensor $\Theta_{\mu\nu}$ of the pure
Yang-Mills gauge sector, basing on half powers of the plaquette variable. The
concept of non-trivial principal square roots of unitary matrices in lattice
gauge theories can be epitomized to reconcile the pretension to a uniform
construction principle for the components of $\Theta_{\mu\nu}$ with general
qualitative thermodynamic demands concerning arguments in favour of a Wilson
form for $<\Theta^\mu_\mu>$ and $\Theta_{44}$. SU(2) Monte Carlo results for
the Euclidean expectation values on a 10**4 lattice are compared with that of
competing hitherto existing lattice models for $\Theta_{\mu\nu}$.


title:
Spontaneous symmetry breaking in strong-coupling lattice QCD at high
  density

abstract:
  We determine the patterns of spontaneous symmetry breaking in strong-coupling
lattice QCD in a fixed background baryon density. We employ a
next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f)
chiral symmetry of the continuum theory. We find that the global symmetry of
the ground state varies with N_f and with the background baryon density. In all
cases the condensate breaks the discrete rotational symmetry of the lattice as
well as part of the chiral symmetry group.


title: On the gauge dependence of the singlet and adjoint potentials

abstract:
  We study gauge dependence of the recently suggested definition of the singlet
and adjoint potentials in SU(2) lattice gauge theory. We find that in the (time
local) maximal tree axial gauge the singlet potential obtained from the gauge
dependent correlator ${Tr} L(x)L^\dagger(y)$ differs from that computed in the
Coulomb gauge. In the generalized Coulomb gauge we find the range of the
parameter values in which the singlet potential differs from that in the
Coulomb gauge.


title:
The Study of the Continuum Limit of the Supersymmetric Ward-Takahashi
  Identity for N=1 Super Yang-Mills Theory

abstract:
  The one-loop corrections to the supersymmetric Ward-Takahashi identity (WTi)
are investigated in the off-shell regime in the Wilson formulation of the
discretized N=1 Super Yang-Mills (SYM) theory. The study of the continuum limit
as well as the renormalization procedure for the supercurrent are presented.


title: Non-perturbative Heavy Quark Effective Theory

abstract:
  We explain how to perform non-perturbative computations in HQET on the
lattice. In particular the problem of the subtraction of power-law divergences
is solved by a non-perturbative matching of HQET and QCD. As examples, we
present a full calculation of the mass of the b-quark in the combined static
and quenched approximation and outline an alternative way to obtain the B-meson
decay constant at lowest order. Since no excessively large lattices are
required, our strategy can also be applied including dynamical fermions.


title: Non perturbative study of QCD on a 2+2 anisotropic lattice

abstract:
  We present preliminary results for a non perturbative determination of the
parameters in the action required to restore Lorentz invariance in long
distance correlators, using the static interquark potential. Comparison with
analytical results is made and further applications are discussed.


title:
Quenched and Unquenched Chiral Perturbation Theory in the
  \epsilon-Regime

abstract:
  The chiral limit of finite-volume QCD is the $\epsilon$-regime of the theory.
We discuss how this regime can be used for determining low-energy observables
of QCD by means of comparisons between lattice simulations and quenched and
unquenched chiral perturbation theory. The quenched theory suffers in the
$\epsilon$-regime from ``quenched finite volume logs'', the finite-volume
analogs of quenched chiral logs.


title: A BCS Gapped Superfluid on the Lattice

abstract:
  We discuss results of numerical analyses of the 3+1 dimensional
Nambu--Jona-Lasinio model at non-zero baryon density. By studying relevant
order parameters, it is shown that the model goes through a transition between
a vacuum with broken chiral symmetry, and a chirally restored phase at high
baryon chemical potential (mu) with a diquark condensate roughly proportional
to the area of the Fermi surface and a broken U(1) baryon number symmetry. The
condensation of diquark pairs from the fermionic spectrum is shown to lead to
an energy gap (Delta) about the Fermi energy (E_F), which is found to be
approximately 15% of the vacuum fermion mass and roughly independent of mu in
the chirally restored phase. The ground-state is believed, therefore, to be
that of a BCS superfluid. We also discuss the effect of simulating on a finite
volume, and any caveats this places on the conclusions made above.


title: The Casimir Energy Paradox of the QCD String

abstract:
  It is widely thought that the early onset of the asymptotic Casimir energy
with unit conformal charge signals bosonic string formation of the confining
flux connecting a static quark-antiquark pair in QCD. This is observed on a
scale where most of the string eigenmodes do not exist and the few stable modes
above the ground state are displaced. Hints for the resolution of this paradox
are suggested.


title: Three flavor dynamical QCD project by CP-PACS/JLQCD

abstract:
  The CP-PACS and JLQCD Collaborations have been made systematic studies of
lattice QCD carrying out both chiral and continuum extrapolations. Importance
of dynamical quark effects has been clarified by a comparison of quenched QCD
and two flavor full QCD simulations. In two flavor simulations, the dynamical
effects of $u$ and $d$ quarks are taken into account, but the third quark $s$
is still treated in a quenched approximation. As the final step towards a fully
realistic lattice simulation of QCD, two collaborations started a joint project
of three flavor QCD, concentrating all big computers available. Based on a
series of preparative studies of exact simulation algorithm and
non-perturbative improvement coefficient, a large scale simulation of three
flavor QCD has been started. I present the results of light hadron spectrum and
light quark masses from the first production runs.


title:
Results on improved KS dynamical configurations: spectrum, decay
  constants, etc

abstract:
  The MILC Collaboration has been producing ensembles of lattice configurations
with three dynamical flavors for the past few years. There are now results for
three lattice spacings for a variety of light and strange quark masses, ranging
down to $m_l=0.1 m_s$, where $m_s$ is the dynamical strange quark mass and
$m_l$ is the common mass of the $u$ and $d$ quarks. Recently, the Fermilab,
HPQCD, MILC and UKQCD collaborations have presented a summary of results
obtained using these lattices. Compared with quenched results, these new
calculations show great improvement in agreement with experiment. This talk
addresses the technical improvements that make these calculations possible and
provides additional details of calculations not presented in the initial
summary. We demonstrate that a wide range of hadronic observables can now be
calculated to 2--3% accuracy.


title:
Properties of charmonium in lattice QCD with 2+1 flavors of improved
  staggered sea quarks

abstract:
  We use the dynamical gluon configurations provided by the MILC collaboration
in a study of the charmonium spectrum and psi leptonic width. We examine sea
quark effects on mass splitting and on the leptonic decay matrix element for
light masses as low as m_s/5, while keeping the strange quark mass fixed and
the lattice spacing nearly constant.


title: Recent Developments of Domain-wall/Overlap Fermions for Lattice QCD

abstract:
  I review the lattice formulations of vector-like gauge theories (e.g. QCD)
with domain-wall/overlap fermions, and discuss how to optimize the chiral
symmetry for any finite $ N_s $ (sites in the fifth dimension). In this
formulation, quark propagators in gauge background can be computed efficiently
through the effective 4D lattice Dirac operator.


title: Higher-order perturbation theory for highly-improved actions

abstract:
  I review techniques and applications of higher-order perturbation theory for
highly-improved lattice actions.