title: Anisotropic Lattice QCD Studies of Penta-quark Anti-decuplet

abstract:
  Anti-decuplet penta-quark baryon is studied with the quenched anisotropic
lattice QCD for accurate measurement of the correlator. Both the positive and
negative parity states are studied using a non-NK type interpolating field with
I=0 and J=1/2. After the chiral extrapolation, the lowest positive parity state
is found at m_{Theta} \simeq 2.25 GeV, which is too massive to be identified
with the experimentally observed Theta^+(1540). The lowest negative parity
state is found at m_{Theta}\simeq 1.75 GeV, which is rather close to the
empirical value. To confirm that this state is a compact 5Q resonance, a new
method with ``hybrid boundary condition (HBC)'' is proposed. The HBC analysis
shows that the observed state in the negative parity channel is an NK
scattering state.


title: Generalized Parton Distributions in Full Lattice QCD

abstract:
  We present recent results on generalized parton distributions from dynamical
lattice QCD calculations. Our set of twelve different combinations of couplings
and quark masses allows for a preliminary study of the pion mass dependence of
the transverse nucleon structure.


title:
The scaling dimension of low lying Dirac eigenmodes and of the
  topological charge density

abstract:
  As a quantitative measure of localization, the inverse participation ratio of
low lying Dirac eigenmodes and topological charge density is calculated on
quenched lattices over a wide range of lattice spacings and volumes. Since
different topological objects (instantons, vortices, monopoles, and artifacts)
have different co-dimension, scaling analysis provides information on the
amount of each present and their correlation with the localization of low lying
eigenmodes.


title: Lattice QCD Study of the Pentaquark Baryons

abstract:
  We study the spin $\frac12$ hadronic state in quenched lattice QCD to search
for a possible $S=+1$ pentaquark resonance. Simulations are carried out on
$8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices
at $\beta$=5.7 at the quenched level with the standard plaquette gauge action
and Wilson quark action. We adopt two independent operators with I=0 and
$J^P=\frac12$ to construct a $2\times 2$ correlation matrix. After the
diagonalization of the correlation matrix, we successfully obtain the energies
of the ground-state and the 1st excited-state in this channel. The volume
dependence of the energies suggests the existence of a possible resonance state
slightly above the NK threshold in I=0 and $J^P=\frac12^-$ channel.


title: Kaon matrix elements in domain-wall QCD with DBW2 gauge action

abstract:
  We present calculations of the decay constants and kaon B-parameter $B_K$ as
the first stage of RBC Collaboration's quenched numerical simulations using
DBW2 gauge action and domain-wall fermions. Some of potential systematic errors
and consistency to previous works are discussed.


title: QCD at Finite temperature and density with staggered and Wilson quarks

abstract:
  One of the most challenging issues in particle physics is to study QCD in
extreme conditions. Precise determination of the QCD phase diagram on
temperature $T$ and chemical potential $\mu$ plane will provide valuable
information for quark-gluon plasma (QGP) and neutron star physics. We present
results for phase structure on the $(\mu, T)$ plane for lattice QCD with Wilson
fermions from strong coupling Hamiltonian analysis and Kogut-Susskind Fermions
from Lagrangian Monte Carlo simulations at intermediate coupling.


title: Infrared Divergent Coulomb Self-Energy in Yang-Mills Theory

abstract:
  It is shown numerically that the Coulomb self-energy of an isolated, color
non-singlet source diverges in an infinite volume. This is in accord with the
Gribov Horizon scenario of confinement advocated by Gribov and Zwanziger. It is
also shown that this divergence can be attributed to the presence of center
vortices in thermalized lattice configurations.


title: Lattice gluodynamics at negative g^2

abstract:
  We consider Wilson's SU(N) lattice gauge theory (without fermions) at
negative values of beta= 2N/g^2 and for N=2 or 3. We show that in the limit
beta -> -infinity, the path integral is dominated by configurations where links
variables are set to a nontrivial element of the center on selected non
intersecting lines. For N=2, these configurations can be characterized by a
unique gauge invariant set of variables, while for N=3 a multiplicity growing
with the volume as the number of configurations of an Ising model is observed.
In general, there is a discontinuity in the average plaquette when g^2 changes
its sign which prevents us from having a convergent series in g^2 for this
quantity. For N=2, a change of variables relates the gauge invariant
observables at positive and negative values of beta. For N=3, we derive an
identity relating the observables at beta with those at beta rotated by +-
2pi/3 in the complex plane and show numerical evidence for a Ising like first
order phase transition near beta=-22. We discuss the possibility of having
lines of first order phase transitions ending at a second order phase
transition in an extended bare parameter space.


title: Leptonic decay constants f_Ds and f_D in three flavor lattice QCD

abstract:
  We determine the leptonic decay constants in three flavor unquenched lattice
QCD. We use O(a^2)-improved staggered light quarks and O(a)-improved charm
quarks in the Fermilab heavy quark formalism. Our preliminary results, based
upon an analysis at a single lattice spacing, are f_Ds = 263(+5-9)(+/-24) MeV
and f_D = 225(+11-13)(+/-21) MeV. In each case, the first reported error is
statistical while the is the combined systematic uncertainty.


title:
The phase structure of lattice QCD with two flavours of Wilson quarks
  and renormalization group improved gluons

abstract:
  The effect of changing the lattice action for the gluon field on the recently
observed [1] first order phase transition near zero quark mass is investigated
by replacing the Wilson plaquette action by the DBW2 action. The lattice action
for quarks is unchanged: it is in both cases the original Wilson action. It
turns out that Wilson fermions with the DBW2 gauge action have a phase
structure where the minimal pion mass and the jump of the average plaquette are
decreased, when compared to Wilson fermions with Wilson plaquette action at
similar values of the lattice spacing. Taking the DBW2 gauge action is
advantageous also from the point of view of the computational costs of
numerical simulations.


title:
Grand canonical potential for a static quark--anti-quark pair at finite
  T/mu

abstract:
  We present numerical results on the static quark--anti-quark grand canonical
potential in full QCD at non-vanishing temperature ($T$) and quark chemical
potential ($\mu$). Non-zero $\mu$-s are reached by means of multi-parameter
reweighting. The dynamical staggered simulations were carried out for $n_f=2+1$
flavors with physical quark masses on $4\times 12^3$ lattices.


title:
Baryon Masses in Partially Quenched Heavy Hadron Chiral Perturbation
  Theory

abstract:
  The masses of baryons containing a heavy quark are calculated to
next-to-leading order in partially quenched heavy hadron chiral perturbation
theory. Calculations are performed for three light flavors in the isospin limit
and additionally for two light non-degenerate flavors. The results presented
are necessary for extrapolating lattice QCD and partially quenched lattice QCD
calculations of the heavy hadron masses.


title: Hadron Spectrum and Decay Constant from $N_F=2$ Domain Wall QCD

abstract:
  We report on the first large-scale study of two flavor QCD with domain wall
fermions (DWF). Simulation has been carried out at three dynamical quark mass
values about 1/2, 3/4, and 1 $m_{strange}$ on $16^3\times 32$ volume with
$L_s=12$ and $a^{-1}\approx 1.7$ GeV. After discussing the details of the
simulation, we report on the light hadron spectrum and decay constants.


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

abstract:
  We continue to construct lattice super Yang-Mills theories along the line
discussed in the previous papers \cite{sugino, sugino2}. In our construction of
${\cal N}=2, 4$ theories in four dimensions, the problem of degenerate vacua
seen in \cite{sugino} is resolved by extending some fields and soaking up
would-be zero-modes in the continuum limit, while in the weak coupling
expansion some surplus modes appear both in bosonic and fermionic sectors
reflecting the exact supersymmetry. A slight modification to the models is made
such that all the surplus modes are eliminated in two- and three-dimensional
models obtained by dimensional reduction thereof. ${\cal N}=4, 8$ models in
three dimensions need fine-tuning of three and one parameters respectively to
obtain the desired continuum theories, while two-dimensional models with ${\cal
N}=4, 8$ do not require any fine-tuning.


title: Failure of Mean Field Theory at Large N

abstract:
  We study strongly coupled lattice QCD with $N$ colors of staggered fermions
in 3+1 dimensions. While mean field theory describes the low temperature
behavior of this theory at large $N$, it fails in the scaling region close to
the finite temperature second order chiral phase transition. The universal
critical region close to the phase transition belongs to the 3d XY universality
class even when $N$ becomes large. This is in contrast to Gross-Neveu models
where the critical region shrinks as $N$ (the number of flavors) increases and
mean field theory is expected to describe the phase transition exactly in the
limit of infinite $N$. Our work demonstrates that close to second order phase
transitions infrared fluctuations can sometimes be important even when $N$ is
strictly infinite.

categories: hep-lat cond-mat.stat-mech hep-ph hep-th


title: Baryon magnetic moments in the external field method

abstract:
  We present a calculation of the magnetic moments of the baryon octet and
decuplet using the external field method and standard Wilson gauge and fermion
actions in the quenched approximation. Progressively smaller static magnetic
fields are introduced on a $24^4$ latticeat beta=6.0 and the pion mass is
probed down to about 500 MeV. Magnetic moments are extracted from the linear
response of the masses to the external field.


title: Confinement in the lattice Landau Gauge QCD simulation

abstract:
  The running coupling and the Kugo-Ojima parameter of the confinement
criterion are measured for the quenched SU(3) \beta=6.4, 6.45, 56^4 lattice and
the unquenched \beta=5.2, 20^3 x 48 lattice of JLQCD, \beta=2.1, \kappa=0.1357,
0.1382, 24^3 x 48 lattice of CP-PACS and \beta_{imp}=6.76,a m_{u,d}=0.007,
6.83,a m_{u,d}=0.040, 20^3 x 64 lattice of MILC collaboration.
  The quenched SU(3) 56^4 lattice data suggest presence of infrared fixed point
of \alpha_s=2.5(5) and the approach of the ensemble of the 1st copy to the
Gribov boundary. The running coupling of q>2GeV can be fitted by the
perturbative QCD(pQCD) + c/q^2 correction. We find the Kugo-Ojima parameter
u(0)=-0.83(3).
  The rotational symmetry of the gluon propagator of the unquenched SU(3) is
partially recovered, but its magnitude depends on whether the Wilson fermion or
the Kogut-Susskind(KS) fermion are coupled to the gauge field. The gluon
propagator coupled to KS fermion is more suppressed than that coupled to Wilson
fermion. The running coupling inherits the same trend. The unquenched running
coupling of the of q>3GeV can be fitted by the pQCD without c/q^2 term. The
Kugo-Ojima parameter of unquenched configurations with light fermion masses is
consistent with u(0)=-1.0.


title: The dual Meissner effect in SU(2) Landau gauge

abstract:
  The dual Meissner effect is observed without monopoles in quenched SU(2) QCD
with Landau gauge-fixing. Abelian as well as non-Abelian electric fields are
squeezed. Magnetic displacement currents which are time-dependent Abelian
magnetic fields play a role of solenoidal currents squeezing Abelian electric
fields. Monopoles are not always necessary to the dual Meissner effect. The
squeezing of the electric flux means the dual London equation and the
massiveness of the Abelian electric fields as an asymptotic field. The mass
generation of the Abelian electric fields is related to a gluon condensate
$<A^a_{\mu}A^a_{\mu}>\neq 0$ of mass dimension 2.


title:
Dependence of Dirac eigenmodes on boundary conditions for SU(2) lattice
  gauge theory

abstract:
  We analyze zero modes of the Dirac operator for SU(2) lattice gauge theory.
We find that the zero modes are strongly localized in all 4 directions. The
position of these lumps depends on the boundary conditions we use for the Dirac
operator. We compare periodic boundary conditions and anti-periodic boundary
conditions and find that the position of the zero modes jumps for about one
third of the configurations.


title: Less naive about supersymmetric lattice quantum mechanics

abstract:
  We explain why naive discretization results that have appeared in
[hep-lat/0006013] do not appear to yield the desired continuum limit. The
fermion propagator on the lattice inevitably yields a diagram with nonvanishing
UV degree D=0 contribution in lattice perturbation theory, in contrast to what
occurs in the continuum. This diagram gives a finite correction to the boson
2-point function that must be subtracted off in order to obtain the
perturbation series of the continuum theory, in the limit where the lattice
spacing $a$ vanishes. Using a transfer matrix approach, we provide a
nonperturbative proof that this counterterm suffices to yield the desired
continuum limit. This analysis also allows us to improve the action to O(a). We
demonstrate by Monte Carlo simulation that the spectrum of the continuum theory
is well-approximated at finite but small $a$, for both weak and strong
coupling. We contrast the above situation for the naive lattice action to what
occurs for the supersymmetric lattice action, which preserves a discrete
version of half the supersymmetry. There, cancellations between D=0 diagrams
occur, obviating the need for counterterms.


title: Volume dependences from lattice chiral perturbation theory

abstract:
  The physics of pions within a finite volume is explored using lattice
regularized chiral perturbation theory. This regularization scheme permits a
straightforward computational approach to be used in place of analytical
continuum techniques. Using the pion mass, decay constant, form factor and
charge radius as examples, it is shown how numerical results for volume
dependences are obtained at the one-loop level from simple summations.


title: Spontaneous CP violation and quark mass ambiguities

abstract:
  I explore the regions of quark masses where CP will be spontaneously broken
in the strong interactions. The boundaries of these regions are controlled by
the chiral anomaly, which manifests itself in ambiguities in the definition of
non-degenerate quark masses. In particular, the concept of a single massless
quark is ill defined.


title: The Kaon B-parameter from Two-Flavour Dynamical Domain Wall Fermions

abstract:
  We report on the calculation of the kaon B-parameter using two dynamical
flavours of domain wall fermions. Our analysis is based on three ensembles of
configurations, each consisting of about 5,000 HMC trajectories, with a lattice
spacing of approximately 1.7 GeV for 16^3x32 lattices; dynamical quark masses
range from approximately the strange quark mass to half of that. Both
degenerate and non-degenerate quark masses are used for the kaons.


title: Quark propagator in Landau and Laplacian gauges with overlap fermions

abstract:
  The properties of the momentum space quark propagator in Landau gauge and
Gribov copy free Laplacian gauge are studied for the overlap quark action in
quenched lattice QCD. Numerical calculations are done on two lattices with
different lattice spacing $a$ and the same physical volume. We have calculated
the nonperturbative wave function renormalization function $Z(q)$ and the
nonperturbative mass function $M(p)$ for a variety of bare quark masses and
perform a simple linear extrapolation to the chiral limit. We focus on the
comparison of the behavior of $Z(q)$ and $M(p)$ in the chiral limit in the two
gauge fixing schemes as well as the behavior on two lattices with different
lattice spacing $a$. We find that the mass functions $M(p)$ are very similar
for the two gauges while the wave-function renormalization function $Z(q)$ is
more strongly infrared suppressed in the Laplacian gauge than in the Landau
gauge on the finer lattice. For Laplacian gauge, it seems that the finite $a$
error is large on the coarse lattice which has a lattice spacing $a$ of about
0.124 fm.


title:
The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs
  Global Behavior in Local Observables and Dirac Eigenmodes

abstract:
  The structure of QCD vacuum can be studied from first principles using
lattice-regularized theory. This line of research entered a qualitatively new
phase recently, wherein the space-time structure (at least for some quantities)
can be directly observed in configurations dominating the QCD path integral,
i.e. without any subjective processing of typical configurations. This approach
to QCD vacuum structure does not rely on any proposed picture of QCD vacuum but
rather attempts to characterize this structure in a model-independent manner,
so that a coherent physical picture of the vacuum can emerge when such unbiased
numerical information accumulates to a sufficient degree. An important part of
this program is to develop a set of suitable quantitative characteristics
describing the space-time structure in a meaningful and physically relevant
manner. One of the basic pertinent issues here is whether QCD vacuum dynamics
can be understood in terms of localized vacuum objects, or whether such objects
behave as inherently global entities. The first direct studies of vacuum
structure strongly support the latter. In this paper, we develop a formal
framework which allows to answer this question in a quantitative manner. We
discuss in detail how to apply this approach to Dirac eigenmodes and to basic
scalar and pseudoscalar composites of gauge fields (action density and
topological charge density). The approach is illustrated numerically on overlap
Dirac zeromodes and near-zeromodes. This illustrative data provides direct
quantitative evidence supporting our earlier arguments for the global nature of
QCD Dirac eigenmodes.


title: Twisted mass QCD for the pion electromagnetic form factor

abstract:
  The pion form factor is computed using quenched twisted mass QCD and the
GMRES-DR matrix inverter. The momentum averaging procedure of Frezzotti and
Rossi is used to remove leading lattice spacing artifacts, and numerical
results for the form factor show the expected improvement with respect to the
standard Wilson action. Although some matrix inverters are known to fail when
applied to twisted mass QCD, GMRES-DR is found to be a viable and powerful
option. Results obtained for the pion form factor are consistent with the
published results from other O(a) improved actions and are also consistent with
the available experimental data.


title: The Infrared Landau Gauge Gluon Propagator from Lattice QCD

abstract:
  The quenched Landau gauge gluon propagator is investigated in lattice QCD
with large assimetric lattices, accessing momenta as low as $q \sim 100$ MeV or
smaller. Our investigation focus on the IR limit of the gluon dressing
function, testing the compatibility with recent solutions of the
Dyson-Schwinger equations. In particular, the low energy parameters $\kappa$
and $\alpha (0)$ are measured.


title: PC Clusters for Lattice QCD

abstract:
  In the last several years, tightly coupled PC clusters have become widely
applied, cost effective resources for lattice gauge computations. This paper
discusses the practice of building such clusters, in particular balanced design
requirements. I review and quantify the improvements over time of key
performance parameters and overall price to performance ratio. Applying these
trends and technology forecasts given by computer equipment manufacturers, I
predict the range of price to performance for lattice codes expected in the
next several years.


title: Hadron Spectrum from Dynamical Lattice QCD Simulations

abstract:
  Recent progress in unquenched lattice QCD simulations is reviewed with
emphasis on understanding of chiral behavior for light quark masses.


title: The role of Lattice QCD in flavor physics

abstract:
  Understanding flavor physics is one of the most important tasks of particle
physics today, which is motivating an extraordinary experimental and
theoretical investigational effort. Important progress in this field has
already been achieved in the last few years, with Lattice QCD calculations
playing an essential role in this effort. I will describe some lattice
contributions to the studies of flavor physics by focusing particularly on the
determination of the CKM matrix and on the study of CP violation in the
Standard Model.


title:
A geometrical approach to N=2 super Yang-Mills theory on the two
  dimensional lattice

abstract:
  We propose a discretization of two dimensional Euclidean Yang-Mills theories
with N=2 supersymmetry which preserves exactly both gauge invariance and an
element of supersymmetry. The approach starts from the twisted form of the
continuum super Yang Mills action which we show may be written in terms of two
real Kahler-Dirac fields whose components transform into each other under the
twisted supersymmetry. Once the theory is written in this geometrical language
it is straightforward to discretize by mapping the component tensor fields to
appropriate geometrical structures in the lattice and by replacing the
continuum exterior derivative and its adjoint by appropriate lattice covariant
difference operators. The lattice action is local and possesses a unique vacuum
state while the use of Kahler-Dirac fermions ensures the model does not exhibit
spectrum doubling.


title: Going chiral: overlap versus twisted mass fermions

abstract:
  We compare the behavior of overlap fermions, which are chirally invariant,
and of Wilson twisted mass fermions at full twist in the approach to the chiral
limit. Our quenched simulations reveal that with both formulations of lattice
fermions pion masses of O(250 MeV) can be reached in practical applications.
Our comparison is done at a fixed value of the lattice spacing a=0.123 fm. A
number of quantities are measured such as hadron masses, pseudoscalar decay
constants and quark masses obtained from Ward identities. We also determine the
axial vector renormalization constants in the case of overlap fermions.


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

abstract:
  I present quenched domain wall fermion and 2+1 flavor improved Kogut-Susskind
fermion calculations of the hadronic vacuum polarization which are used to
calculate the ${\cal O}(\alpha^2)$ hadronic contribution to the anomalous
magnetic moment of the muon. Together with previous quenched calcuations, the
new results confirm that in the quenched theory the hadronic contribution is
signifcantly smaller ($\sim 30%$) than the value obtained from the total cross
section of $e^+e^-$ annhilation to hadrons. The 2+1 flavor results show an
increasing contribution to $g-2$ as the quark mass is reduced.


title: Neutron Electric Dipole Moment with Domain Wall Quarks

abstract:
  We present preliminary results for nucleon dipole moments computed with
domain wall fermions. Our main target is the electric dipole moment of the
neutron arising from the theta term in the gauge part of the QCD lagrangian.
The calculated magnetic dipole moments of the proton and neutron are in rough
accord with experimental values.


title: Overlap of the Wilson loop with the broken-string state

abstract:
  Numerical experiments on most gauge theories coupled with matter failed to
observe string-breaking effects while measuring Wilson loops only. We show
that, under rather mild assumptions, the overlap of the Wilson loop operator
with the broken-string state obeys a natural upper bound implying that the
signal of string-breaking is in general too weak to be detected by the
conventional updating algorithms.
  In order to reduce the variance of the Wilson loops in 3-D Z_2 gauge Higgs
model we use a new algorithm based on the L\"uscher-Weisz method combined with
a non-local cluster algorithm which allows to follow the decay of rectangular
Wilson loops up to values of the order of 10^{-24}. In this way a sharp signal
of string breaking is found.


title: Lattice QCD with mixed actions

abstract:
  We discuss some of the implications of simulating QCD when the action used
for the sea quarks is different from that used for the valence quarks. We
present exploratory results for the hadron mass spectrum and pseudoscalar meson
decay constants using improved staggered sea quarks and HYP-smeared overlap
valence quarks. We propose a method for matching the valence quark mass to the
sea quark mass and demonstrate it on UKQCD clover data in the simpler case
where the sea and valence actions are the same.


title: Lattice QCD with two dynamical flavors of domain wall quarks

abstract:
  We present results from the first large-scale study of two flavor QCD using
domain wall fermions (DWF), a chirally symmetric fermion formulation which has
proven to be very effective in the quenched approximation. We work on lattices
of size 16^3x32, with a lattice cut-off of a^{-1}\approx 1.7 GeV, and dynamical
(or sea) quark masses in the range m_{strange}/2 \simle m_{sea} \simle
m_{strange}. After discussing the algorithmic and implementation issues
involved in simulating dynamical DWF, we report on the low-lying hadron
spectrum, decay constants, static quark potential, and the important kaon weak
matrix element describing indirect CP violation in the Standard Model, B_K. In
the latter case we include the effect of non-degenerate quark masses (m_s \neq
m_u = m_d), finding B_K(MS-bar, 2 GeV) = 0.495(18).


title: Before sailing on a domain-wall sea

abstract:
  We discuss the very different roles of the valence-quark and the sea-quark
residual masses ($m_{res}^v$ and $m_{res}^s$) in dynamical domain-wall fermions
simulations. Focusing on matrix elements of the effective weak hamiltonian
containing a power divergence, we find that $m_{res}^v$ can be a source of a
much bigger systematic error. To keep all systematic errors due to residual
masses at the 1% level, we estimate that one needs $a m_{res}^s \le 10^{-3}$
and $a m_{res}^v \le 10^{-5}$, at a lattice spacing $a\sim 0.1$ fm. The
practical implications are that (1) optimal use of computer resources calls for
a mixed scheme with different domain-wall fermion actions for the valence and
sea quarks; (2) better domain-wall fermion actions are needed for both the sea
and the valence sectors.


title: Nucleon structure with domain wall fermions

abstract:
  We report the status of RBCK calculations on nucleon structure with quenched
and dynamical domain wall fermions. The quenched results for the moments of
structure functions (< x >_q), (< x>_{\Delta u - \Delta d}), and (< 1 >_{\delta
q}) from 1.3 GeV cutoff lattices are complete with non perturbative
renormalization (NPR). The dynamical results with two degenerate dynamical
quark flavors from 1.7 GeV cutoff lattices are without NPR while the axial
charge result is naturally renormalized.


title: An Experimenter's View of Lattice QCD

abstract:
  Lattice QCD has the potential this decade to maximize the sensitivity of the
entire flavor physics program to new physics and pave the way for understanding
physics beyond the Standard Model at the LHC in the coming decade. However, the
challenge for the Lattice is to demonstrate reliability at the level of a few
per cent given a past history of 10-20% errors. The CLEO-c program at the
Cornell Electron Storage Ring is providing the data that will make the
demonstration possible.


title: Instantons and Monte Carlo Methods in Quantum Mechanics

abstract:
  In these lectures we describe the use of Monte Carlo simulations in
understanding the role of tunneling events, instantons, in a quantum mechanical
toy model. We study, in particular, a variety of methods that have been used in
the QCD context, such as Monte Carlo simulations of the partition function,
cooling and heating, the random and interacting instanton liquid model, and
numerical simulations of non-Gaussian corrections to the semi-classical
approximation.


title: Fermion Determinants: Some Recent Analytic Results

abstract:
  The use of known analytic results for the continuum fermion determinants in
QCD and QED as benchmarks for zero lattice spacing extrapolations of lattice
fermion determinants is proposed. Specifically, they can be used as a check on
the universality hypothesis relating the continuum limits of the na\"{\i}ve,
staggered and Wilson fermion determinants.


title: Dirac zero-modes in compact U(1) gauge theory

abstract:
  We study properties of the zero and near-zero eigenmodes of the overlap Dirac
operator in compact U(1) gauge theory. In the confinement phase the exact
zero-modes are localized as found by studying the values of the inverse
participation ratio and other features. Non-zero-eigenmodes are less localized
in the confinement phase. In the Coulomb phase no zero-modes are observed and
the eigenmodes show no localization at all.


title: Physics at Tevatron Run II

abstract:
  We present recent physics results from the Tevatron Collider experiments CDF
and D0. (contribution to Lattice 2004)


title: Searching for chiral logs in the static-light decay constant

abstract:
  Using the clover fermion action in unquenched QCD with pion masses as low as
420 MeV, we look for evidence for chiral logs in the static-light decay
constant. There is some evidence for a chiral log term, if the original static
theory of Eichten and Hill is used. However, the more precise data from the
static action of the ALPHA collaboration do not show any evidence for
non-linear dependence of the static-light decay constant on the light quark
mass. We make some comments on the connection between chiral perturbation
theory for decay constants of the pion and static-light meson.


title: B_s mesons from the lattice: Excited states

abstract:
  The energies of different angular momentum states of a heavy-light meson were
measured on a lattice in PRD 58, 34506 (1998) . We have now continued this
study using several different lattices, quenched and unquenched, that have
different physical lattice sizes, clover coefficients, hopping parameters and
quark-gluon couplings. The heavy quark is taken to be infinitely heavy, whereas
the light quark mass is approximately that of the strange quark. By
interpolating in the heavy and light quark masses we can thus compare the
lattice results with the B_s meson. Most interesting is the lowest P-wave B_s
state, since it is possible that it lies below the BK threshold and hence is
very narrow. Unfortunately, there are no experimental results on P-wave B_s
mesons available at present.
  In addition to the energy spectrum, we measured earlier also vector (charge)
and scalar (matter) radial distributions of the light quark in the S-wave
states of a heavy-light meson on a lattice (PRD 65, 014512 (2002) and Eur.
Phys. J. C 28, 79 (2003)). Now we are extending the study of radial
distributions to P-wave states.


title:
SU(3)-breaking effects in kaon and hyperon semileptonic decays from
  lattice QCD

abstract:
  We discuss the result of a recent quenched lattice calculation of the K -> pi
vector form factor at zero-momentum transfer, relevant for the determination of
|V_us| from K-> pi l nu decays. Using suitable double ratios of three-point
correlation functions, we show that it is possible to calculate this quantity
at the percent-level precision. The leading quenched effects are corrected for
by means of quenched chiral perturbation theory. The final result, f+(0) =
0.960 +- 0.005_stat +- 0.007_syst, turns out to be in good agreement with the
old quark model estimate made by Leutwyler and Roos. In this paper, we discuss
the phenomenological impact of the lattice result for the extraction of |V_us|,
by updating the analysis of K -> pi l nu decays with the most recent
experimental data. We also present a preliminary lattice study of hyperon Sigma
-> n l nu decays, based on a similar strategy.


title: Matrix product variational formulation for lattice gauge theory

abstract:
  For hamiltonian lattice gauge theory, we introduce the matrix product anzats
inspired from density matrix renormalization group. In this method,
wavefunction of the target state is assumed to be a product of finite matrices.
As a result, the energy becomes a simple function of the matrices, which can be
evaluated using a computer. The minimum of the energy function corresponds to
the vacuum state. We show that the S=1/2 Heisenberg chain model are well
described with the ansatz. The method is also applied to the two-dimensional
S=1/2 Heisenberg and U(1) plaquette chain models.


title:
Non-perturbative definition of five-dimensional gauge theories on the
  R^4 x S^1/Z_2 orbifold

abstract:
  We construct a Z_2 orbifold projection of SU(N) gauge theories formulated in
five dimensions with a compact fifth dimension. We show through a
non-perturbative argument that no boundary mass term for the Higgs field,
identified with some of the fifth dimensional components of the gauge field, is
generated, which would be quadratically divergent in the five-dimensional
ultraviolet cutoff. This opens the possibility of studying these theories
non-perturbatively in order to establish if they can be used as effective
weakly interacting theories at low energies. We make preparations for a study
on the lattice. In particular we show that only Dirichlet boundary conditions
are needed, which specify the breaking pattern of the gauge group at the
orbifold fixpoints.


title: The Pseudoscalar Decay Constant

abstract:
  We discuss insights that may be drawn from our recent 2 flavour
O(a)--improved Wilson quark simulations. We discuss the evidence of the onset
of chiral logarithms in the pion decay constant. An overview is given of
current extrapolation methods and a modification of chiral perturbation theory
is presented as an approach for sensibly extrapolating to the physical quark
masses.


title: Large Field Cutoffs in Lattice Gauge Theory

abstract:
  In pure gauge SU(3) near beta = 6, weak and strong coupling expansions break
down and the MC method seems to be the only practical alternative. We discuss
the possibility of using a modified version of perturbation theory which relies
on a large field cutoff and has been successfully applied to the double-well
potential (Y. M., PRL 88 141601). Generically, in the case of scalar field
theory, the weak coupling expansion is unable to reproduce the exponential
suppression of the large field configurations. This problem can be solved by
introducing a large field cutoff. The value of this cutoff can be chosen to
reduce the discrepancy with the original problem. This optimization can be
approximately performed using the strong coupling expansion and bridges the gap
between the two expansions. We report recent attempts to extend this procedure
for SU(3) gauge theory on the lattice. We compare gauge invariant and gauge
dependent (in the Landau gauge) criteria to sort the configurations into
``large-field'' and ``small-field'' configurations. %We discuss the effects of
discarding the large field configurations. We discuss the convergence of
lattice perturbation theory and the way it can be modified in order to obtain
results similar to the scalar case.


title: Twisted mass chiral perturbation theory at next-to-leading order

abstract:
  We study the properties of pions in twisted mass lattice QCD (with two
degenerate flavors) using chiral perturbation theory (ChPT). We work to
next-to-leading order (NLO) in a power counting scheme in which m_q ~ a
\Lambda_QCD^2, with m_q the physical quark mass and a the lattice spacing. We
argue that automatic O(a) improvement of physical quantities at maximal twist,
which has been demonstrated in general if m_q >> a \Lambda_QCD^2, holds even if
m_q ~ a \Lambda_QCD^2, as long as one uses an appropriate non-perturbative
definition of the twist angle. We demonstrate this with explicit calculations,
for arbitrary twist angle, of all pionic quantities that involve no more than a
single pion in the initial and final states: masses, decay constants, form
factors and condensates, as well as the differences between alternate
definitions of twist angle. We also calculate the axial and pseudoscalar form
factors of the pion, quantities which violate flavor and parity, and which
vanish in the continuum limit. These are of interest because they are not
automatically O(a) improved at maximal twist. They allow a determination of the
unknown low energy constants introduced by discretization errors, and provide
tests of the accuracy of ChPT at NLO. We extend our results into the regime
where m_q ~ a^2 \Lambda_QCD^3, and argue in favor of a recent proposal that
automatic O(a) improvement at maximal twist remains valid in this regime.


title: Scaling tests with dynamical overlap and rooted staggered fermions

abstract:
  We present a scaling analysis in the 1-flavor Schwinger model with the full
overlap and the rooted staggered determinant. In the latter case the chiral and
continuum limit of the scalar condensate do not commute, while for overlap
fermions they do. For the topological susceptibility a universal continuum
limit is suggested, as is for the partition function and the Leutwyler-Smilga
sum rule. In the heavy-quark force no difference is visible even at finite
coupling. Finally, a direct comparison between the complete overlap and the
rooted staggered determinant yields evidence that their ratio is constant up to
$O(a^2)$ effects.


title:
Phase diagram of QCD at finite temperature and chemical potential from
  lattice simulations with dynamical Wilson quarks

abstract:
  We present the first results for lattice QCD at finite temperature $T$ and
chemical potential $\mu$ with four flavors of Wilson quarks. The calculations
are performed using the imaginary chemical potential method at $\kappa=0$,
0.001, 0.15, 0.165, 0.17 and 0.25, where $\kappa$ is the hopping parameter,
related to the bare quark mass $m$ and lattice spacing $a$ by
$\kappa=1/(2ma+8)$. Such a method allows us to do large scale Monte Carlo
simulations at imaginary chemical potential $\mu=i \mu_I$. By analytic
continuation of the data with $\mu_I < \pi T/3$ to real values of the chemical
potential, we expect at each $\kappa\in [0,\kappa_{chiral}]$, a transition line
on the $(\mu, T)$ plane, in a region relevant to the search for quark gluon
plasma in heavy-ion collision experiments. The transition is first order at
small or large quark mass, and becomes a crossover at intermediate quark mass.


title:
N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one
  exact supersymmetry

abstract:
  We formulate ${\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two
dimensional transverse lattice using supersymmetric discrete light cone
quantization in the large-$N_c$ limit. This formulation is free of fermion
species doubling. We are able to preserve one supersymmetry. We find a rich,
non-trivial behavior of the mass spectrum as a function of the coupling
$g\sqrt{N_c}$, and see some sort of "transition" in the structure of a bound
state as we go from the weak coupling to the strong coupling. Using a toy model
we give an interpretation of the rich behavior of the mass spectrum. We present
the mass spectrum as a function of the winding number for those states whose
color flux winds all the way around in one of the transverse directions. We use
two fits to the mass spectrum and the one that has a string theory
justification appears preferable. For those states whose color flux is
localized we present an extrapolated value for $m^2$ for some low energy bound
states in the limit where the numerical resolution goes to infinity.


title: Computation of the strong coupling in QCD with two dynamical flavours

abstract:
  We present a non-perturbative computation of the running of the coupling
alpha_s in QCD with two flavours of dynamical fermions in the Schroedinger
functional scheme. We improve our previous results by a reliable continuum
extrapolation. The Lambda-parameter characterizing the high-energy running is
related to the value of the coupling at low energy in the continuum limit. An
estimate of Lambda*r_0 is given using large-volume data with lattice spacings a
from 0.07 fm to 0.1 fm. It translates into Lambda_{MSbar}^{(2)}=245(16)(16) MeV
[assuming r_0=0.5 fm]. The last step still has to be improved to reduce the
uncertainty.


title:
Automatically generating Feynman rules for improved lattice field
  theories

abstract:
  Deriving the Feynman rules for lattice perturbation theory from actions and
operators is complicated, especially when improvement terms are present. This
physically important task is, however, suitable for automation. We describe a
flexible algorithm for generating Feynman rules for a wide range of lattice
field theories including gluons, relativistic fermions and heavy quarks. We
also present an efficient implementation of this in a freely available,
multi-platform programming language (\python), optimised to deal with a wide
class of lattice field theories.


title: Mass of the B_c Meson in Three-Flavor Lattice QCD

abstract:
  We use lattice QCD to predict the mass of the $B_c$ meson. We use the MILC
Collaboration's ensembles of lattice gauge fields, which have a quark sea with
two flavors much lighter than a third. Our final result is
$m_{B_c}=6304\pm12^{+18}_{- 0} MeV$. The first error bar is a sum in quadrature
of statistical and systematic uncertainties, and the second is an estimate of
heavy-quark discretization effects.


title: Lattice Computations of the Pion Form Factor

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


title:
A path-integral representation of the free one-flavour staggered-fermion
  determinant

abstract:
  Lattice fermion actions are constructed with path integrals which are
equivalent to the free one-flavour staggered fermion determinant. The Dirac
operators used are local and have an identical spectrum of states to the
staggered theory. Operators obeying a generalised Ginsparg-Wilson relation are
developed.


title: On the fourth root prescription for dynamical staggered fermions

abstract:
  With the aim of resolving theoretical issues associated with the fourth root
prescription for dynamical staggered fermions in Lattice QCD simulations, we
consider the problem of finding a viable lattice Dirac operator D such that
(det D_{staggered})^{1/4} = det D. Working in the flavour field representation
we show that in the free field case there is a simple and natural candidate D
satisfying this relation, and we show that it has acceptable locality behavior:
exponentially local with localisation range vanishing ~ (a/m)^{1/2} for lattice
spacing a -> 0. Prospects for the interacting case are also discussed, although
we do not solve this case here.


title: Asymptotic series for distributions

abstract:
  Asymptotic expansions for a wide class of distribution are studied. A simple
method for computation of the series coefficients is suggested. The case when
regularization parameter of the distribution depends on the asymptotic
parameter is considered.


title:
Relations between the Gribov-horizon and center-vortex confinement
  scenarios

abstract:
  We review numerical evidence on connections between the center-vortex and
Gribov-horizon confinement scenarios.


title: Twisted Boundary Conditions in Lattice Simulations

abstract:
  By imposing twisted boundary conditions on quark fields it is possible to
access components of momenta other than integer multiples of 2pi/L on a lattice
with spatial volume L^3. We use Chiral Perturbation Theory to study
finite-volume effects with twisted boundary conditions for quantities without
final-state interactions, such as meson masses, decay constants and
semileptonic form factors, and confirm that they remain exponentially small
with the volume. We show that this is also the case for "partially twisted"
boundary conditions, in which (some of) the valence quarks satisfy twisted
boundary conditions but the sea quarks satisfy periodic boundary conditions.
This observation implies that it is not necessary to generate new gluon
configurations for every choice of the twist angle, making the method much more
practicable. For K->pipi decays we show that the breaking of isospin symmetry
by the twisted boundary conditions implies that the amplitudes cannot be
determined in general (on this point we disagree with a recent claim).


title:
New results on cut-off effects in spectroscopy with the fixed point
  action

abstract:
  Our study on the cut-off effects in quenched light hadron spectroscopy and
pion scattering length with the fixed point action is extended by results
obtained at a lattice spacing a=0.102 fm in a box of size L=1.8 fm. The cut-off
effects are small, but clearly seen as the resolution is increased from a=0.153
fm to a=0.102 fm. In the quark mass region where the errors are small and under
control, our results on the APE plot lie close to the extrapolated numbers of
the CP-PACS Collaboration.


title:
Analyticity in theta on the lattice and the large volume limit of the
  topological susceptibility

abstract:
  Non-analyticity of QCD with a \theta term at \theta=0 may signal a
spontaneous breaking of both parity and time reversal invariance. We address
this issue by investigating the large volume limit of the topological
susceptibility $\chi$ in pure SU(3) gauge theory. We obtain an upper bound for
the symmetry breaking order parameter <Q> and, as a byproduct, the value
\chi=(173.4(+/- 0.5)(+/- 1.2)(+1.1 / -0.2) MeV)^4 at \beta=6 (a approx= 0.1
fermi). The errors are the statistical error from our data, the one derived
from the value used for \Lambda_L and an estimate of the systematic error
respectively.


title:
Progress Towards finding Quark Masses and the QCD scale Lambda from the
  Lattice

abstract:
  We discuss recent work trying to extract the renormalised quark masses and
Lambda, the QCD scale, from dynamical simulations in lattice gauge theory.


title: Staggered Fermion, its Symmetry and Ichimatsu-Patterned Lattice

abstract:
  We investigate exact symmetries of a staggered fermion in D dimensions. The
Dirac operator is reformulated by SO(2D) Clifford algebra. The chiral symmetry,
rotational invariance and parity symmetries are clarified in any dimension.
Local scalar and pseudo-scalar modes are definitely determined, in which we
find non-standard modes. The relation to Ichimatsu-patterned lattice approach
is discussed.


title: Bosonic color-flavor transformation for the special unitary group

abstract:
  We extend Zirnbauer's color-flavor transformation in the bosonic sector to
the color group SU(N_c). Because the flavor group U(N_b, N_b) is non-compact,
the algebraic method by which the original color-flavor transformation was
derived leads to a useful result only for 2N_b \le N_c. Using the character
expansion method, we obtain a different form of the transformation in the
extended range N_b \le N_c. This result can also be used for the color group
U(N_c). The integrals to which the transformation can be applied are of
relevance for the recently proposed boson-induced lattice gauge theory.


title:
Confinement and the effective string theory in SU(N->oo) : a lattice
  study

abstract:
  We calculate in the SU(6) gauge theory the mass of the lightest flux loop
that winds around a spatial torus, as a function of the torus size, taking care
to achieve control of the main systematic errors. For comparison we perform a
similar calculation in SU(4). We demonstrate approximate linear confinement and
show that the leading correction is consistent with what one expects if the
flux tube behaves like a simple bosonic string at long distances. We obtain
similar but less accurate results for stable (k-)strings in higher
representations. We find some evidence that for k>1 the length scale at which
the bosonic string correction becomes dominant increases as N increases. We
perform all these calculations not just for long strings, up to about 2.5`fm'
in length, but also for shorter strings, down to the minimum length, lc = 1/Tc,
where Tc is the deconfining temperature. We find that the mass of the
ground-state string, at all length scales, is not very far from the simple
Nambu-Goto string theory prediction, and that the fit improves as N increases
from N=4 to N=6. We estimate the mass of the first excited string and find that
it also follows the Nambu-Goto prediction, albeit more qualitatively. We
comment upon the significance of these results for the string description of
SU(N) gauge theories in the limit of infinite N.


title: Systematics of Staggered Fermion Spectral Properties and Topology

abstract:
  The spectral properties of a variety of improved staggered operators are
studied in quenched QCD. The systematic dependence of the infrared eigenvalue
spectrum on i) improvement in the staggered operator, ii) improvement in the
gauge field action, iii) lattice spacing and iv) lattice volume, is analyzed.
It is observed that eigenmodes with small eigenvalues and large chirality
appear as the level of improvement increases or as one approaches the continuum
limit. These eigenmodes can be identified as the ``zero modes'' which
contribute to the chirality associated, via the index theorem, with the
topology of the background gauge field. This gives evidence that staggered
fermions are sensitive to gauge field topology. After successfully identifying
these would-be chiral zero modes, the distribution of the remaining non-chiral
modes is compared with the predictions of Random Matrix Theory in different
topological sectors. Satisfactory agreement is obtained.


title: P-wave Radial distributions of a Heavy-light meson on a lattice

abstract:
  This is a follow-up to our earlier work for the charge (vector) and matter
(scalar) distributions for S-wave states in a heavy-light meson, where the
heavy quark is static and the light quark has a mass about that of the strange
quark. The calculation is again carried out with dynamical fermions on a
16^3x24 lattice with a lattice spacing of about 0.14 fm. It is shown that
several features of the S- and P-wave distributions are in qualitative
agreement with what one expects from a simple one-body Dirac equation
interpretation.


title: Flux tube counting or Casimir scaling

abstract:
  QCD confines quarks in all representations. From lattice calculations and fat
center vortices model, we discuss that the coefficient of the linear term in
the potential is proportional to both casimir scaling and the number of
fundamental strings.


title: Derivation of Chiral Lagrangians from Random Lattice QCD

abstract:
  In our work we extend the ideas of the derivation of the chiral effective
theory from the lattice QCD [1] to the case of the random lattice
regularization of QCD. Such procedure allows in principle to find contribution
of any order into the chiral effective lagrangian. It is shown that an infinite
subseries of the chiral perturbation can be summed up into tne Born-Infeld term
and the logarithmic correction to them.


title: Physics issues in simulations with dynamical overlap fermions

abstract:
  We discuss the impact of various improvements on simulations of dynamical
overlap fermions using the Hybrid Monte Carlo algorithm. We focus on the usage
of fat links and multiple pseudo-fermion fields.


title: Spin Correlations and Velocity-Scaling in NRQCD Matrix Elements

abstract:
  We compute spin-dependent matrix elements for decays of S-wave quarkonia in
lattice NRQCD. They appear to be in approximate agreement with the
velocity-scaling rules of NRQCD.


title: The Lattice Calculation of Moments of Structure Functions

abstract:
  Some aspects of recent QCDSF-UKQCD nucleon moments of structure function
computations (both quenched and unquenched) are reviewed in an effort to
explore the light quark mass regime, lattice spacing effects and quenching
artefacts.


title: Plaquette expectation value and gluon condensate in three dimensions

abstract:
  In three dimensions, the gluon condensate of pure SU(3) gauge theory has
ultraviolet divergences up to 4-loop level only. By subtracting the
corresponding terms from lattice measurements of the plaquette expectation
value and extrapolating to the continuum limit, we extract the finite part of
the gluon condensate in lattice regularization. Through a change of
regularization scheme to MSbar and (inverse) dimensional reduction, this result
would determine the first non-perturbative coefficient in the weak-coupling
expansion of hot QCD pressure.


title: Lattice Study of Anisotropic QED-3

abstract:
  We present results from a Monte Carlo simulation of non-compact lattice QED
in 3 dimensions on a $16^3$ lattice in which an explicit anisotropy between $x$
and $y$ hopping terms has been introduced into the action. This formulation is
inspired by recent formulations of anisotropic QED$_3$ as an effective theory
of the non-superconducting portion of the cuprate phase diagram, with
relativistic fermion degrees of freedom defined near the nodes of the gap
function on the Fermi surface, and massless photon degrees of freedom
reproducing the dynamics of the phase disorder of the superconducting order
parameter. Using a parameter set corresponding to broken chiral symmetry in the
isotropic limit, our results show that the renormalised anisotropy, defined in
terms of the ratio of correlation lengths of gauge invariant bound states in
the $x$ and $y$ directions, exceeds the explicit anisotropy $\kappa$ introduced
in the lattice action, implying in contrast to recent analytic results that
anisotropy is a relevant deformation of QED$_3$. There also appears to be a
chiral symmetry restoring phase transition at $\kappa_c\simeq4.5$, implying
that the pseudogap phase persists down to T=0 in the cuprate phase diagram.


title: Gauge Singularities in the SU(2) Vacuum on the Lattice

abstract:
  SU(2) configurations, which have been generated by the Wilson action, are
transformed to a Landau gauge and smoothed by Fourier filtering. This leads to
sharp peaks in the field strengths and in related quantities. These spikes are
caused by gauge singularities. Their density is determined as 1.5 spikes per
fm**4, and it scales with the string tension. The number of spikes vanishes
when approaching the deconfinement regions. Correlations of spikes with Gribov
copies, with cooled action maxima and with the gluon propagator are studied.


title: The influence of Gribov copies on the gluon and ghost propagator

abstract:
  The dependence of the gluon and ghost propagator in pure SU(3) gauge theory
on the choice of Gribov copies in Landau gauge is studied. Simulations were
performed on several lattice sizes at $\beta$=5.8, 6.0 and 6.2. In the infrared
region the ghost propagator turns out to depend on the choice, while the impact
on the gluon propagator is not resolvable. Also the eigenvalue distribution of
the Faddeev-Popov operator is sensitive to Gribov copies.


title:
Detailed Analysis of the Tetraquark Potential and Flip-Flop in SU(3)
  Lattice QCD

abstract:
  We perform the detailed study of the tetraquark (4Q) potential $V_{\rm 4Q}$
for various QQ-$\rm \bar{Q}\bar{Q}$ systems in SU(3) lattice QCD with
$\beta=6.0$ and $16^3 \times 32$ at the quenched level. For about 200 different
patterns of 4Q systems, $V_{\rm 4Q}$ is extracted from the 4Q Wilson loop in
300 gauge configurations, with the smearing method to enhance the ground-state
component. We calculate $V_{\rm 4Q}$ for planar, twisted, asymmetric, and
large-size 4Q configurations, respectively. Here, the calculation for
large-size 4Q configurations is done by identifying $16^2 \times 32$ as the
spatial size and 16 as the temporal one, and the long-distance confinement
force is particularly analyzed in terms of the flux-tube picture. When QQ and
$\rm \bar{Q}\bar{Q}$ are well separated, $V_{\rm 4Q}$ is found to be expressed
as the sum of the one-gluon-exchange Coulomb term and multi-Y type linear term
based on the flux-tube picture. When the nearest quark and antiquark pair is
spatially close, the system is described as a "two-meson" state. We observe a
flux-tube recombination called as "flip-flop" between the connected 4Q state
and the "two-meson" state around the level-crossing point. This leads to
infrared screening of the long-range color forces between (anti)quarks
belonging to different mesons, and results in the absence of the color van der
Waals force between two mesons.


title: Chiral extrapolations

abstract:
  The comparison of chiral perturbation theory formulae with data from lattice
QCD simulations is discussed. Observables in the pion sector as well as in the
baryon sector are considered, including the nucleon mass in a finite volume.


title:
Locality of the fourth root of the Staggered-fermion determinant:
  renormalization-group approach

abstract:
  Consistency of present-day lattice QCD simulations with dynamical (``sea'')
staggered fermions requires that the determinant of the staggered-fermion Dirac
operator, $det(D)$, be equal to $det^4(D_{rg}) det(T)$ where $D_{rg}$ is a
local one-flavor lattice Dirac operator, and $T$ is a local operator containing
only excitations with masses of the order of the cutoff. Using
renormalization-group (RG) block transformations I show that, in the limit of
infinitely many RG steps, the required decomposition exists for the free
staggered operator in the ``flavor representation.'' The resulting one-flavor
Dirac operator $D_{rg}$ satisfies the Ginsparg-Wilson relation in the massless
case. I discuss the generalization of this result to the interacting theory.


title:
The 4d one component lattice $\phi^4$ model in the broken phase
  revisited

abstract:
  Measurements of various physical quantities in the symmetry broken phase of
the one component lattice $\phi^4_4$ with standard action, are shown to be
consistent with the critical behavior obtained by renormalization group
analyses. This is in contrast to recent conclusions by another group, who
further claim that the unconventional scaling behavior they observe, when
extended to the complete Higgs sector of the Standard Model, would alter the
conventional triviality bound on the mass of the Higgs.


title: Experiences with dynamical chirally improved fermions

abstract:
  We simulate Quantum Chromodynamics (QCD) in four Euclidean dimensions with
two (degenerate mass) flavors of dynamical quarks. The Dirac operator we use is
the so-called chirally improved Dirac operator. We discuss the algorithm used
for the simulation as well as the checks and some results on lattices up to
size 8**4 for fermion mass parameters down to 0.1. This is the first attempt to
introduce dynamical quarks with the chirally improved Dirac operator.


title: Lattice Gauge Actions for Fixed Topology

abstract:
  We test a set of lattice gauge actions for QCD that suppress small plaquette
values and in this way also suppress transitions between topological sectors.
This is well suited for simulations in the epsilon-regime and it is expected to
help in numerical simulations with dynamical quarks.


title: On the derivation of effective field theories

abstract:
  A general self-consistency approach allows a thorough treatment of the
corrections to the standard mean-field approximation (MFA). The natural
extension of standard MFA with the help of a cumulant expansion leads to a new
point of view on the effective field theories. The proposed approach can be
used for a systematic treatment of fluctuation effects of various length scales
and, perhaps, for the development of a new coarse graining procedure. We
outline and justify our method by some preliminary calculations. Concrete
results are given for the critical temperature and the Landau parameters of the
$\phi^4_d$-theory - the field counterpart of the Ising model. An important
unresolved problem of the modern theory of phase transitions - the problem for
the calculation of the true critical temperature, is considered within the
framework of the present approach. A comprehensive description of the ground
state properties of many-body systems is also demonstrated.


title:
Errors and ambiguity in transition from Fourier series to Fourier
  integrals

abstract:
  Transition from Fourier series to Fourier integrals is considered and error
introduced by ordinary substitution of integration for summing is estimated.
Ambiguity caused by transition from discrete function to continuous one is
examined and conditions under which this ambiguity does not arise are
suggested.


title:
Study of dynamical supersymmetry breaking for the two dimensional
  lattice Wess-Zumino model

abstract:
  A new approach to the study of the transition point in a class of two
dimensional Wess-Zumino models is presented. The method is based on the
calculation of rigorous lower bounds on the ground state energy density in the
infinite lattice limit. Such bounds are useful in the discussion of
supersymmetry phase transition. The transition point is then determined and
compared with recent results based on large-scale Green Function Monte Carlo
simulations with good agreement.


title: The spectrum of SU(N) gauge theories in finite volume

abstract:
  We compute the spatial-volume dependence of the spectrum of 4D SU(3 <= N <=
6) gauge theories by lattice Monte-Carlo techniques. Setting the scale with the
string tension, the spatial volume is L^3 with 0.78fm <= L <= 2.3fm. The
Euclidean `time' direction is kept large enough to be considered infinite and
the boundary conditions are periodic in all four dimensions. We study the
mixing of torelon pairs with the scalar and tensor glueballs, using a 2x2
Hamiltonian based on large-N counting rules. Looking to the other symmetry
channels, finite-volume effects on the glueball spectrum are already
surprisingly small in SU(3), and they become rapidly smaller as N is increased:
several low-lying SU(6) states have no finite-volume corrections at the 1-2%
level, at least down to L=0.9fm. We discuss the relation of this work with
analytic calculations in small and intermediate volume, and with Eguchi-Kawai
reduction in the planar limit.


title: The FLIC Overlap Quark Propagator

abstract:
  FLIC overlap fermions are a variant of the standard (Wilson) overlap action,
with the FLIC (Fat Link Irrelevant Clover) action as the overlap kernel rather
than the Wilson action. The structure of the FLIC overlap fermion propagator in
momentum space is studied, and a comparison against previous studies of the
Wilson overlap propagator in quenched QCD is performed. To explore the scaling
properties of the propagator for the two actions, numerical calculations are
performed in Landau Gauge across three lattices with different lattice spacing
$a$ and similar physical volumes. We find that at light quark masses the acti
ons agree in both the infrared and the ultraviolet, but at heavier masses some
disagreement in the ultraviolet appears. This is attributed to the two action s
having different discretisation errors with the FLIC overlap providing superior
performance in this regime. Both actions scale reasonably, but some scaling
violations are observed.


title: Twisted valence quarks and hadron interactions on the lattice

abstract:
  We consider QCD with valence and sea quarks obeying different boundary
conditions. We point out that the energy of low lying two hadron states do not
depend on the boundary condition of the sea quarks (up to exponentially small
corrections). Thus, the advantages in using twisted boundary conditions on the
lattice QCD extraction of nucleon-nucleon phase shifts can be gained without
the need of new gauge configurations, even in fully unquenched calculations.


title: Schroedinger functional formalism with Ginsparg-Wilson fermion

abstract:
  The Schroedinger functional formalism is given as a field theory in a finite
volume with a Dirichlet boundary condition in temporal direction. When one
tries to construct this formalism with the Ginsparg-Wilson fermion including
the overlap Dirac operator and the domain-wall fermion one easily runs into
difficulties. The reason is that if the Dirichlet boundary condition is simply
imposed on the Wilson Dirac operator $DW$ inside of the overlap Dirac operator
an exponentially small eigenvalue appears in $DW$, which affects the locality
properties of the operator. In this paper we propose a new procedure to impose
the Schroedinger functional Dirichlet boundary condition on the overlap Dirac
operator using an orbifolding projection.


title:
Baryon Electromagnetic Properties in Partially Quenched Heavy Hadron
  Chiral Perturbation Theory

abstract:
  The electromagnetic properties of baryons containing a heavy quark are
calculated at next-to-leading order in partially quenched heavy hadron chiral
perturbation theory. Calculations are performed for three light flavors in the
isospin limit and additionally for two light non-degenerate flavors. We use
partially-quenched charge matrices that are easy to implement on the lattice.
The results presented are necessary for the light quark mass extrapolation and
zero-momentum extrapolation of lattice QCD and partially quenched lattice QCD
calculations of heavy hadron electromagnetic properties. Additionally relations
between the sextet electromagnetic form factors and transition form factors are
derived.


title:
Lattice QCD Study for the Interquark Force in Three-Quark and
  Multi-Quark Systems

abstract:
  We study the three-quark and multi-quark potentials in SU(3) lattice QCD.
  From the accurate calculation for more than 300 different patterns of 3Q
systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found
to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz)
within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube
formation is actually observed on the lattice in maximally-Abelian projected
QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation
for the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ by diagonalizing
the QCD Hamiltonian in the presence of three quarks, and find a large
gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm
e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of
the success of the quark model. $\Delta E_{\rm 3Q}$ is found to be reproduced
by the ``inverse Mercedes Ansatz'', which indicates a complicated bulk
excitation for the gluonic-excitation mode. We study also the tetra-quark and
the penta-quark potentials in lattice QCD, and find that they are well
described by the OGE Coulomb plus multi-Y type linear potential, which supports
the flux-tube picture even for the multi-quarks. Finally, the narrow decay
width of penta-quark baryons is discussed in terms of the QCD string theory.


title: Anisotropic lattice with nonperturbative accuracy

abstract:
  We determine the nonperturbative anisotropic parameter of the gauge action in
the quenched approximation with less than 1% accuracy using the Sommer scale
measured by the L\"uscher-Weisz algorithm or smearing technique. We also study
the nonperturbative O(a)-improvement of the quark action. The bare quark
anisotropy is determined using the masses from the temporal and spatial
directions. For the determination of the $O(a)$ improvement coefficients, we
apply the Schr\"odinger functional method.


title:
The monopole content of topological clusters : have KvB calorons been
  found?

abstract:
  Using smearing of equilibrium lattice fields generated at finite temperature
in the confined phase of SU(2) lattice gauge theory, we have investigated the
emerging topological objects (clusters of topological charge). Analysing their
monopole content according to the Polyakov gauge and the maximally Abelian
gauge, we characterize part of them to correspond to nonstatic calorons or
static dyons in the context of Kraan-van Baal caloron solutions with
non-trivial holonomy. The behaviour of the Polyakov loop inside these clusters
and the (model-dependent) topological charges of these objects support this
interpretation.


title:
An exploratory lattice study of DI=3/2 K -> pi pi decays at
  next-to-leading order in the chiral expansion

abstract:
  We present the first direct evaluation of DI = 3/2 K -> pi pi matrix elements
with the aim of determining all the low-energy constants at NLO in the chiral
expansion. Our numerical investigation demonstrates that it is indeed possible
to determine the K -> pi pi matrix elements directly for the masses and momenta
used in the simulation with good precision. In this range however, we find that
the matrix elements do not satisfy the predictions of NLO chiral perturbation
theory. For the chiral extrapolation we therefore use a hybrid procedure which
combines the observed polynomial behaviour in masses and momenta of our lattice
results, with NLO chiral perturbation theory at lower masses. In this way we
find stable results for the quenched matrix elements of the electroweak penguin
operators (<pi pi (I=2)|O_8|K^0>= (0.68 +- 0.09) GeV^3 and <pi pi
(I=2)|O_7|K^0>= (0.12 +- 0.02) GeV^3 in the NDR-MSbar scheme at the scale 2
GeV), but not for the matrix elements of O_4 (for which there are too many
Low-Energy Constants at NLO for a reliable extrapolation). For all three
operators we find that the effect of including the NLO corrections is
significant (typically about 30%). We present a detailed discussion of the
status of the prospects for the reduction of the systematic uncertainties.


title:
Order of the Chiral and Continuum Limits in Staggered Chiral
  Perturbation Theory

abstract:
  Durr and Hoelbling recently observed that the continuum and chiral limits do
not commute in the two dimensional, one flavor, Schwinger model with staggered
fermions. I point out that such lack of commutativity can also be seen in
four-dimensional staggered chiral perturbation theory (SChPT) in quenched or
partially quenched quantities constructed to be particularly sensitive to the
chiral limit. Although the physics involved in the SChPT examples is quite
different from that in the Schwinger model, neither singularity seems to be
connected to the trick of taking the nth root of the fermion determinant to
remove unwanted degrees of freedom ("tastes"). Further, I argue that the
singularities in SChPT are absent in most commonly-computed quantities in the
unquenched (full) QCD case and do not imply any unexpected systematic errors in
recent MILC calculations with staggered fermions.


title: Gauge transformations in lattice chiral theories

abstract:
  We show that gauge-transformation properties of correlation functions in
chiral gauge theories on the finite lattice are determined in a general way.


title: Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory

abstract:
  We study the interplay between Dirac eigenmodes and center vortices in SU(2)
lattice gauge theory. In particular we focus on vortex-removed configurations
and compare them to an ensemble of configurations with random changes of the
link variables. We show that removing the vortices destroys all zero modes and
the near zero modes are no longer coupled to topological structures. The Dirac
spectrum for vortex-removed configurations in many respects resembles a free
spectrum thus leading to a vanishing chiral condensate. Configurations with
random changes leave the topological features of the Dirac eigensystem intact.
We finally show that smooth center vortex configurations give rise to zero
modes and topological near zero modes.


title:
Center Vortex Model for the Infrared Sector of SU(3) Yang-Mills Theory -
  Vortex Free Energy

abstract:
  The vortex free energy is studied in the random vortex world-surface model of
the infrared sector of SU(3) Yang-Mills theory. The free energy of a center
vortex extending into two spatial directions, which is introduced into
Yang-Mills configurations when acting with the 't Hooft loop operator, is
verified to furnish an order parameter for the deconfinement phase transition.
It is shown to exhibit a weak discontinuity at the critical temperature,
corresponding to the weak first order character of the transition.


title: A Numerical Study of Improved Quark Actions on Anisotropic Lattices

abstract:
  Tadpole improved Wilson quark actions with clover terms on anisotropic
lattices are studied numerically.
  Using asymmetric lattice volumes, the pseudo-scalar meson dispersion
relations are measured for 8 lowest lattice momentum modes with quark mass
values ranging from the strange to the charm quark with various values of the
gauge coupling $\beta$ and 3 different values of the bare speed of light
parameter $\nu$. These results can be utilized to extrapolate or interpolate to
obtain the optimal value for the bare speed of light parameter $\nu_{opt}(m)$
at a given gauge coupling for all bare quark mass values $m$. In particular,
the optimal values of $\nu$ at the physical strange and charm quark mass are
given for various gauge couplings.
  The lattice action with these optimized parameters can then be used to study
physical properties of hadrons involving either light or heavy quarks.


title: The critical end point of QCD

abstract:
  We investigate the critical end point of QCD with two flavours of light
dynamical quarks at finite lattice cutoff a=1/4T using a Taylor expansion of
the baryon number susceptibility. We find a strong volume dependence of the
position of the critical end point. In the large volume limit we obtain T^E/T_c
\~ 0.95 and mu_B^E/T^E ~ 1.1, where T_c is the cross over temperature at zero
chemical potential, and T^E and mu_B^E are the temperature and the baryon
chemical potential at the critical end point. The small value of mu_B^E places
it in the range of observability in energy scans at the RHIC.


title:
The speed of sound and specific heat in the QCD plasma: hydrodynamics,
  fluctuations and conformal symmetry

abstract:
  We report the continuum limits of the speed of sound, c_s, and the specific
heat at constant volume, c_v, in quenched QCD at temperatures of 2Tc and 3Tc.
At these temperatures, c_s is within 2-sigma of the ideal gas value, whereas
c_v differs significantly from the ideal gas. However, both are compatible with
results expected in a theory with conformal symmetry. We investigate effective
measures of conformal symmetry in the high temperature phase of QCD.


title: Meson correlators above deconfinement

abstract:
  We review recent progress in studying spectral functions for mesonic
observables at finite temperatures, by analysis of imaginary time correlators
directly calculated on isotropic lattices. Special attention is paid to the
lattice artifacts present in such calculations.


title:
Thermodynamic Properties of Strongly Interacting Matter at Non-zero
  Baryon Number Density

abstract:
  We present recent lattice results on QCD thermodynamics at non-vanishing
baryon number density obtained from a 6th order Taylor expansion in the
chemical potential. Results for bulk thermodynamic observables, in particular
for fluctuations in the baryon number density, are found to be well described
by a hadron resonance gas model at low temperature and an ideal quark gluon gas
at high temperature. We also analyze the radius of convergence of the Taylor
series and discuss the information it provides on the occurrence of a second
order phase transition point in the QCD phase diagram.


title: Genuine Symmetry of Staggered Fermion

abstract:
  We present a new formulation of the staggered fermion on the D-dimensional
lattice based on the SO(2D) Clifford algebra, which is naturally present in the
action. The action of the massless staggered fermion is invariant under the
discrete rotation and the SO(2D) chiral and other discrete transformations.
  From transformation properties of the fermion, we find two local meson
operators (one scalar and one pseudoscalar) in addition to two standard meson
operators.


title:
Dual formulations of non-abelian spin models: local representation and
  low-temperature asymptotics

abstract:
  Non-abelian lattice spin models with symmetry group SU(N) or U(N) can be
formulated in terms of link variables which are subject to the Bianchi
constraints. Using this representation we derive exact and local dual
formulation for the partition function of such models on a cubic lattice in
arbitrary dimension D. Locality means that the dual action is given by a sum
over some subset of hypercubes of the dual lattice and the interaction between
dual variables ranges over one given hypercube. Dual variables are in general
discrete-valued and live on (D-2)-cell of the dual lattice, in close analogy
with the XY model. We use our construction to study in details the dual of
SU(2) principal chiral model in two dimensions. We give dual expressions also
for two-point correlation function in arbitrary representation and for the free
energy of defects. Leading terms of the asymptotic expansion of the dual
Boltzmann factor are computed and it is proven that at low temperatures it
converges to a certain Gaussian distribution uniformly in all fluctuations of
dual variables. This result enables us to define the semiclassical limit of the
dual formulation and to determine an analog of the vortex--spin-wave
representation for the partition function. Such representation is used to
extract leading perturbative contribution to the correlation function which
shows power-like decay at weak coupling. We also present some analytical
evidences that the low-temperature limit of the dual formulation is completely
described by ISO(2)-like approximation of SU(2) matrix elements.


title: Anomalous gauge theories revisited

abstract:
  A possible formulation of chiral gauge theories with an anomalous fermion
content is re-examined in light of the lattice framework based on the
Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class
of anomalous non-abelian theories cannot consistently be formulated within this
lattice framework. In particular, in 4 dimension, {\it all} anomalous
non-abelian theories are included in this class. Anomalous abelian chiral gauge
theories cannot be formulated with compact $\U(1)$ link variables, while a
non-compact formulation is possible at least for the vacuum sector in the space
of lattice gauge fields. Our conclusion is not applied to effective low-energy
theories with an anomalous fermion content which are obtained from an
underlying anomaly-free theory by sending the mass of some of fermions to
infinity. For theories with an anomalous fermion content in which the anomaly
is cancelled by the Green-Schwarz mechanism, a possibility of a consistent
lattice formulation is not clear.


title:
A local formulation of lattice Wess-Zumino model with exact $\U(1)_R$
  symmetry

abstract:
  A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson
fermions. In perturbation theory, our formulation is equivalent to the
formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is,
however, free from a singular nature of the latter formulation due to an
additional auxiliary chiral supermultiplet on a lattice. The model posssesses
an exact $\U(1)_R$ symmetry as a supersymmetric counterpart of the L\"uscher
lattice chiral $\U(1)$ symmetry. A restration of the supersymmetric
Ward-Takahashi identity in the continuum limit is analyzed in renormalized
perturbation theory. In the one-loop level, a supersymmetric continuum limit is
ensured by suitably adjusting a coefficient of a single local term $\tilde
F^*\tilde F$. The non-renormalization theorem holds to this order of
perturbation theory. In higher orders, on the other hand, coefficents of local
terms with dimension $\leq4$ that are consistent with the $\U(1)_R$ symmetry
have to be adjusted for a supersymmetric continuum limit. The origin of this
complexicity in higher-order loops is clarified on the basis of the Reisz power
counting theorem. Therefore, from a view point of supersymmetry, the present
formulation is not quite better than a lattice Wess-Zumino model formulated by
using Wilson fermions, although a number of coefficients which require
adjustment is much less due to the exact $\U(1)_R$ symmetry. We also comment on
an exact non-linear fermionic symmetry which corresponds to the one studied by
Bonini and Feo; an existence of this exact symmetry itself does not imply a
restoration of supersymmetry in the continuum limit without any adjustment of
parameters.


title: The Origins of Lattice Gauge Theory

abstract:
  An anecdotal account of the author's role in the origins of lattice gauge
theory, prepared for delivery on the thirtieth anniversary of the publication
of "Confinement of Quarks" [Phys. Rev. D10 (1974) 2445].

categories: hep-lat cond-mat.other hep-ph hep-th physics.hist-ph


title: Full CKM matrix with lattice QCD

abstract:
  We show that it is now possible to fully determine the CKM matrix, for the
first time, using lattice QCD. |V_{cd}|, |V_{cs}|, |V_{ub}|, |V_{cb}| and
|V_{us}| are, respectively, directly determined with our lattice results for
form factors of semileptonic D->pi l nu, D->K l nu, B->pi l nu, B->D l nu, and
K->pi l nu decays. The error from the quenched approximation is removed by
using the MILC unquenched lattice gauge configurations, where the effect of u,d
and s quarks is included. The error from the ``chiral'' extrapolation
(m_l->m_{ud}) is greatly reduced by using improved staggered quarks. The
accuracy is comparable to that of the Particle Data Group averages. In
addition, |V_{ud}|, |V_{tb}|, |V_{ts}| and |V_{td}| are determined by using
unitarity of the CKM matrix and the experimental result for sin{(2beta)}. In
this way, we obtain all 9 CKM matrix elements, where the only theoretical input
is lattice QCD. We also obtain all the Wolfenstein parameters, for the first
time, using lattice QCD.


title:
Monte Carlo simulations of the NJL model near the nonzero temperature
  phase transition

abstract:
  We present results from numerical simulations of the Nambu-Jona-Lasinio model
with an SU(2)xSU(2) chiral symmetry and N_c=4,8, and 16 quark colors at nonzero
temperature. We performed the simulations by utilizing the hybrid Monte Carlo
and hybrid Molecular Dynamics algorithms. We show that the model undergoes a
second order phase transition. The critical exponents measured are consistent
with the classical 3d O(4) universality class and hence in accordance with the
dimensional reduction scenario. We also show that the Ginzburg region is
suppressed by a factor of 1/N_c in accordance with previous analytical
predictions.


title:
Charmonium properties at finite temperature on quenched anisotropic
  lattices

abstract:
  We study charmonium properties below and above $T_c$ up to 1.8$T_c$, on
quenched anisotropic lattices. Information of the spectral functions is
extracted using the maximum entropy method and the constrained curve fitting.
We also calculate the color singlet and averaged free energies and evaluate the
charmonium spectrum with the potential model analysis. The relation between the
lattice result of the spectral function analysis and the potential model is
discussed.


title:
The Logarithmic Triviality of Compact QED Coupled to a Four Fermi
  Interaction

abstract:
  This is the completion of an exploratory study of Compact lattice Quantum
Electrodynamics with a weak four-fermi interaction and four species of massless
fermions. In this formulation of Quantum Electrodynamics massless fermions can
be simulated directly and Finite Size Scaling analyses can be performed at the
theory's chiral symmetry breaking critical point. High statistics simulations
on lattices ranging from $8^4$ to $24^4$ yield the equation of state, critical
indices, scaling functions and cumulants. The measurements are well fit with
the orthodox hypothesis that the theory is logarithmically trivial and its
continuum limit suffers from Landau's zero charge problem.


title: Gluon field distribution in baryons

abstract:
  Methods for revealing the distribution of gluon fields within the three-quark
static-baryon potential are presented. In particular, we outline methods for
studying the sensitivity of the source on the emerging vacuum response for the
three-quark system. At the same time, we explore the possibility of revealing
gluon-field distributions in three-quark systems in QCD without the use of
gauge-dependent smoothing techniques. Renderings of flux tubes from a
preliminary high-statistics study on a 12^3 X 24 lattice are presented.


title: Generalized Parton Distributions from Lattice QCD

abstract:
  I review the LHPC Collaboration's lattice QCD calculations of the generalized
parton distributions of the nucleon and highlight those aspects of nucleon
structure best illuminated by lattice QCD, the nucleon's spin decomposition and
transverse quark structure.


title:
Comments on "Various Super Yang-Mills Theories with Exact Supersymmetry
  on the Lattice"

abstract:
  We make corrections on the paper by Sugino [{\it JHEP} {\bf 0501} (2005)
016].


title: Twist-two matrix elements at finite and infinite volume

abstract:
  We present one-loop results for the forward twist-two matrix elements
relevant to the unpolarised, helicity and transversity baryon structure
functions, in partially-quenched (N_f=2 and N_f=2+1) heavy baryon chiral
perturbation theory. The full-QCD limit can be straightforwardly obtained from
these results and we also consider SU(2|2) quenched QCD. Our calculations are
performed in finite volume as well as in infinite volume. We discuss features
of lattice simulations and investigate finite volume effects in detail. We find
that volume effects are not negligible, typically around 5--10% in current
partially-quenched and full QCD calculations, and are possibly larger in
quenched QCD. Extensions to the off-forward matrix elements and potential
difficulties that occur there are also discussed.


title: Canonical Approach to Ginsparg-Wilson Fermion

abstract:
  Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson
relation, we investigate canonical formulation of massless fermion on the
spatial lattice. For free fermion system exact chiral symmetry can be
implemented without species doubling. In the presence of gauge couplings the
chiral symmetry is violated. We show that the divergence of the axial vector
current is related to the chiral anomaly in the classical continuum limit.


title: Efficient Simulation of Heavy Quark Vacuum Polarization

abstract:
  We outline a simple way to include heavy quark vacuum polarization in lattice
QCD simulations. The method, based on effective field theory, requires only a
trivial modification of the gluon action and has no impact on simulation times.
We assess the range of validity for this procedure, and the impact that it may
have.


title:
CP, T and CPT in the non-perturbative formulation of chiral gauge
  theories

abstract:
  In spite of significant recent progress on the non-perturbative formulation
of chiral gauge theories there remained several unsolved problems. One of them
is the puzzle that the left- and right-handed projectors, and so the left- and
right-handed actions, break CP-symmetry on the lattice. We show in this letter
that they break T-symmetry also, while CPT remains intact.


title: Looking for pentaquarks in Lattice QCD

abstract:
  Pentaquark states in lattice QCD probably lie close in energy to two particle
scattering states. Correctly identifying the resonant state is a challenging,
yet tractable, problem given the terascale computing facilities available
today. We summarize the initial round of exploratory lattice calculations and
discuss what should be accomplished in the next round.


title: Simulating chiral quarks in the epsilon-regime of QCD

abstract:
  We present simulation results for lattice QCD with chiral fermions in small
volumes, where the epsilon-expansion of chiral perturbation theory applies. Our
data for the low lying Dirac eigenvalues, as well as mesonic correlation
functions, are in agreement with analytical predictions. This allows us to
extract values for the leading Low Energy Constants F_{pi} and Sigma.


title:
Large logarithmic rescaling of the scalar condensate: a subtlety with
  substantial phenomenological implications

abstract:
  Lattice data, taken since 1998 near the critical line of a 4D Ising model,
have been supporting the large logarithmic rescaling of the scalar condensate
predicted in the alternative description of symmetry breaking proposed by
Consoli and Stevenson. This conclusion has been challenged in a recent paper by
Balog et al. In this paper we respond to the criticism of these authors,
recapitulate the theoretical and numerical evidences in favour of the
alternative interpretation of `triviality' and reiterate our conclusion:
`triviality', by itself, cannot be used to place upper bounds on the Higgs
boson mass.


title:
Decay Constants of Pseudoscalar Mesons to Two Loops in Three-Flavor
  Partially Quenched $\chi$PT

abstract:
  This paper presents a first study of the decay constants of the charged, or
flavor-off-diagonal, pseudoscalar mesons to two loops for three flavors of sea
quarks, in Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT). Explicit
analytical expressions up to ${\cal O}(p^6)$ in the momentum expansion are
given. The calculations have been performed within the supersymmetric
formulation of PQ$\chi$PT. We also present some numerical results to indicate
the size of the corrections.


title: Effective theory for quenched lattice QCD and the Aoki phase

abstract:
  We discuss the symmetries of quenched QCD with Wilson fermions, starting from
its lagrangian formulation, taking into account the constraints needed for
convergence of the ghost-quark functional integral. We construct the
corresponding chiral effective lagrangian, including terms linear and quadratic
in the lattice spacing. This allows us to study the phase structure of the
quenched theory, and compare it to that in the unquenched theory. In particular
we study whether there may be an Aoki phase (with parity and flavor
spontaneously broken) or a first order transition line (with no symmetry
breaking but meson masses proportional to the lattice spacing), which are the
two possibilities in the unquenched theory. The presence of such phase
structure, and the concomitant long-range correlations, has important
implications for numerical studies using both quenched and dynamical overlap
and domain-wall fermions. We argue that the phase structure is qualitatively
the same as in the unquenched theory, with the choice between the two
possibilities depending on the sign of a parameter in the low-energy effective
theory.


title: Curci-Ferrari mass and the Neuberger problem

abstract:
  We study the massive Curci-Ferrari model as a starting point for defining
BRST quantisation for Yang-Mills theory on the lattice. In particular, we
elucidate this proposal in light of topological approaches to gauge-fixing and
study the case of a simple one-link Abelian model.


title: Measure in the 2D Regge quantum gravity

abstract:
  We propose a version of the 2D Regge calculus, in which the areas of all
triangles are equal to each other. In this discretization Lund - Regge measure
over link lengths is simplified considerably. Contrary to the usual Regge
models with Lund - Regge measure, where this measure is nonlocal and rather
complicated, the models based on our approach can be investigated using the
numerical simulations in a rather simple way.


title: Strong Isospin Breaking in the Nucleon and Delta Masses on the Lattice

abstract:
  Strong isospin breaking in the spectrum of the nucleons and deltas can be
studied in lattice QCD with the help of chiral perturbation theory. At leading
order in the chiral expansion, the mass splittings between the proton and
neutron and between the deltas are linear in the quark mass difference. The
next-to-leading order contributions to these splittings vanish even away from
the strong-isospin limit. Therefore, any non-linear quark mass dependence of
these mass splittings is a signal of the next-to-next-to-leading order mass
contributions, thus providing access to LECs at this order. We determine the
mass splittings of the nucleons and deltas in two-flavor, heavy baryon chiral
perturbation theory to next-to-next-to-leading order. We also derive
expressions for the nucleon and delta masses in partially quenched chiral
perturbation theory to the same order. The resulting mass expressions will be
useful both for the extrapolation of lattice data on baryon masses, and for the
study of strong isospin breaking.


title: Unquenched quark propagator in Landau gauge

abstract:
  We present an unquenched calculation of the quark propagator in Landau gauge
with 2+1 flavors of dynamical quarks. We use configurations generated with an
improved staggered (``Asqtad'') action by the MILC collaboration. This quark
action has been seen to have excellent rotational symmetry and scaling
properties in the quenched quark propagator. Quenched and dynamical
calculations are performed on a $20^3\times 64$ lattice with a nominal lattice
spacing of $a = 0.125$ fm. The matched quenched and dynamical lattices allow us
to investigate the relatively subtle sea quark effects, and even in the
quenched case the physical volume of these lattices gives access to lower
momenta than our previous study. We calculate the quark mass function and
renormalization function for a variety of valence and sea quark masses.


title: Baryon masses at O(a^2) in chiral perturbation theory

abstract:
  The chiral Lagrangian for the Symanzik action through O(a^2) for baryons is
obtained. We consider two flavor unquenched and partially quenched lattice
theories, allowing for mixed actions in the latter. As an application, we
calculate masses to O(a^2) for the nucleons and deltas, and investigate the
corrections due to the violation of O(4) rotational invariance. These results
are contrasted with those in the meson sector for lattice simulations using
mixed and unmixed actions of Wilson and Ginsparg-Wilson quarks.


title: Baryon Masses in Lattice QCD with Exact Chiral Symmetry

abstract:
  We investigate the baryon mass spectrum in quenched lattice QCD with exact
chiral symmetry. For 100 gauge configurations generated with Wilson gauge
action at $ \beta = 6.1 $ on the $ 20^3 \times 40 $ lattice, we compute
(point-to-point) quark propagators for 30 quark masses in the range $ 67 {MeV}
\le m_q \le 1790 {MeV} $. For baryons only composed of strange and charm
quarks, their masses are extracted directly from the time correlation
functions, while for those containing $ u (d) $ light quarks, their masses are
obtained by chiral extrapolation to $ m_\pi = 135 $ MeV. Our results of baryon
masses are in good agreement with experimental values, except for the negative
parity states of $ \Lambda $ and $ \Lambda_c $. Further, our results of charmed
(including doubly-charmed and triply-charmed) baryons can serve as predictions
of QCD.


title: Penta-quark in Anisotropic Lattice QCD

abstract:
  Penta-quark (5Q) baryons are studied using anisotropic lattice QCD for
high-precision measurement of temporal correlators. A non-NK-type interpolating
field is employed to study the 5Q states with J^P=1/2^{\pm} and I=0. In
J^P=1/2^+ channel, the lowest-lying state is found at m_{5Q} \simeq 2.25 GeV,
which is too massive to be identified as the Theta^+(1540). In J^P=1/2^-
channel, the lowest-lying state is found at m_{5Q} \simeq 1.75 GeV. To
distinguish a compact 5Q resonance state from an NK scattering state, a new
method with ``hybrid boundary condition (HBC)'' is proposed. As a result of the
HBC analysis, the observed state in the negative-parity channel turns out to be
an $NK$ scattering state.


title: An example of optimal field cut in lattice gauge perturbation theory

abstract:
  We discuss the weak coupling expansion of a one plaquette SU(2) lattice gauge
theory. We show that the conventional perturbative series for the partition
function has a zero radius of convergence and is asymptotic. The average
plaquette is discontinuous at g^2=0. However, the fact that SU(2) is compact
provides a perturbative sum that converges toward the correct answer for
positive g^2. This alternate methods amounts to introducing a specific coupling
dependent field cut, that turns the coefficients into g-dependent quantities.
Generalizing to an arbitrary field cut, we obtain a regular power series with a
finite radius of convergence. At any order in the modified perturbative
procedure, and for a given coupling, it is possible to find at least one (and
sometimes two) values of the field cut that provide the exact answer. This
optimal field cut can be determined approximately using the strong coupling
expansion. This allows us to interpolate accurately between the weak and strong
coupling regions. We discuss the extension of the method to lattice gauge
theory on a D-dimensional cubic lattice.


title: Baryon masses, chiral extrapolations, and all that

abstract:
  We calculate the baryon octet masses to fourth order in chiral perturbation
theory employing dimensional and cut-off regularization. We analyze the pion
and kaon mass dependences of the baryon masses based on the MILC data. We show
that chiral perturbation theory gives stable chiral extrapolation functions for
pion (kaon) masses below 550 (600) MeV. The pion-nucleon sigma term in SU(3) is
also investigated, we find \sigma_{\pi N} (0) = 50.7 - 53.7 MeV.