title: Propagators in Yang-Mills theory for different gauges

abstract:
  Green's functions are gauge-dependent quantities. Thus, the manifestation of
confinement in these correlation functions also depends on the gauge. Here we
use lattice gauge theory to study the gluon and the ghost propagators in a
gauge (the so-called lambda-gauge) interpolating between the Landau and the
Coulomb gauge. Results are compared to the usual minimal Landau gauge.


title: The spectrum of radial, orbital and gluonic excitations of charmonium

abstract:
  We present results for the charmonium spectrum from $N_f=2$ dynamical QCD
simulations on $12^3\times 80$ anisotropic lattices. Using all-to-all
propagators we determine the ground and excited states of S, P and D waves and
hybrids. We also evaluate the disconnected (OZI suppressed) contribution to the
$\eta_c$ and $J/\Psi$


title:
Comparison among HB-inspired algorithms for continuous-spin systems and
  gauge fields

abstract:
  We propose a new local algorithm for the thermalization of n-vector spin
models, which can also be used in the numerical simulation of SU(N) lattice
gauge theories. The algorithm combines heat-bath (HB) and micro-canonical
updates in a single step -- as opposed to the hybrid overrelaxation method,
which alternates between the two kinds of update steps -- while preserving
ergodicity. We test our proposed algorithm in the case of the one-dimensional
4-vector spin model and compare its performance with the standard HB algorithm
and with other HB-inspired algorithms.


title: Numerical Simulation of N-vector Spin Models in a Magnetic Field

abstract:
  Three-dimensional N-vector spin models may define universality classes for
such diverse phenomena as i) the superfluid transition in liquid helium
(currently investigated in the micro-gravity environment of the Space Shuttle)
and ii) the transition from hadronic matter to a quark-gluon plasma, studied in
heavy-ion collisions at the laboratories of Brookhaven and CERN. The models
have been extensively studied both by field-theoretical and by statistical
mechanical methods, including Monte Carlo simulations using cluster algorithms.
These algorithms are applicable also in the presence of a magnetic field. Key
quantities for the description of the transitions above -- such as universal
critical amplitude ratios and the location of the so-called pseudo-critical
line -- can be obtained from the models' magnetic equation of state, which
relates magnetization, external magnetic field and temperature. Here we present
an improved parametrization for the equation of state of the models, allowing a
better fit to the numerical data. Our proposed form is inspired by perturbation
theory, with coefficients determined nonperturbatively from fits to the data.


title:
Electromagnetic Corrections in Partially Quenched Chiral Perturbation
  Theory

abstract:
  We introduce photons in Partially Quenched Chiral Perturbation Theory and
calculate the resulting electromagnetic loop-corrections at NLO for the charged
meson masses and decay constants. We also present a numerical analysis to
indicate the size of the different corrections. We show that several
phenomenologically relevant quantities can be calculated consistently with
photons which couple only to the valence quarks, allowing the use of gluon
configurations produced without dynamical photons.


title:
Infrared divergence of the color-Coulomb self-energy in Coulomb gauge
  QCD

abstract:
  We investigate the spectrum of the Faddeev-Popov operator in Coulomb gauge
QCD using quenched SU(3) lattice simulation. In the confinement phase, we
observe the accumulation of the near-zero modes of the FP operator at large
lattice volumes, and the color-Coulomb self-energy diverges in the infrared
limit. Moreover, even in the deconfinement phase, the behavior of the FP
eigenvalue density is qualitatively the same as in the confinement phase and
the color-Coulomb self-energy is infrared divergent.


title: Towards a quantitative understanding of the Delta I=1/2 rule

abstract:
  A recently proposed strategy to quantify the role of the charm quark mass in
the $\Delta I=1/2$ rule is reviewed. Results for the low-energy couplings of
the $\Delta S=1$ chiral effective Hamiltonian in a theory with a light charm
quark (GIM limit) are obtained through a matching of three-point correlation
functions computed in Chiral Perturbation Theory and in quenched lattice QCD.
We observe a large $\Delta I=1/2$ enhancement, which is not large enough to
explain the experimental result, but suggests significant long-distance
contributions to the physical $\Delta I=1/2$ which are unrelated to penguin
contractions or operators.


title:
Studying the infrared behaviour of gluon and ghost propagators using
  large asymmetric lattices

abstract:
  We report on the infrared limit of the quenched lattice Landau gauge gluon
propagator computed from large asymmetric lattices. In particular, the
compatibility of the pure power law infrared solution $(q^2)^{2\kappa}$ of the
Dyson-Schwinger equations is investigated and the exponent $\kappa$ is
measured. Some results for the ghost propagator and for the running coupling
constant will also be shown.


title: A Critique of the Link Approach to Exact Lattice Supersymmetry

abstract:
  We examine the link approach to constructing a lattice theory of N=2 super
Yang Mills theory in two dimensions. The goal of this construction is to
provide a discretization of the continuum theory which preserves all
supersymmetries at non-zero lattice spacing. We show that this approach suffers
from an inconsistency and argue that a maximum of just one of the
supersymmetries can be implemented on the lattice.


title: Infrared Maximally Abelian Gauge

abstract:
  The confinement scenario in Maximally Abelian gauge (MAG) is based on the
concepts of Abelian dominance and of dual superconductivity. Recently, several
groups pointed out the possible existence in MAG of ghost and gluon condensates
with mass dimension 2, which in turn should influence the infrared behavior of
ghost and gluon propagators. We present preliminary results for the first
lattice numerical study of the ghost propagator and of ghost condensation for
pure SU(2) theory in the MAG.


title: Two Meson Systems with Ginsparg-Wilson Valence Quarks

abstract:
  Unphysical effects associated with finite lattice spacing and partial
quenching may lead to the presence of unphysical terms in chiral extrapolation
formulae. These unphysical terms must then be removed during data analysis
before physical predictions can be made. In this work, we show that through
next-to-leading order, there are no unphysical counterterms in the
extrapolation formulae, expressed in lattice-physical parameters, for meson
scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work
applies to most sea quark discretization, provided that chiral perturbation
theory is a valid approximation. We demonstrate our results with explicit
computations and show that, in favorable circumstances, the extrapolation
formulae do not depend on the unknown constant C_Mix appearing at lowest order
in the mixed action chiral Lagrangian. We show that the I=1 KK scattering
length does not depend on C_Mix in contrast to the I=3/2 K-pi scattering
length. In addition, we show that these observables combined with f_K / f_pi
and the I=2 pi-pi scattering length share only two linearly independent sets of
counterterms, providing a means to test the mixed action theory at one lattice
spacing. We therefore make a prediction for the I=1 KK scattering length.


title: Exact Nonperturbative Renormalization

abstract:
  We propose an exact renormalization group equation for Lattice Gauge
Theories, that has no dependence on the lattice spacing. We instead relate the
lattice spacing properties directly to the continuum convergence of the support
of each local plaquette. Equivalently, this is formulated as a convergence
prescription for a characteristic polynomial in the gauge coupling that allows
the exact meromorphic continuation of a nonperturbative system arbitrarily
close to the continuum limit.


title:
2-loop additive mass renormalization with clover fermions and Symanzik
  improved gluons

abstract:
  We calculate the critical value of the hopping parameter, kappa_c, in Lattice
QCD, up to two loops in perturbation theory. We employ the
Sheikholeslami-Wohlert (clover) improved action for Wilson fermions and the
Symanzik improved gluon action for 4- and 6-link loops.
  The quantity which we study is a typical case of a vacuum expectation value
resulting in an additive renormalization; as such, it is characterized by a
power (linear) divergence in the lattice spacing, and its calculation lies at
the limits of applicability of perturbation theory.
  Our results are polynomial in c_{SW} (clover parameter) and cover a wide
range of values for the Symanzik coefficients c_i. Furthermore, the dependence
on the number of colors N and the number of fermionic flavors N_f is shown
explicitly. In order to compare our results to non perturbative evaluations of
kappa_c coming from Monte Carlo simulations, we employ an improved perturbation
theory method applied to improved actions.


title: Exotic and higher spin mesons in the charmonium

abstract:
  Exotic and higher spin (> 1) mesons are still not throughly investigated in
lattice QCD. Using a set of derivative based operators we report our
exploratory study of these mesons in charmonium region. We use a 12^3 X 48
anisotropic (xi = 3) clover lattice with inverse temporal lattice spacing a^-1
= 6.05 GeV. Techniques developed in this exploratory study will be utilized in
our future comprehensive study of light hybrid mesons that are to be explored
in the 12 GeV GlueX experiment at Jefferson Laboratory.


title: Vacuum structure as seen by overlap fermions

abstract:
  Three complementary views on the QCD vacuum structure, all based on
eigenmodes of the overlap operator, are reported in their interrelation: (i)
spectral density, localization and chiral properties of the modes, (ii) the
possibility of filtering the field strength with the aim to detect selfdual and
antiselfdual domains and (iii) the various faces of the topological charge
density, with and without a cutoff \lambda_{\rm cut} = O(\Lambda_{QCD}). The
techniques are tested on quenched SU(3) configurations.


title: N and N to Delta transition form factors from Lattice QCD

abstract:
  We present recent lattice QCD results on nucleon form factors and N to Delta
transition form factors. We predict the parity violating asymmetry in N to
Delta and check the off-diagonal Goldberger-Treiman relation.


title: B meson decays from moving-NRQCD on fine MILC lattices

abstract:
  Lattice simulations of $B\to\pi l\nu$ decays are problematic in the low
$q^{2}$ region when the pion has to have large momentum in the lattice frame
for a $B$ meson at rest or moving slowly. The moving-NRQCD formalism provides a
way around this by giving an accurate discretization of a $b$ quark moving at
arbitrary velocity $v$, and therefore a $B$ meson moving at high momentum in
the lattice frame. Here we show results from simulations of the moving-NRQCD
action complete through $O(1/M)$ coupled to the asqtad action on a MILC fine
ensemble. We show $B$, $B^{*}$ masses as a function of $v$ and demonstrate how
to determine the meson kinetic mass and the renormalization of $v$
non-perturbatively. We will also discuss the perturbative renormalization of
the moving-NRQCD action from high-$\beta$ Monte Carlo simulations.


title: The condensate for two dynamical chirally improved quarks in QCD

abstract:
  We compare the eigenvalue spectra of the Dirac operator from a simulation
with two mass degenerate dynamical chirally improved fermions with Random
Matrix Theory. Comparisons with distribution of k-th eigenvalues (k=1,2) in
fixed topological sectors (nu=0,1) are carried out using the Kolmogorov-Smirnov
test. The eigenvalue distributions are well described by the RMT predictions.
The match allows us to read off the quark condensate in the chiral limit
directly. Correcting for finite size and renormalization we obtain a mean value
of -(276 (11)(16) MeV)**3 in the MS-bar scheme.


title: Lattice Formulation of Two Dimensional Topological Field Theory

abstract:
  We investigate an integrable property and observables of 2 dimensional
N=(4,4) topological field theory defined on a discrete lattice by using the
"orbifolding" and "deconstruction" methods. We show that our lattice model
possesses the integrability and the partition function reduces to matrix
integrals of scalar fields on sites in consequence. We make clear meaningful
differences between the discrete lattice and differentiable manifold, which
would be important to a study of topological quantities on the lattice. We also
propose a new construction of N=(2,2) supersymmetric lattice theory, which is
realized by a suitable truncation of scalar fields from the N=(4,4) theory.


title: Composite boson dominance in relativistic field theories

abstract:
  We apply a new bosonization technique to relativistic field theories of
fermions whose partition function is dominated by bosonic composites, and
derive the effective action for these bosons. The derivation respects all
symmetries, including gauge invariance, with the exception of Euclidean
invariance which must be checked a posteriori. We use a lattice regularization
which should make applications to gauge theories easier. We test the method on
a fermion field theory with quartic interaction in the limit when the number of
flavours N_f is large, and show that it reproduces the exact results in the
bosonic sector, namely condensation of a compositeboson with the right mass
which breaks the discrete chiral invariance of the model. Moreover we determine
the structure function of the condensed composite, whose spatial part turns out
to be identical to that of the Cooper pairs of the BCS model of
superconductivity.


title:
High-loop perturbative renormalization constants for Lattice QCD (I):
  finite constants for Wilson quark currents

abstract:
  We present a high order perturbative computation of the renormalization
constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The
computational setup is the one provided by the RI'-MOM scheme. Three- and
four-loop expansions are made possible by Numerical Stochastic Perturbation
Theory. Results are given for various numbers of flavours and/or (within a
finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also
present four-loop results. Finite size effects are well under control and the
continuum limit is taken by means of hypercubic symmetric Taylor expansions.
The main indetermination comes from truncation errors, which should be assessed
in connection with convergence properties of the series. The latter is best
discussed in the framework of Boosted Perturbation Theory, whose impact we try
to assess carefully. Final results and their uncertainties show that high-loop
perturbative computations of Lattice QCD RC's are feasible and should not be
viewed as a second choice. As a by-product, we discuss the perturbative
expansion for the critical mass, also for which results are for generic n_f up
to three loops, while a four-loop result is obtained for n_f=2.


title:
The order of the quantum chromodynamics transition predicted by the
  standard model of particle physics

abstract:
  We determine the nature of the QCD transition using lattice calculations for
physical quark masses. Susceptibilities are extrapolated to vanishing lattice
spacing for three physical volumes, the smallest and largest of which differ by
a factor of five. This ensures that a true transition should result in a
dramatic increase of the susceptibilities.No such behaviour is observed: our
finite-size scaling analysis shows that the finite-temperature QCD transition
in the hot early Universe was not a real phase transition, but an analytic
crossover (involving a rapid change, as opposed to a jump, as the temperature
varied). As such, it will be difficult to find experimental evidence of this
transition from astronomical observations.


title: SU(3)-breaking effects in hyperon semileptonic decays

abstract:
  We present the first quenched lattice QCD study of all the vector and axial
form factors relevant for the hyperon semileptonic decay Sigma- -> n l nu.


title: Massive Overlap Fermions on Anisotropic Lattices

abstract:
  We formulate the massive overlap fermions on anisotropic lattices.
  We find that the dispersion relation for the overlap fermion resembles the
continuum form in the low-momentum region once the bare parameters are properly
tuned. The quark self-energy and the quark field renormalization constants are
calculated to one-loop in bare lattice perturbation theory.
  We argue that massive domain wall quarks might be helpful in lattice QCD
studies on heavy-light hadron spectroscopy.


title:
Quarkonium correlators and spectral functions at zero and finite
  temperature

abstract:
  We study quarkonium correlators and spectral functions at zero and finite
temperature using the anisotropic Fermilab lattice formulation with anisotropy
xi=2 and 4. To control cutoff effects we use several different lattice
spacings. The spectral functions were extracted from lattice correlators with
Maximum Entropy Method based on a new algorithm. We find evidence for the
survival of 1S quarkonium states in the deconfined medium till relatively high
temperatures as well as for dissolution of 1P quarkonium states right above the
deconfinement temperature.


title: Improved Superlinks for Higher Spin Operators

abstract:
  Traditional smearing or blocking techniques serve well to increase the
overlap of operators onto physical states but allow for links orientated only
along lattice axes. Recent attempts to construct more general propagators have
shown promise at resolving the higher spin states but still rely on iterative
smearing. We present a new method of superlink construction which creates
meared links from (sparse) matrix multiplications, allowing for gluonic
propagation in arbitrary directions. As an application and example, we compute
the positive-parity, even-spin glueball spectrum up to spin 6 for pure gauge
SU(2) at beta = 6, L = 16, in D = 2+1 dimensions.


title: Chiral phase transition in lattice QCD as a metal-insulator transition

abstract:
  We investigate the lattice QCD Dirac operator with staggered fermions at
temperatures around the chiral phase transition. We present evidence of a
metal-insulator transition in the low lying modes of the Dirac operator around
the same temperature as the chiral phase transition. This strongly suggests the
phenomenon of Anderson localization drives the QCD vacuum to the chirally
symmetric phase in a way similar to a metal-insulator transition in a
disordered conductor. We also discuss how Anderson localization affects the
usual phenomenological treatment of phase transitions a la Ginzburg-Landau.


title:
Non-perturbative QCD: renormalization, O(a)-improvement and matching to
  Heavy Quark Effective Theory

abstract:
  We give an introduction to three topics in lattice gauge theory:
  I. The Schroedinger Functional and O(a) improvement.
  O(a) improvement has been reviewed several times. Here we focus on explaining
the basic ideas in detail and then proceed directly to an overview of the
literature and our personal assessment of what has been achieved and what is
missing.
  II. The computation of the running coupling, running quark masses and the
extraction of the renormalization group invariants.
  We focus on the basic strategy and on the large effort that has been invested
in understanding the continuum limit. We point out what remains to be done.
  III. Non-perturbative Heavy Quark Effective Theory.
  Since the literature on this subject is still rather sparse, we go beyond the
basic ideas and discuss in some detail how the theory works in principle and in
practice.


title: Lattice QCD simulations with light dynamical quarks

abstract:
  I report recent results from full QCD simulations by CP-PACS and JLQCD
collaborations.


title: Lattice QCD as a video game

abstract:
  The speed, bandwidth and cost characteristics of today's PC graphics cards
make them an attractive target as general purpose computational platforms. High
performance can be achieved also for lattice simulations but the actual
implementation can be cumbersome. This paper outlines the architecture and
programming model of modern graphics cards for the lattice practitioner with
the goal of exploiting these chips for Monte Carlo simulations. Sample code is
also given.


title: Staggered Baryon Operators with Flavor SU(3) Quantum Numbers

abstract:
  The construction of the first baryon operators for staggered lattice QCD
exploited the taste symmetry to emulate physical quark flavor; contemporary 2+1
flavor simulations explicitly include three physical quark flavors and
necessitate interpreting a valence sector with twelve quarks. After discussing
expected features of the resulting baryon spectrum, I consider the spectra of
operators transforming irreducibly under SU(3)xGTS, the direct product of
flavor SU(3) and the geometrical time-slice group of the 1-flavor staggered
theory. I then describe the construction of a set of maximally local baryon
operators transforming irreducibly under SU(3)xGTS and enumerate this set. In
principle, the operators listed here could be used to extract the masses of all
the lightest spin-1/2 and spin-3/2 baryon resonances of staggered QCD. Using
appropriate operators from this set in partially quenched simulations should
allow for particularly clean 2+1 flavor calculations of the masses of the
nucleon and the lightest decuplet.


title: Low energy constants from the MILC Collaboration

abstract:
  Based on ongoing simulations, we update our results for low energy constants,
decay constants, and light quark masses. The simulations employ three dynamical
flavors of improved staggered quarks.


title: Effects of the anomaly on the QCD chiral phase transition

abstract:
  We study a lattice field theory described by two flavors of massless
staggered fermions interacting with U(1) gauge fields in the strong coupling
limit. We show that the lattice model has a $SU(2)\times SU(2)\times U(1)$
chiral symmetry and can be used to model the two-flavor QCD chiral phase
transition in the absence of the anomaly. It is also possible to add a coupling
to this model which breaks the chiral symmetry to $SU(2)\times SU(2)$ and thus
mimics the effects of the anomaly in two-flavor QCD. We construct an efficient
directed loop algorithm to study such a model. We show that the chiral phase
transition in our model is first order in the absence of the anomaly, while it
becomes second order with O(4) exponents when the anomaly is turned on.


title: Pion physics in two flavor strong coupling lattice QED

abstract:
  We consider the lattice field theory involving two flavors of staggered
quarks which interact with $U_A(1)$ gauge fields in the strong coupling limit.
For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times U_A(1)$
symmetry. We show explicitly how pions emerge through the phenomena of
confinement in this theory. We also show how one can incorporate the physics of
the anomaly in this theory. Thus, our approach is a good pedagogical tool to
explain how pions arise in real QCD. Another advantage of our approach is that
we can easily design efficient cluster algorithms to compute a variety of
quantities close to the chiral limit, thus allowing us to understand the low
energy physics in a QCD-like setting from first principles.


title: Towards the QCD phase diagram

abstract:
  We summarize our recent results on the phase diagram of QCD with N_f=2+1
quark flavors, as a function of temperature T and quark chemical potential \mu.
Using staggered fermions, lattices with temporal extent N_t=4, and the exact
RHMC algorithm, we first determine the critical line in the quark mass plane
(m_{u,d},m_s) where the finite temperature transition at \mu=0 is second order.
We confirm that the physical point lies on the crossover side of this line. Our
data are consistent with a tricritical point at (m_{u,d},m_s) = (0,\sim 500)
MeV.
  Then, using an imaginary chemical potential, we determine in which direction
this second-order line moves as the chemical potential is turned on. Contrary
to standard expectations, we find that the region of first-order transitions
shrinks in the presence of a chemical potential, which is inconsistent with the
presence of a QCD critical point at small chemical potential.
  The emphasis is put on clarifying the translation of our results from lattice
to physical units, and on discussing the apparent contradiction of our findings
with earlier lattice studies.


title: Light quark electromagnetic structure of baryons

abstract:
  Fascinating aspects of the light quark-mass behavior of baryon
electromagnetic form factors are highlighted. Using FLIC fermions on $20^3
\times 40$ quenched ${\cal O}(a^2)$-improved gauge fields, we explore charge
radii and magnetic moments at pion masses as light as 300 MeV. Of particular
interest is chiral curvature of proton charge radii and magnetic moments, the
environmental dependence of strange quark properties in hyperons, and the
remarkable signature of quenched chiral-nonanalytic behavior in the magnetic
moment of $\Delta$ baryon resonances.


title: Vector meson electromagnetic form factors

abstract:
  The charge, magnetic and quadrupole form factors of vector mesons and the
charge form factor of pseudo-scalar mesons are calculated in quenched lattice
QCD. The charge radii and magnetic moments are derived. The quark sector
contributions to the form factors are calculated separately and we highlight
the environmental sensitivity of the light-quark contribution to charge radii.


title:
Optimised Dirac Operators on the Lattice: Construction, Properties and
  Applications

abstract:
  We review a number of topics related to block variable renormalisation group
transformations of quantum fields on the lattice, and to the emerging perfect
lattice actions. We first illustrate this procedure by considering scalar
fields. Then we proceed to lattice fermions, where we discuss perfect actions
for free fields, for the Gross-Neveu model and for a supersymmetric spin model.
We also consider the extension to perfect lattice perturbation theory, in
particular regarding the axial anomaly and the quark gluon vertex function.
Next we deal with properties and applications of truncated perfect fermions,
and their chiral correction by means of the overlap formula. This yields a
formulation of lattice fermions, which combines exact chiral symmetry with an
optimisation of further essential properties. We summarise simulation results
for these so-called overlap-hypercube fermions in the two-flavour Schwinger
model and in quenched QCD. In the latter framework we establish a link to
Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In
particular we present an evaluation of the leading Low Energy Constants of the
chiral Lagrangian - the chiral condensate and the pion decay constant - from
QCD simulations with extremely light quarks.


title: QCD equation of state with 2+1 flavors of improved staggered quarks

abstract:
  We report results for the interaction measure, pressure and energy density
for nonzero temperature QCD with 2+1 flavors of improved staggered quarks. In
our simulations we use a Symanzik improved gauge action and the Asqtad $O(a^2)$
improved staggered quark action for lattices with temporal extent $N_t=4$ and
6. The heavy quark mass $m_s$ is fixed at approximately the physical strange
quark mass and the two degenerate light quarks have masses $m_{ud}\approx0.1
m_s$ or $0.2 m_s$. The calculation of the thermodynamic observables employs the
integral method where energy density and pressure are obtained by integration
over the interaction measure.


title:
Neutron electric dipole moment with external electric field method in
  lattice QCD

abstract:
  We discuss a possibility that the Neutron Electric Dipole Moment (NEDM) can
be calculated in lattice QCD simulations in the presence of the CP violating
$\theta$ term. In this paper we measure the energy difference between spin-up
and spin-down states of the neutron in the presence of an uniform and static
external electric field. We first test this method in quenched QCD with the RG
improved gauge action on a $16^3\times 32$ lattice at $a^{-1}\simeq$ 2 GeV,
employing two different lattice fermion formulations, the domain-wall fermion
and the clover fermion for quarks, at relatively heavy quark mass $(m_{PS}/m_V
\simeq 0.85)$. We obtain non-zero values of NEDM from calculations with both
fermion formulations. We next consider some systematic uncertainties of our
method for NEDM, using $24^3\times 32$ lattice at the same lattice spacing only
with the clover fermion. We finally investigate the quark mass dependence of
NEDM and observe a non-vanishing behavior of NEDM toward the chiral limit. We
interpret this behavior as a manifestation of the pathology in the quenched
approximation.


title:
First Nonperturbative Test of a Relativistic Heavy Quark Action in
  Quenched Lattice QCD

abstract:
  We perform a numerical test of a relativistic heavy quark(RHQ) action,
recently proposed by Tsukuba group, in quenched lattice QCD at $a\simeq 0.1$
fm. With the use of the improvement parameters previously determined at
one-loop level for the RHQ action, we investigate a restoration of rotational
symmetry for heavy-heavy and heavy-light meson systems around the charm quark
mass. We focused on two quantities, the meson dispersion relation and the
pseudo-scalar meson decay constants. It is shown that the RHQ action
significantly reduces the discretization errors due to the charm quark mass. We
also calculate the S-state hyperfine splittings for the charmonium and
charmed-strange mesons and the $D_s$ meson decay constant. The remaining
discretization errors in the physical quantities are discussed.


title: Localization properties of fermions and bosons

abstract:
  The topological structure of the QCD vacuum can be probed by monitoring the
spatial localization of the low-lying Dirac eigenmodes. This approach can be
pursued on the lattice, and unlike the traditional one requires no smoothing of
the gauge field. I review recent lattice studies, attempting to extract a
consistent description. What emerges is a picture of the vacuum as a
``topological sandwich'' of alternating, infinitely thin 3d layers of opposite
topological charge, as originally seen in direct measurements of the
topological charge density.


title:
Phase structure of lattice QCD with two flavors of Wilson quarks at
  finite temperature and chemical potential

abstract:
  We present results for phase structure of lattice QCD with two degenerate
flavors ($N_f=2$) of Wilson quarks at finite temperature $T$ and small baryon
chemical potential $\mu_B$. Using the imaginary chemical potential for which
the fermion determinant is positive, we perform simulations at points where the
ratios of pseudo-scalar meson mass to the vector meson mass $m_\pi/m_\rho$ are
between $0.943(3)$ and $0.899(4)$ as well as in the quenched limit. By analytic
continuation to real quark chemical potential $\mu$, we obtain the transition
temperature as a function of small $\mu_B$. We attempt to determine the nature
of transition at imaginary chemical potential by histogram, MC history, and
finite size scaling. In the infinite heavy quark limit, the transition is of
first order. At intermediate values of quark mass $m_q$ corresponding to the
ratio of $m_\pi/m_\rho$ in the range from $0.943(3)$ to $0.899(4)$ at
$a\mu_I=0.24$, the MC simulations show absence of phase transition.


title:
Non-perturbative renormalization of the static axial current in
  two-flavour QCD

abstract:
  We perform the non-perturbative renormalization of matrix elements of the
static-light axial current by a computation of its scale dependence in lattice
QCD with two flavours of massless O(a) improved Wilson quarks. The
regularization independent factor that relates any running renormalized matrix
element of the axial current in the static effective theory to the
renormalization group invariant one is evaluated in the Schroedinger functional
scheme, where in this case we find a significant deviation of the
non-perturbative running from the perturbative prediction. An important
technical ingredient to improve the precision of the results consists in the
use of modified discretizations of the static quark action introduced earlier
by our collaboration. As an illustration how to apply the renormalization of
the static axial current presented here, we connect the bare matrix element of
the current to the B_s-meson decay constant in the static approximation for one
value of the lattice spacing, a ~ 0.08 fm, employing large-volume N_f=2 data at
beta=5.3.


title:
Study of the finite temperature transition in 3-flavor QCD using the R
  and RHMC algorithms

abstract:
  We study the finite temperature transition in QCD with three flavors of equal
masses using the R and RHMC algorithm on lattices with temporal extent
N_{\tau}=4 and 6. For the transition temperature in the continuum limit we find
r_0 T_c=0.429(8) for the light pseudo-scalar mass corresponding to the end
point of the 1st order transition region. When comparing the results obtained
with the R and RHMC algorithms for p4fat3 action we see no significant
step-size errors down to a lightest pseudo-scalar mass of m_{ps} r_0=0.4.


title: String tension scaling in models of the confined phase

abstract:
  We introduce a D-dimensional Hamiltonian formalism for the study of Polyakov
loop models of finite temperature gauge theories in D+1 dimensions. Polyakov
loop string tensions are obtained from energy eigenstates of the Hamiltonian.
For D=1, the gauge theory reduces to quantum mechanics on the gauge group; for
D>1, the Hamiltonian includes hopping terms that link sites on the transverse
lattice. The deconfined phase is associated with a ground state which breaks
Z(N) symmetry, and Svetitsky-Yaffe critical universality emerges naturally for
D>1. A minimal model is proposed which naturally reproduces approximate Casimir
scaling for a range of couplings. Different classes of potentials lead to
different pictures of how confinement is realized. Such potential energy terms
also modify string tension scaling laws, as we demonstrate using two
potentials: one representing the perturbative thermal contributions from
gluons, and the other arising from magnetic monopoles in certain confining
supersymmetric theories.


title: Improving perturbation theory with cactus diagrams

abstract:
  We study a systematic improvement of perturbation theory for gauge fields on
the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders
in the coupling constant, a dominant subclass of tadpole diagrams.
  This method, originally proposed for the Wilson gluon action, is extended
here to encompass all possible gluon actions made of closed Wilson loops; any
fermion action can be employed as well. The effect of resummation is to replace
various parameters in the action (coupling constant, Symanzik and clover
coefficient) by ``dressed'' values; the latter are solutions to certain coupled
integral equations, which are easy to solve numerically.
  Some positive features of this method are: a) It is gauge invariant, b) it
can be systematically applied to improve (to all orders) results obtained at
any given order in perturbation theory, c) it does indeed absorb in the dressed
parameters the bulk of tadpole contributions.
  Two different applications are presented: The additive renormalization of
fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector
(axial) current. In many cases where non-perturbative estimates of
renormalization functions are also available for comparison, the agreement with
improved perturbative results is consistently better as compared to results
from bare perturbation theory.


title: Lattice Results in Coulomb Gauge

abstract:
  We discuss recent numerical results obtained for gluon and ghost propagators
in lattice Coulomb gauge and the status of the so-called Gribov-Zwanziger
confinement scenario in this gauge. Particular emphasis will be given to the
eigenvalue spectrum of the Faddeev-Popov matrix.


title:
First results from 2+1-Flavor Domain Wall QCD: Mass Spectrum, Topology
  Change and Chiral Symmetry with $L_s=8$

abstract:
  We present results for the static interquark potential, light meson and
baryon masses, and light pseudoscalar meson decay constants obtained from
simulations of domain wall QCD with one dynamical flavour approximating the $s$
quark, and two degenerate dynamical flavours with input bare masses ranging
from $m_s$ to $m_s/4$ approximating the $u$ and $d$ quarks. We compare these
quantities obtained using the Iwasaki and DBW2 improved gauge actions, and
actions with larger rectangle coefficients, on $16^3\times32$ lattices. We seek
parameter values at which both the chiral symmetry breaking residual mass due
to the finite lattice extent in the fifth dimension and the Monte Carlo time
history for topological charge are acceptable for this set of quark masses at
lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best,
demonstrating the feasibility of using QCDOC to generate ensembles which are
good representations of the QCD path integral on lattices of up to 3 fm in
spatial extent with lattice spacings in the range 0.09-0.13 fm. Despite large
residual masses and a limited number of sea quark mass values with which to
perform chiral extrapolations, our results for light hadronic physics scale and
agree with experimental measurements within our statistical uncertainties.


title:
More about chiral symmetry restoration at finite temperature in the
  planar limit

abstract:
  In the planar limit, in the deconfined phase, the Euclidean Dirac operator
has a spectral gap around zero. We show that functions of eigenvalues close to
the spectral edge, which are independent of common rescalings and shifts gauge
configuration by gauge configuration, have distributions described by a
Gaussian Hermitian matrix model. However, combinations of eigenvalues that are
scale and shift invariant only on the average, do not match this matrix model.


title: Meson spectral functions with chirally symmetric lattice fermions

abstract:
  In order to enhance our understanding of spectral functions in lattice QCD
obtained with the help of the Maximum Entropy Method, we study meson spectral
functions for lattice fermions with chiral symmetry. In particular we analyse
lattice artefacts for standard overlap, overlap hypercube and domain wall
fermions in the free field limit. We also present first results for
pseudoscalar spectral functions in dynamical QCD with 2+1 flavours of domain
wall fermions, using data generated by the UKQCD and RBC collaborations on
QCDOC machines.


title:
On the restoration of supersymmetry in twisted two-dimensional lattice
  Yang-Mills theory

abstract:
  We study a discretization of ${\cal N}=2$ super Yang-Mills theory which
possesses a single exact supersymmetry at non-zero lattice spacing. This
supersymmetry arises after a reformulation of the theory in terms of {\it
twisted} fields. In this paper we derive the action of the other twisted
supersymmetries on the component fields and study, using Monte Carlo
simulation, a series of corresponding Ward identities. Our results for SU(2)
and SU(3) support a restoration of these additional supersymmetries without
fine tuning in the infinite volume continuum limit. Additionally we present
evidence supporting a restoration of (twisted) rotational invariance in the
same limit. Finally we have examined the distribution of scalar field
eigenvalues and find evidence for power law tails extending out to large
eigenvalue. We argue that these tails indicate that the classical moduli space
does not survive in the quantum theory.


title:
Infrared features of unquenched finite temperature lattice Landau gauge
  QCD

abstract:
  The color diagonal and color antisymmetric ghost propagators slightly above
$T_c$ of $N_f=2$ MILC $24^3\times 12$ lattices are measured and compared with
zero temperature unquenched $N_f=2+1$ MILC$_c$ $20^3\times 64$ and MILC$_f$
$28^3\times 96$ lattices and zero temperature quenched $56^4$ $\beta=6.4$ and
6.45 lattices. The expectation value of the color antisymmetric ghost
propagator $\phi^c(q)$ is zero but its Binder cumulant, which is consistent
with that of $N_c^2-1$ dimensional Gaussian distribution below $T_c$, decreases
above $T_c$. Although the color diagonal ghost propagator is temperature
independent, the $l^1$ norm of the color antisymmetric ghost propagator is
temperature dependent. The expectation value of the ghost condensate observed
at zero temperature unquenched configuration is consistent with 0 in $T>T_c$.
  We also measure transverse, magnetic and electric gluon propagator and
extract gluon screening masses. The running coupling measured from the product
of the gluon dressing function and the ghost dressing function are almost
temperature independent but the effect of $A^2$ condensate observed at zero
temperature is consistent with 0 in $T>T_c$.
  The transverse gluon dressing function at low temperature has a peak in the
infrared but it becomes flatter at high temperature. Its absolute value in the
high momentum is larger for high temperature and similar to the magnetic gluon
dressing function. The electric gluon propagator at high momentum is
temperature independent. These data imply that the magnetic gluon propagator
and the color antisymmetric ghost propagator are affected by the presence of
dynamical quarks and there are strong non-perturbative effects through the
temperature dependent color anti-symmetric ghost propagator.


title:
Chiral crystals in strong-coupling lattice QCD at nonzero chemical
  potential

abstract:
  We study the effective action for strong-coupling lattice QCD with
one-component staggered fermions in the case of nonzero chemical potential and
zero temperature. The structure of this action suggests that at large chemical
potentials its ground state is a crystalline `chiral density wave' that
spontaneously breaks chiral symmetry and translation invariance. In mean-field
theory, on the other hand, we find that this state is unstable. We show that
lattice artifacts are partly responsible for this, and suggest that if this
phase exists in QCD, then finding it in Monte-Carlo simulations would require
simulating on relatively fine lattices. In particular, the baryon mass in
lattice units, m_B, should be considerably smaller than its strong-coupling
limit of m_B~3.


title: Reweighting method in finite density lattice QCD

abstract:
  Finite density simulations require dynamical fermions which are
computationally demanding. We employ Ferrenberg and Swendsen reweighting method
to reduce the number of ensembles needed. We use their method to do a combined
reweighting in both $\beta$ and quark number $k$ on an ensemble generated by
the Kentucky group.


title: QCD with one compact spatial dimension

abstract:
  The realization of global symmetries can depend on the geometry of the
underlying space. In particular, compactification can lead to spontaneous
breaking of such symmetries. Four-dimensional QCD with fundamental
representation fermions embedded in a space with one compact spatial dimension
has a critical length, at which the theory undergoes a phase transition and
develops a ground state that is no longer charge conjugation invariant. We show
this behavior with simulations of three color, four flavor QCD. We use unrooted
staggered fermion at two values of the lattice spacing and several quark
masses. We discuss the dependence of the transition on the dynamical fermion
mass as well as its connection to the finite temperature and chiral phase
transitions.


title: Current Physics Results from Staggered Chiral Perturbation Theory

abstract:
  We review several results that have been obtained using lattice QCD with the
staggered quark formulation. Our focus is on the quantities that have been
calculated numerically with low statistical errors and have been extrapolated
to the physical quark mass limit and continuum limit using staggered chiral
perturbation theory. We limit our discussion to a brief introduction to
staggered quarks, and applications of staggered chiral perturbation theory to
the pion mass, decay constant, and heavy-light meson decay constants.


title:
Disorder parameter and canonical quantization approach in lattice gauge
  theory

abstract:
  The work is dedicated to the derivation of the 'functional' integral
representation of the disorder parameter. This derivation resolves the problem
of the choice of the so called modifed action as well as the problem of the
choice of the boundary conditions along the 'time' direction. The question of
the gauge fixing in the functional integral representation is also discussed.


title:
Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler
  operators

abstract:
  We present a matrix technique to obtain the spectrum and the analytical index
of some elliptic operators defined on compact Riemannian manifolds. The method
uses matrix representations of the derivative which yield exact values for the
derivative of a trigonometric polynomial. These matrices can be used to find
the exact spectrum of an elliptic operator in particular cases and in general,
to give insight into the properties of the solution of the spectral problem. As
examples, the analytical index and the eigenvalues of the Dirac operator on the
torus and on the sphere are obtained and as an application of this technique,
the spectrum of the Dirac-Kahler operator on the sphere is explored.


title:
The spectrum of massive excitations of 3d 3-state Potts model and
  universality

abstract:
  We consider the mass spectrum of the 3$d$ 3-state Potts model in the broken
phase (a) near the second order Ising critical point in the temperature -
magnetic field plane and (b) near the weakly first order transition point at
zero magnetic field. In the case (a), we compare the mass spectrum with the
prediction from universality of mass ratios in the 3$d$ Ising class; in the
case (b), we determine a mass ratio to be compared with the corresponding one
in the spectrum of screening masses of the (3+1)$d$ SU(3) pure gauge theory at
finite temperature in the deconfined phase near the transition. The agreement
in the comparison in the case (a) would represent a non-trivial test of
validity of the conjecture of spectrum universality. A positive answer to the
comparison in the case (b) would suggest the possibility to extend this
conjecture to weakly first order phase transitions.


title: Lattice QCD at finite density: imaginary chemical potential

abstract:
  I describe the results for the critical line and the thermodynamics of
different phases of QCD which have been obtained by lattice simulations with an
imaginary chemical potential, and review motivations and merits of the
different strategies -- Taylor expansion, Fourier analysis and Pade'
approximants -- for analytic continuation from imaginary to real chemical
potential. I consider phenomenological models which can be easily extended to
the complex chemical potential plane, thus affording a direct comparison with
lattice data at imaginary $\mu$: the hadronic phase and the high temperature
limit are amenable to a simple description, while a rather subtle interplay
between thermodynamics and critical behaviour emerges in the hot phase close to
$T_c$


title:
Analytic continuation from imaginary to real chemical potential in
  two-color QCD

abstract:
  The method of analytic continuation from imaginary to real chemical potential
is one of the most powerful tools to circumvent the sign problem in lattice
QCD. Here we test this method in a theory, 2-color QCD, which is free from the
sign problem. We find that the method gives reliable results, within
appropriate ranges of the chemical potential, and that a considerable
improvement can be achieved if suitable functions are used to interpolate data
with imaginary chemical potential.


title: Bound States of (Anti-)Scalar-Quarks in SU(3)_c Lattice QCD

abstract:
  Light scalar-quarks \phi (colored scalar particles or idealized diquarks) and
their color-singlet hadronic states are studied with quenched SU(3)_c lattice
QCD in terms of mass generation. We investigate ``scalar-quark mesons''
\phi^\dagger \phi and ``scalar-quark baryons'' \phi\phi\phi as the bound states
of scalar-quarks \phi. We also investigate the bound states of scalar-quarks
\phi and quarks \psi, i.e., \phi^\dagger \psi, \psi\psi\phi and \phi\phi\psi,
which we name ``chimera hadrons''. All the new-type hadrons including \phi are
found to have a large mass due to large quantum corrections by gluons, even for
zero bare scalar-quark mass m_\phi=0 at a^{-1}\sim 1{\rm GeV}. We conjecture
that all colored particles generally acquire a large effective mass due to
dressed gluon effects.


title: Complete spectra of the Dirac operator and their relation to confinement

abstract:
  We compute complete spectra of the staggered lattice Dirac operator for
quenched SU(3) gauge configurations below and above the critical temperature.
The confined and the deconfined phase are characterized by a different response
of the Dirac eigenvalues to a change of the fermionic boundary conditions. We
analyze the role of the eigenvalues in recently developed spectral sums
representing the Polyakov loop. We show that the Polyakov loop gets its main
contributions from the UV end of the spectrum.


title: Precision study of the SU(3) topological susceptibility in the continuum

abstract:
  We determine the topological susceptibility in the SU(3) pure gauge theory.
We perform a series of high-statistics lattice studies and take the combined
continuum and infinite volume limit. We find chi_{top}r_0^4=0.0524(7)(6) which
translates into chi_{top}^{1/4}=193(1)(8)MeV with the second error exclusively
due to the intrinsic scale ambiguity.


title:
Perturbative renormalization for static and domain-wall bilinears and
  four-fermion operators with improved gauge actions

abstract:
  We calculate one-loop renormalization factors for heavy-light bilinears as
well as four-fermion operators relevant for $B^{0} - \bar{B}^{0}$ mixing
calculations on the lattice. We use the static approximation for heavy quarks
and the domain-wall formulation for light quarks. We present results for
different choices of improved gauge action.


title: Hot QCD and warm dark matter

abstract:
  One of the possible explanations for the dark matter needed in the standard
cosmological model is so-called warm dark matter, in the form of right-handed
("sterile") neutrinos with a mass in the keV range. I describe how various
properties of QCD at temperatures of a few hundred MeV play an important role
in the theoretical computations that are needed for consolidating or falsifying
this scenario. In particular the points where lattice QCD could help are
underlined.


title: Quantitative comparison of filtering methods in lattice QCD

abstract:
  We systematically compare filtering methods used to extract topological
excitations (like instantons, calorons, monopoles and vortices) from lattice
gauge configurations, namely APE-smearing and spectral decompositions based on
lattice Dirac and Laplace operators. Each of these techniques introduces
ambiguities, which can invalidate the interpretation of the results. We show,
however, that all these methods, when handled with care, reveal very similar
topological structures. Hence, these common structures are free of ambiguities
and faithfully represent infrared degrees of freedom in the QCD vacuum. As an
application we discuss an interesting power-law for the clusters of filtered
topological charge.


title: The spectrum of charmonium-like vector mesons in lattice QCD

abstract:
  We present the first lattice results of the spectrum of exotic vector mesons
extracted from the molecular and diquark-antidiquark operators, with quark
fields c-q-cbar-qbar, and c-s-cbar-qbar (c-q-cbar-sbar) respectively, in
lattice QCD with exact chiral symmetry. Our results suggest that X(3872) and
Y(4260) are in the spectrum of QCD, with J^{PC} = 1^{++} and 1^{--}
respectively. Moreover, we obtain the spectrum of heavier exotic mesons with
c-s-cbar-ubar (c-u-cbar-sbar), c-s-cbar-dbar (c-d-cbar-sbar), c-s-cbar-sbar,
and c-c-cbar-cbar, as the first theoretical predictions from lattice QCD.


title: Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD

abstract:
  We present results of the first fully-dynamical lattice QCD determination of
hyperon-nucleon scattering. One s-wave phase shift was determined for n Lambda
scattering in both spin-channels at pion masses of 350, 490, and 590 MeV, and
for n Sigma- scattering in both spin channels at pion masses of 490, and 590
MeV. The calculations were performed with domain-wall valence quarks on
dynamical, staggered gauge configurations with a lattice spacing of b ~ 0.125
fm.


title:
Generalised parton distributions of the pion in partially-quenched
  chiral perturbation theory

abstract:
  We consider the pion matrix elements of the isoscalar and isovector
combinations of the vector and tensor twist-two operators that determine the
moments of the various pion generalised parton distributions. Our analysis is
performed using partially-quenched chiral perturbation theory. We work in the
SU(2) and SU(4|2) theories and present our results at infinite volume and also
at finite volume where some subtleties arise. These results are useful for
extrapolations of lattice calculations of these matrix elements at small
momentum transfer to the physical regime.


title:
Matrix elements of the complete set of \Delta B = 2 and \Delta C = 2
  operators in heavy meson chiral perturbation theory

abstract:
  Using heavy meson chiral perturbation theory, we consider the light
quark-mass and spatial volume dependence of the matrix elements of \Delta B=2
and \Delta C=2 four-quark operators relevant for
B^{0}_{(s)}{-}\bar{B}^{0}_{(s)} and D^{0}{-}\bar{D}^{0} mixing, and the B_{s}
meson width difference. Our results for these matrix elements are obtained in
the N_{f}=2+1 partially quenched theory, which becomes full QCD in the limit
where sea and valence quark masses become equal. They can be used in
extrapolation of lattice calculations of these matrix elements to the physical
light quark masses and to infinite volume. An important conclusion of this
paper is that the chiral extrapolations for matrix elements of heavy-light
meson mixing beyond the Standard Model, and those relevant for the B_s width
difference are more complicated than that for the Standard Model mixing matrix
elements.


title: Precision study of B^* B\pi coupling for the static heavy-light meson

abstract:
  We compute the B^*B\pi coupling \hat{g}_{\infty} for static heavy-light meson
using all-to-all propagators. It is shown that low-mode averaging with 100
low-lying eigenmodes indeed improves the signal for the 2-point and 3-point
functions for heavy-light meson significantly. Our study suggests that the
all-to-all propagator will be a very efficient method for high precision
computation of the B^*B\pi coupling especially in unquenched QCD where the
number of configurations is limited.


title:
Flavor symmetry breaking and scaling for improved staggered actions in
  quenched QCD

abstract:
  We present a study of the flavor symmetry breaking in the pion spectrum for
various improved staggered fermion actions. To study the effects of link
fattening and tadpole improvement, we use three different variants of the p4
action - p4fat3, p4fat7, and p4fat7tad. These are compared to Asqtad and also
to naive staggered. To study the pattern of symmetry breaking, we measure all
15 meson masses in the 4-flavor staggered theory. The measurements are done on
a quenched gauge background, generated using a one-loop improved Symanzik
action with $\beta=10/g^2 = 7.40, 7.75,$ and 8.00, corresponding to lattice
spacings of approximately a = .31 fm., .21 fm., and .14 fm. We also study how
the lattice scale set by the $\rho$ mass on each of these ensembles compares to
one set by the static quark potential.


title: Three dimensional four-fermion models - A Monte Carlo study

abstract:
  We present results from numerical simulations of three different 3d
four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral
symmetries, respectively. We performed the simulations by using the hybrid
Monte Carlo algorithm. We employed finite size scaling methods on lattices
ranging from 8^3 to 40^3 to study the properties of the second order chiral
phase transition in each model. The corresponding critical coupling defines an
ultraviolet fixed point of the renormalization group. In our high precision
simulations, we detected next-to-leading order corrections for various critical
exponents and we found them to be in good agreement with existing analytical
large-N_f calculations.


title: Transverse spin structure of the nucleon from lattice QCD simulations

abstract:
  We present the first calculation in lattice QCD of the lowest two moments of
transverse spin densities of quarks in the nucleon. They encode correlations
between quark spin and orbital angular momentum. Our dynamical simulations are
based on two flavors of clover-improved Wilson fermions and Wilson gluons. We
find significant contributions from certain quark helicity flip generalized
parton distributions, leading to strongly distorted densities of transversely
polarized quarks in the nucleon. In particular, based on our results and recent
arguments by Burkardt [Phys. Rev. D 72 (2005) 094020], we predict that the
Boer-Mulders-function $h_1^\perp$, describing correlations of transverse quark
spin and intrinsic transverse momentum of quarks, is large and negative for
both up and down quarks.


title: Couplings of hybrid operators to ground and excited states of bottomonia

abstract:
  We analyze the overlap of local color-octet meson operators with the
$\Upsilon$ and the $\eta_b$ and their low-lying excited states, especially the
first radial excitations. Our analysis is based on NRQCD and includes all terms
up to order $v^4$. We use a variety of source and sink operators as a basis for
the variational method, which enables us to clearly separate the mass
eigenstates and hence to extract the desired amplitudes. The results show the
usefulness of the variational method for determining couplings to excited
hadronic states.


title: QCD phase diagram: an overview

abstract:
  The aim of this review is to summarize the contemporary understanding of the
QCD phase diagram as a function of temperature and baryo-chemical potential.
The focus is on recent theoretical developments due to lattice simulations of
the phase diagram.


title: Understanding nucleon structure using lattice simulations

abstract:
  This review focuses on the discussion of three key results of nucleon
structure calculations on the lattice. These three results are the quark
contribution to the nucleon spin, J_q, the nucleon-Delta transition form
factors, and the nucleon axial coupling, g_A. The importance for phenomenology
and experiment is discussed and the requirements for future simulations are
pointed out.


title:
Chiral Lattice Gauge Theories and The Strong Coupling Dynamics of a
  Yukawa-Higgs Model with Ginsparg-Wilson Fermions

abstract:
  The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge
theories described in hep-lat/0605003 uses exact lattice chirality to decouple
the massless chiral fermions from a mirror sector, whose strong dynamics is
conjectured to give cutoff-scale mass to the mirror fermions without breaking
the chiral gauge symmetry. In this paper, we study the mirror sector dynamics
of a two-dimensional chiral gauge theory in the limitof strong Yukawa and
vanishing gauge couplings, in which case it reduces to an XY model coupled to
Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass
it is believed to be important that the XY model remain in its "high
temperature" phase, where there is no algebraic ordering--a conjecture
supported by the results of our work. We use analytic and Monte-Carlo methods
with dynamical fermions to study the scalar and fermion susceptibilities, and
the mirror fermion spectrum. Our results provide convincing evidence that the
strong dynamics does not "break" the chiral symmetry (more precisely, that the
mirror fermions do not induce algebraic ordering in two-dimensions), and that
the mirror fermions decouple from the infrared physics.


title: Constant contribution in meson correlators at finite temperature

abstract:
  We discuss a constant contribution to meson correlators at finite
temperature. In the deconfinement phase of QCD, a colored single quark state is
allowed as a finite energy state, which yields to a contribution of wraparound
quark propagation to temporal meson correlators. We investigate the effects in
the free quark case and quenched QCD at finite temperature. The ``scattering''
contribution causes a constant mode in meson correlators with zero spatial
momentum and degenerate quark masses, which can dominate the correlators in the
region of large imaginary times. In the free spectral function, the
contribution yields a term proportional to $\omega\delta(\omega)$. Therefore
this contribution is related to transport phenomena in the quark gluon plasma.
It is possible to distinguish the constant contribution from the other part
using several analysis methods proposed in this paper. As a result of the
analyses, we find that drastic changes in charmonium correlators for $\chi_c$
states just above the deconfinement transition are due to the constant
contribution. The other differences in the $\chi_c$ states are small. It may
indicate the survival of $\chi_c$ states after the deconfinement transition
until, at least, $1.4T_c$.


title: Advances and applications of lattice supersymmetry

abstract:
  I review motivations for the study of supersymmetric field theories by
lattice techniques. In particular, some of the more interesting potential
applications are described. These are models of quantum gravity, that rely on
the AdS/CFT correspondence. The dual gauge theory is an ideal place for lattice
studies to make a contribution. I also survey some of the recent advances in
lattice formulations of supersymmetric theories.


title:
Deconfining Phase Transition on Lattices with Boundaries at Low
  Temperature

abstract:
  In lattice gauge theory (LGT) equilibrium simulations of QCD are usually
performed with periodic boundary conditions (BCs). In contrast to that
deconfined regions created in heavy ion collisions are bordered by the confined
phase. Here we discuss BCs in LGT, which model a cold exterior of the lattice
volume. Subsequently we perform Monte Carlo (MC) simulations of pure SU(3) LGT
with a thus inspired simple change of BCs using volumes of a size comparable to
those typically encountered in the BNL relativistic heavy ion collider (RHIC)
experiment. Corrections to the usual LGT results survive in the finite volume
continuum limit and we estimate them as function of the volume size. In
magnitude they are found comparable to those of including quarks. As
observables we use a pseudocritical temperature, which rises opposite to the
effect of quarks, and the width of the transition, which broadens similar to
the effect of quarks.


title: Lattice measurement of $B_{B_s}$ with a chiral light quark action

abstract:
  The computation on the lattice of the bag parameter $B_{B_s}$ associated to
the $B_s - \bar{B_s}$ mixing amplitude in the Standard Model is presented. The
estimation has been made by combining the static limit of HQET and the
Neuberger light quark action which preserves the chiral symmetry on the
lattice. We find $B^{\bar{MS}}{stat}}_{B_s}(m_b)=0.92(3)$.


title:
QCD with light Wilson quarks on fine lattices (II): DD-HMC simulations
  and data analysis

abstract:
  In this second report on our recent numerical simulations of two-flavour QCD,
we provide further technical details on the simulations and describe the
methods we used to extract the meson masses and decay constants from the
generated ensembles of gauge fields. Among the topics covered are the choice of
the DD-HMC parameters, the issue of stability, autocorrelations and the
statistical error analysis. Extensive data tables are included as well as a
short discussion of the quark-mass dependence in partially quenched QCD,
supplementing the physics analysis that was presented in the first paper in
this series.


title: Equilibrium Thermodynamics of Lattice QCD

abstract:
  Lattice QCD allows us to simulate QCD at non-zero temperature and/or
densities. Such equilibrium thermodynamics calculations are relevant to the
physics of relativistic heavy-ion collisions. I give a brief review of the
field with emphasis on our work.


title:
Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a
  Landau-like gauge

abstract:
  The infrared behavior of the gluon propagator is directly related to
confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement
predicts an infrared vanishing (transverse) gluon propagator in Landau-like
gauges, implying violation of reflection positivity and gluon confinement.
Finite-volume effects make it very difficult to observe (in the minimal Landau
gauge) an infrared suppressed gluon propagator in lattice simulations of the
four-dimensional case. Here we report results for the SU(2) gluon propagator in
a gauge that interpolates between the minimal Landau gauge (for gauge parameter
lambda equal to 1) and the minimal Coulomb gauge (corresponding to lambda = 0).
For small values of lambda we find that the spatially-transverse gluon
propagator D^tr(0,|\vec p|), considered as a function of the spatial momenta
|\vec p|, is clearly infrared suppressed. This result is in agreement with the
Gribov-Zwanziger scenario and with previous numerical results in the minimal
Coulomb gauge. We also discuss the nature of the limit lambda -> 0 (complete
Coulomb gauge) and its relation to the standard Coulomb gauge (lambda = 0). Our
findings are corroborated by similar results in the three-dimensional case,
where the infrared suppression is observed for all considered values of lambda.


title: Dynamical Twisted Mass Fermions with Light Quarks

abstract:
  We present results of dynamical simulations with 2 flavours of degenerate
Wilson twisted mass quarks at maximal twist in the range of pseudo scalar
masses from 300 to 550 MeV. The simulations are performed at one value of the
lattice spacing a \lesssim 0.1 fm. In order to have O(a) improvement and aiming
at small residual cutoff effects, the theory is tuned to maximal twist by
requiring the vanishing of the untwisted quark mass. Precise results for the
pseudo scalar decay constant and the pseudo scalar mass are confronted with
chiral perturbation theory predictions and the low energy constants F,
\bar{l}_3 and \bar{l}_4 are evaluated with small statistical errors.


title:
2+1 flavor domain wall QCD on a (2 fm)^3 lattice: light meson
  spectroscopy with Ls = 16

abstract:
  We present results for light meson masses and pseudoscalar decay constants
from the first of a series of lattice calculations with 2+1 dynamical flavors
of domain wall fermions and the Iwasaki gauge action. The work reported here
was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice,
which amounts to a spatial volume of (2 fm)^3 in physical units. The number of
sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these
simulations. Three values of input light sea quark masses, m_l^{sea} \approx
0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the
physical light quark limit, whilst the heavier sea quark mass was fixed to
approximately the physical strange quark mass m_s. The exact rational hybrid
Monte Carlo algorithm was used to evaluate the fractional powers of the fermion
determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV,
f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical
only, which are in good agreement with the experimental values.


title:
Renormalisation group evolution for the $\Delta S = 1$ effective
  Hamiltonian with $N_f=2+1$

abstract:
  We discuss the renormalisation group (RG) evolution for the $\Delta S = 1$
operators in unquenched QCD with $N_f = 3$ ($m_u=m_d=m_s$) or, more generally,
$N_f = 2+1$ ($m_u=m_d \ne m_s$) flavors. In particular, we focus on the
specific problem of how to treat the singularities which show up only for
$N_f=3$ or $N_f = 2+1$ in the original solution of Buras {\it et al.} for the
RG evolution matrix at next-to-leading order. On top of Buras {\it et al.}'s
original treatment, we use a new method of analytic continuation to obtain the
correct solution in this case. It is free of singularities and can therefore be
used in numerical analysis of data sets calculated in lattice QCD.


title:
Decay constants of charm and beauty pseudoscalar heavy-light mesons on
  fine lattices

abstract:
  We compute decay constants of heavy-light mesons in quenched lattice QCD with
a lattice spacing of a ~ 0.04 fm using non-perturbatively O(a) improved Wilson
fermions and O(a) improved currents. We obtain f_{D_s} = 220(6)(5)(11) MeV, f_D
= 206(6)(3)(22) MeV, f_{B_s} = 205(7)(26)(17) MeV and f_B = 190(8)(23)(25) MeV,
using the Sommer parameter r_0 = 0.5 fm to set the scale. The first error is
statistical, the second systematic and the third from assuming a +-10%
uncertainty in the experimental value of r_0. A detailed discussion is given in
the text. We also present results for the meson decay constants f_K and f_\pi
and the \rho meson mass.


title: Critical Flavor Number in the Three Dimensional Thirring Model

abstract:
  We present results of a Monte Carlo simulation of the three dimensional
Thirring model with the number of fermion flavors N_f varied between 2 and 18.
By identifying the lattice coupling at which the chiral condensate peaks,
simulations are be performed at couplings g^2(N_f) corresponding to the strong
coupling limit of the continuum theory. The chiral symmetry restoring phase
transition is studied as N_f is increased, and the critical number of flavors
estimated as N_{fc}=6.6(1). The critical exponents measured at the transition
do not agree with self-consistent solutions of the Schwinger-Dyson equations;
in particular there is no evidence for the transition being of infinite order.
Implications for the critical flavor number in QED_3 are briefly discussed.


title: Heavy quark thermodynamics in full QCD

abstract:
  We analyze the large-distance behaviour of static quark-anti-quark pair
correlations in QCD. The singlet free energy is calculated and the entropy
contribution to it is identified allowing us to calculate the excess internal
energy. The free energy has a sharp drop in the critical region, leading to
sharp peaks in both excess entropy and internal energy.


title: Chiral anomalies and rooted staggered fermions

abstract:
  A popular approximation in lattice gauge theory is an extrapolation in the
number of fermion species away from the four fold degeneracy natural with the
staggered fermion formulation. I show that the extrapolation procedure
mutilates the expected continuum holomorphic behavior in the quark masses. The
conventional resolution proposes canceling the unphysical singularities with a
plethora of extra states appearing at finite lattice spacing. This unproven
conjecture requires an explicit loss of unitarity and locality. Even if
correct, the approach implies large cutoff effects in the low-energy
flavor-neutral sector.


title: QCD thermodynamics at zero and non-zero density

abstract:
  We present recent results on thermodynamics of QCD with almost physical light
quark masses and a physical strange quark mass value. These calculations have
been performed with an improved staggerd action especially designed for finite
temperature lattice QCD. In detail we present a calculation of the transition
temperature, using a combined chiral and continuum extrapolation. Furthermore
we present preliminary results on the interaction measure and energy density at
almost realistic quark masses. Finally we disscuss the response of the pressure
to a finite quark chemical potential. Within the Taylor expansion formalism we
calculate quark number susceptibilities and leading order corrections to finite
chemical potential. This is particularly usefull for mapping out the critical
region in the QCD phase diagram.


title:
The Stefan-Boltzmann law in a small box and the pressure deficit in hot
  SU(N) lattice gauge theory

abstract:
  The blackbody radiation in a box L^3 with periodic boundary conditions in
thermal equilibrium at a temperature T is affected by finite-size effects.
These bring about modifications of the thermodynamic functions which can be
expressed in a closed form in terms of the dimensionless parameter LT. For
instance, when LT~4 - corresponding to the value where the most reliable SU(N)
gauge lattice simulations have been performed above the deconfining temperature
T_c - the deviation of the free energy density from its thermodynamic limit is
about 5%. This may account for almost half of the pressure deficit observed in
lattice simulations at T~ 4 T_c.

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


title: Radially Excited States of 1P Charmonia and X(3872)

abstract:
  The excited states of charmonia are numerically investigated in quenched
lattice QCD with improved gauge and Wilson fermion actions formulated on
anisotropic lattices. Through a constrained curve fitting algorithm, the masses
of the first excited states in $0^{++}$, $1^{++}$, and $1^{+-}$ channels are
determined to be 3.825(88), 3.853(57), and 3.858(70) GeV, respectively.
Furthormore, a node structure is also observed in the Bethe-Salpeter amplitude
of the $1^{++}$ first excited state. These observations indicate that X(3872)
could be the first radial excitation of $\chi_{c1}$.


title: The density of states method at non-zero chemical potential

abstract:
  We study the QCD phase diagram by first principle lattice calculations at so
far unreached high densities. For this purpose we employ the density of states
method. Unimproved staggered fermions, which describe four quark flavors in the
continuum are used in this analysis. Though the method is quite expensive,
small lattices show an indication for a triple-point connecting three different
phases on the phase diagram.


title: Diquark correlations in baryons on the lattice with overlap quarks

abstract:
  We evaluate baryon wave functions in both the Coulomb and Landau gauge in
lattice QCD. These are constructed from quark propagators calculated with the
overlap Dirac operator on quenched gauge configurations at beta = 6. By
comparing baryon states that differ in their diquark content, we find evidence
for enhanced correlation in the scalar diquark channel, as favored by quark
models. We also summarize earlier results for diquark masses in the Landau
gauge, casting them in a form more easily compared with subsequent studies.


title:
Phase diagram at finite temperature and quark density in the strong
  coupling region of lattice QCD for color SU(3)

abstract:
  We study the phase diagram of quark matter at finite temperature (T) and
chemical potential (mu) in the strong coupling region of lattice QCD for color
SU(3). Baryon has effects to extend the hadron phase to a larger mu direction
relative to Tc at low temperatures in the strong coupling limit. With the 1/g^2
corrections, Tc is found to decrease rapidly as g decreases, and the shape of
the phase diagram becomes closer to that expected in the real world.


title:
A semi-variational approach to QCD at finite temperature and baryon
  density

abstract:
  Recently a new bosonization method has been used to derive, at zero fermion
density, an effective action for relativistic field theories whose partition
function is dominated by fermionic composites, chiral mesons in the case of
QCD. This approach shares two important features with variational methods: the
restriction to the subspace of the composites, and the determination of their
structure functions by a variational calculation. But unlike standard
variational methods it treats excited states at the same time and on the same
footing as the ground state. I extend this method including states of
nonvanishing fermion (baryon) number and derive an effective action for QCD at
finite temperature and baryon density. I test the result on a four-fermion
interaction model.


title: Infrared behavior of the Faddeev-Popov operator in Coulomb gauge QCD

abstract:
  We calculate the eigenvalue distribution of the Faddeev-Popov operator in
Coulomb gauge QCD using quenched SU(3) lattice simulation. In the confinement
phase, the density of the low-lying eigenvalues increases with lattice volume,
and the confinement criterion is satisfied. Moreover, even in the deconfinement
phase, the behavior of the FP eigenvalue density is qualitatively the same as
in the confinement phase. This is consistent with the fact that the
color-Coulomb potential is not screened in the deconfined phase.


title:
Two-flavor lattice QCD simulation in the epsilon-regime with exact
  chiral symmetry

abstract:
  We perform lattice simulations of two-flavor QCD using Neuberger's overlap
fermion, with which the exact chiral symmetry is realized at finite lattice
spacings. The epsilon-regime is reached by decreasing the light quark mass down
to 3 MeV on a 16^3 32 lattice with a lattice spacing \sim 0.11 fm. We find a
good agreement of the low-lying Dirac eigenvalue spectrum with the analytical
predictions of the chiral random matrix theory, which reduces to the chiral
perturbation theory in the epsilon-regime. The chiral condensate is extracted
as \Sigma(2 GeV) = (251(7)(11) MeV)^3, where the errors are statistical and an
estimate of the higher order effects in the epsilon-expansion.


title:
Heavy-Quark Free Energy, Debye Mass, and Spatial String Tension at
  Finite Temperature in Two Flavor Lattice QCD with Wilson Quark Action

abstract:
  We study Polyakov loop correlations and spatial Wilson loop at finite
Temperature in two-flavor QCD simulations with the RG-improved gluon action and
the clover-improved Wilson quark action on a $ 16^3 \times 4$ lattice. From the
line of constant physics at $m_{\rm PS}/m_{\rm V}=0.65$ and 0.80, we extract
the heavy-quark free energies, the effective running coupling $g_{\rm eff}(T)$
and the Debye screening mass $m_D(T)$ for various color channels of heavy
quark--quark and quark--anti-quark pairs above the critical temperature. The
free energies are well approximated by the screened Coulomb form with the
appropriate Casimir factors at high temperature. The magnitude and the
temperature dependence of the Debye mass are compared to those of the
next-to-leading order thermal perturbation theory and to a phenomenological
formula in terms of $g_{\rm eff}(T)$. We make a comparison between our results
with the Wilson quark action and the previous results with the staggered quark
action. The spatial string tension is also studied in the high temperature
phase and is compared to the next-to-next-leading order prediction in an
effective theory with dimensional reduction.


title:
Thermodynamics of two-flavor lattice QCD with an improved Wilson quark
  action at non-zero temperature and density

abstract:
  We report the current status of our systematic studies of the QCD
thermodynamics by lattice QCD simulations with two flavors of improved Wilson
quarks. We evaluate the critical temperature of two flavor QCD in the chiral
limit at zero chemical potential and show the preliminary result. Also we
discuss fluctuations at none-zero temperature and density by calculating the
quark number and isospin susceptibilities and their derivatives with respect to
chemical potential.


title: Energies and radial distributions of B_s mesons on the lattice

abstract:
  This is a follow-up to our earlier work for the energies and 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. We now study excited states of these mesons with
higher angular momentum and with radial nodes.
  The calculation is carried out with dynamical fermions on a 16^3 times 32
lattice with a lattice spacing approximately 0.10 fm. The lattice
configurations were generated by the UKQCD Collaboration. Attempts are now
being made to understand these results in terms of the Dirac equation. In
nature the closest equivalent of this heavy-light system is the B_s meson,
which allows us to compare our lattice calculations to experimental results
(where available) or give a prediction where the P-wave states should lie. We
pay particular attention to the spin-orbit splitting, to see which one of the
states (for a given angular momentum L) has the lower energy.


title: Loop Approach to Lattice Gauge Theories

abstract:
  We solve the Gauss law and the corresponding Mandelstam constraints in the
loop Hilbert space ${\cal H}^{L}$ using the prepotential formulation of $(d+1)$
dimensional SU(2) lattice gauge theory. The resulting orthonormal and complete
loop basis, explicitly constructed in terms of the $d(2d-1)$ prepotential
intertwining operators, is used to transcribe the gauge dynamics directly in
${\cal H}^{L}$ without any redundant gauge and loop degrees of freedom. Using
generalized Wigner-Eckart theorem and Biedenharn -Elliot identity in ${\cal
H}^L$, we show that the loop dynamics for pure SU(2) lattice gauge theory in
arbitrary dimension, is given by the real symmetric $3nj$ symbols of first kind
(e.g., n=6, 10 for d=2, 3 respectively). The corresponding "ribbon diagrams"
representing SU(2) loop dynamics are constructed. The prepotential techniques
are trivially extended to include fundamental matter fields leading to a
description in terms of loops and strings. The SU(N) gauge group is briefly
discussed.


title: Lattice QCD with a chiral twist

abstract:
  In these lectures I explain how chiral symmetry of continuum QCD naturally
leads to a class of lattice regularisations known as twisted mass QCD (tmQCD).
As compared to standard Wilson quarks, its advantages are the absence of
unphysical zero modes, the possibility to circumvent lattice renormalisation
problems and automatic O(a) improvement. On the other hand, the physical parity
and flavour symmetries are explicitly broken. I discuss these aspects and then
turn to the theory in a finite space-time volume with Schroedinger functional
boundary conditions. Again, chiral transformations of the continuum theory may
be used as a guide to formulate an alternative lattice regularisation of the
Schr\"odinger functional, with interesting applications to renormalization
problems in QCD.


title: Color Screening and Quark-Quark Interactions in Finite Temperature QCD

abstract:
  We analyze the screening of static diquark sources in 2-flavor QCD and
compare results with the screening of static quark-antiquark pairs. We show
that a two quark system in a fixed color representations is screened at short
distances like a single quark source in the same color representation whereas
at large distances the two quarks are screened independently. At high
temperatures we observe that the relative strength of the interaction in
diquark and quark-antiquark systems, respectively, obeys Casimir scaling. We
use this result to examine the possible existence of heavy quark-quark bound
states in the high temperature phase of QCD. We find support for the existence
of $bb$ states up to about $2T_c$ while $cc$ states are unlikely to be formed
above $T_c$.


title: Radial and orbital excitations of static-light mesons

abstract:
  We present results for the spectrum of static-light mesons from Nf=2 lattice
QCD. These results were obtained using all-to-all light quark propagators on an
anisotropic lattice, yielding an improved signal resolution when compared to
more conventional lattice techniques. With a light quark mass close to the
strange quark, we have measured the splittings between the ground-state S-wave
static-light meson and higher excitations. We attempt to identify the quantum
numbers of the excited states in the context of the reduced spatial symmetries
of the lattice.


title: The QCD Sign Problem for Small Chemical Potential

abstract:
  The expectation value of the complex phase factor of the fermion determinant
is computed in the microscopic domain of QCD at nonzero chemical potential. We
find that the average phase factor is non-vanishing below a critical value of
the chemical potential equal to the half the pion mass and vanishes
exponentially in the volume for larger values of the chemical potential. This
holds for QCD with dynamical quarks as well as for quenched and phase quenched
QCD. The average phase factor has an essential singularity for zero chemical
potential and cannot be obtained by analytic continuation from imaginary
chemical potential or by means of a Taylor expansion. The leading order
correction in the $p$-expansion of the chiral Lagrangian is calculated as well.


title: The Delta-resonance in a finite volume

abstract:
  We study the extraction of Delta-resonance parameters from lattice data for
small quark masses, corresponding to the case of an unstable Delta. To this
end, we calculate the spectrum of the correlator of two Delta-fields in a
finite Euclidian box up-to-and-including O(epsilon^3) in the small scale
expansion using infrared regularization. On the basis of our numerical study,
we argue that the extraction of the parameters of the Delta-resonance (in
particular, of the mass and the pion-nucleon-delta coupling constant) from the
measured volume dependence of the lowest energy levels should be feasible.


title:
Spontaneous chiral symmetry breaking in QCD:a finite-size scaling study
  on the lattice

abstract:
  Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite
volume can be seen in a finite box by studying, for instance, the dependence of
the chiral condensate from the volume and the quark mass. We perform a
feasibility study of this program by computing the quark condensate on the
lattice in the quenched approximation of QCD at small quark masses. We carry
out simulations in various topological sectors of the theory at several
volumes, quark masses and lattice spacings by employing fermions with an exact
chiral symmetry, and we focus on observables which are infrared stable and free
from mass-dependent ultraviolet divergences. The numerical calculation is
carried out with an exact variance-reduction technique, which is designed to be
particularly efficient when spontaneous symmetry breaking is at work in
generating a few very small low-lying eigenvalues of the Dirac operator. The
finite-size scaling behaviour of the condensate in the topological sectors
considered agrees, within our statistical accuracy, with the expectations of
the chiral effective theory. Close to the chiral limit we observe a detailed
agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the
volume and the topology dependence of our results with the predictions of the
chiral effective theory, we extract the corresponding low-energy constant.


title: Light dynamical fermions on the lattice: toward the chiral regime of QCD

abstract:
  Algorithmic and technical progress achieved over the last few years makes QCD
simulations with light dynamical quarks much faster than before. As a result
lattices with pions as light as 250--300 MeV can be simulated with the present
generation of computers. I review recent conceptual and numerical progress in
this field, with particular emphasis on results obtained and difficulties
encountered in simulations with significantly smaller quark masses with respect
to previous computations. I also attempt to compare physical results for pion
masses and decay constants available to date in the two-flavour theory with
expectations from chiral perturbation theory.


title: Renormalization Group Therapy

abstract:
  We point out a general problem with the procedures commonly used to obtain
improved actions from MCRG decimated configurations. Straightforward
measurement of the couplings from the decimated configurations, by one of the
known methods, can result into actions that do not correctly reproduce the
physics on the undecimated lattice. This is because the decimated
configurations are generally not representative of the equilibrium
configurations of the assumed form of the effective action at the measured
couplings. Curing this involves fine-tuning of the chosen MCRG decimation
procedure, which is also dependent on the form assumed for the effective
action. We illustrate this in decimation studies of the SU(2) LGT using
Swendsen and Double Smeared Blocking decimation procedures. A single-plaquette
improved action involving five group representations and free of this pathology
is given.


title:
Lattice Field Theory with the Sign Problem and the Maximum Entropy
  Method

abstract:
  Although numerical simulation in lattice field theory is one of the most
effective tools to study non-perturbative properties of field theories, it
faces serious obstacles coming from the sign problem in some theories such as
finite density QCD and lattice field theory with the $\theta$ term. We
reconsider this problem from the point of view of the maximum entropy method.


title:
Flavour symmetry restoration and kaon weak matrix elements in quenched
  twisted mass QCD

abstract:
  We simulate two variants of quenched twisted mass QCD (tmQCD), with
degenerate Wilson quarks of masses equal to or heavier than half the strange
quark mass. We use Ward identities in order to measure the twist angles of the
theory and thus check the quality of the tuning of mass parameters to a physics
condition which stays constant as the lattice spacing is varied. Flavour
symmetry breaking in tmQCD is studied in a framework of two fully twisted and
two standard Wilson quark flavours, tuned to be degenerate in the continuum.
Comparing pseudoscalar masses, obtained from connected quark diagrams made of
tmQCD and/or standard Wilson quark propagators, we confirm that flavour
symmetry breaking effects, which are at most 5%, decrease as we approach the
continuum limit. We also compute the pseudoscalar decay constant in the
continuum limit, with reduced systematics. As a consequence of improved tuning
of the mass parameters at $\beta = 6.1$, we reanalyse our previous $B_K$
results. Our main phenomenological findings are $r_0 f_K = 0.421(7)$ and $\hat
B_K = 0.735(71)$.


title: Normalized entropy density of the 3D 3-state Potts model

abstract:
  Using a multicanonical Metropolis algorithm we have performed Monte Carlo
simulations of the 3D 3-state Potts model on $L^3$ lattices with L=20, 30, 40,
50. Covering a range of inverse temperatures from $\beta_{\min}=0$ to
$\beta_{\max}=0.33$ we calculated the infinite volume limit of the entropy
density $s(\beta)$ with its normalization obtained from $s(0)=\ln 3$. At the
transition temperature the entropy and energy endpoints in the ordered and
disordered phase are estimated employing a novel reweighting procedure. We also
evaluate the transition temperature and the order-disorder interface tension.
The latter estimate increases when capillary waves are taken into account.


title: Continuum limit of string formation in 3-d SU(2) LGT

abstract:
  We study the continuum limit of the string-like behaviour of flux tubes
formed between static quarks and anti-quarks in three dimensional SU(2) lattice
gauge theory. We compare our simulation data with the predictions of both
effective string models as well as perturbation theory. On the string side we
obtain clear evidence for convergence of data to predictions of Nambu-Goto
theory. We comment on the scales at which the static potential starts departing
from one loop perturbation theory and then again being well described by
effective string theories. We also estimate the leading corrections to the
one-loop perturbative potential as well as the Nambu-Goto effective string. In
the intermediate regions we find that a modified Lennard-Jones type potential
gives surprisingly good fits.


title: The Monte Carlo method in quantum field theory

abstract:
  This series of six lectures is an introduction to using the Monte Carlo
method to carry out nonperturbative studies in quantum field theories. Path
integrals in quantum field theory are reviewed, and their evaluation by the
Monte Carlo method with Markov-chain based importance sampling is presented.
Properties of Markov chains are discussed in detail and several proofs are
presented, culminating in the fundamental limit theorem for irreducible Markov
chains. The example of a real scalar field theory is used to illustrate the
Metropolis-Hastings method and to demonstrate the effectiveness of an
action-preserving (microcanonical) local updating algorithm in reducing
autocorrelations. The goal of these lectures is to provide the beginner with
the basic skills needed to start carrying out Monte Carlo studies in quantum
field theories, as well as to present the underlying theoretical foundations of
the method.


title:
Fitting two nucleons inside a box: exponentially suppressed corrections
  to the Luscher's formula

abstract:
  Scattering observables can be computed in lattice field theory by measuring
the volume dependence of energy levels of two particle states. The dominant
volume dependence, proportional to inverse powers of the volume, is determined
by the phase shifts. This universal relation (\Lu's formula) between energy
levels and phase shifts is distorted by corrections which, in the large volume
limit, are exponentially suppressed. They may be sizable, however, for the
volumes used in practice and they set a limit on how small the lattice can be
in these studies. We estimate these corrections, mostly in the case of two
nucleons. Qualitatively, we find that the exponentially suppressed corrections
are proportional to the {\it square} of the potential (or to terms suppressed
in the chiral expansion) and the effect due to pions going ``around the world''
vanishes. Quantitatively, the size of the lattice should be greater than
$\approx(5 {fm})^3$ in order to keep finite volume corrections to the phase
less than $1^\circ$ for realistic pion mass.


title:
Infrared properties of propagators in Landau-gauge pure Yang-Mills
  theory at finite temperature

abstract:
  The finite-temperature behavior of gluon and of Faddeev-Popov-ghost
propagators is investigated for pure SU(2) Yang-Mills theory in Landau gauge.
We present nonperturbative results, obtained using lattice simulations and
Dyson-Schwinger equations. Possible limitations of these two approaches, such
as finite-volume effects and truncation artifacts, are extensively discussed.
Both methods suggest a very different temperature dependence for the magnetic
sector when compared to the electric one. In particular, a clear thermodynamic
transition seems to affect only the electric sector. These results imply in
particular the confinement of transverse gluons at all temperatures and they
can be understood inside the framework of the so-called Gribov-Zwanziger
scenario of confinement.


title: Lattice Study of Low-lying Nonet Scalar Mesons in Quenched Approximation

abstract:
  Using lattice QCD simulation in the quenched approximation, we study the
$\kappa$ meson, which is ^3P_0 in the quark model, and compare experimental and
other lattice data. The $\kappa$ is the lowest scalar meson with strangeness
and constitutes the scalar nonet. The obtained mass is much higher than the
recent experimental value, and therefore the $\kappa(800)$ is difficult to
consider as a simple two-body constituent-quark structure, and may have another
unconventional structure.


title: The chiral limit in lattice QCD

abstract:
  It has been a big challenge for lattice QCD to simulate dynamical quarks near
the chiral limit. Theoretically, it is well-known that the naive chiral
symmetry cannot be realized on the lattice (the Nielsen-Ninomiya theorem). Also
practically, the computational cost rapidly grows as the quark mass is reduced.
The JLQCD collaboration started a project to perform simulations with exact but
modified chiral symmetry using the the overlap-Dirac operator and the topology
conserving action. The latter is helpful to reduce the numerical cost of the
dynamical quarks. Our simulation of two-flavor QCD has been successful to
reduce the sea quark mass down to a few MeV.


title:
Phase diagram of QCD with 2+1 flavors of Wilson quarks at finite
  temperature and chemical potential

abstract:
  The first results on lattice at finite temperature $T$ and chemical potential
$\mu$ with 2+1 flavors of Wilson quarks are presented. We have studied the
dependence of chiral phase transition and deconfinement phase transition on
quark mass. Finite volume size analysis and Binder cumulants are used to
determine the properties of phase transition. Phase diagram of QCD with 2+1
flavors of Wilson quarks are presented.


title:
K_l3 form factor with N_f=2+1 dynamical domain wall fermions: A progress
  report

abstract:
  We present the latest results from the UKQCD/RBC collaborations for the K_l3
form factor with 2+1 flavours of dynamical domain wall quarks. Simulations are
performed on 16^3x32x16 and 24^3x64x16 lattices with three values of the light
quark mass, allowing for an extrapolation to the chiral limit. After
interpolating to zero momentum transfer, we obtain the preliminary result
f_+^{K\pi}(0)=0.9609(51) (or \Delta f = -0.0161(51)), which is in agreement
with the result of Leutwyler & Roos.


title: Improving the improved action

abstract:
  We investigate the construction of improved actions by the Monte Carlo
Renormalization Group method in the context of SU(2) gauge theory utilizing
different decimation procedures and effective actions. We demonstrate that the
basic self-consistency requirement for correct application of MCRG, i.e. that
the decimated configurations are equilibrium configurations of the adopted form
of the effective action, can only be achieved by careful fine-tuning of the
choice of decimation prescription and/or action.