title:
Chiral violations in domain-wall QCD from one-loop perturbation theory
  at finite $N_s$

abstract:
  We present perturbative calculations made with domain-wall fermions which
possess a finite number of points $N_s$ in the extra fifth dimension. We have
derived the required propagator functions, investigated the one-loop properties
of quark amplitudes at finite $N_s$ and evaluated three quantities that can
provide insights on chirality-breaking effects from the perturbative side.
  First we have computed the residual mass for various choices of $N_s$ and of
the domain-wall height $M$. We have found that this radiatively induced mass
approaches zero reasonably fast with the extent of the fifth dimension,
depending on $M$ and on a lesser extent on the coupling $g_0$. We have also
computed the differences of the renormalization constants of the vector and
axial-vector currents and of the scalar and pseudoscalar densities. Finally we
have calculated the chirally-forbidden mixing (which at finite $N_s$ is
suppressed only partially) of an operator which describes the lowest moment of
the $g_2$ structure function. In general we see that at $M=1.8$, where
simulations are usually performed, values of $N_s=20$ or larger would be
desirable in order for chiral violations to be negligible.
  The quantities that we have studied turn out to lose gauge invariance when
$N_s$ is not infinite. We have also found that anomalous dimensions of
operators at finite $N_s$ generally depend on $N_s$ and $M$. In particular, the
vector and axial-vector currents have in general a nonzero anomalous dimension
at finite $N_s$.


title: f_K/f_pi in Full QCD with Domain Wall Valence Quarks

abstract:
  We compute the ratio of pseudoscalar decay constants f_K/f_pi using
domain-wall valence quarks and rooted improved Kogut-Susskind sea quarks. By
employing continuum chiral perturbation theory, we extract the Gasser-Leutwyler
low-energy constant L_5, and extrapolate f_K/f_pi to the physical point. We
find: f_K/f_pi = 1.218 (+- 0.002) (+0.011 -0.024) where the first error is
statistical and the second error is an estimate of the systematic due to chiral
extrapolation and fitting procedures. This value agrees within the
uncertainties with the determination by the MILC collaboration, calculated
using Kogut-Susskind valence quarks, indicating that systematic errors arising
from the choice of lattice valence quark are small.


title: Extrapolations of Lattice Meson Form Factors

abstract:
  We use chiral perturbation theory to study the extrapolations necessary to
make physical predictions from lattice QCD data for the electromagnetic form
factors of pseudoscalar mesons. We focus on the quark mass, momentum, lattice
spacing, and volume dependence and apply our results to simulations employing
mixed actions of Ginsparg-Wilson valence quarks and staggered sea quarks. To
determine charge radii at quark masses on the lattices currently used, we find
that all extrapolations except the one to infinite volume make significant
contributions to the systematic error.


title: Proton decay matrix elements with domain-wall fermions

abstract:
  Hadronic matrix elements of operators relevant to nucleon decay in grand
unified theories are calculated numerically using lattice QCD. In this context,
the domain-wall fermion formulation, combined with non-perturbative
renormalization, is used for the first time. These techniques bring reduction
of a large fraction of the systematic error from the finite lattice spacing.
Our main effort is devoted to a calculation performed in the quenched
approximation, where the direct calculation of the nucleon to pseudoscalar
matrix elements, as well as the indirect estimate of them from the nucleon to
vacuum matrix elements, are performed. First results, using two flavors of
dynamical domain-wall quarks for the nucleon to vacuum matrix elements are also
presented to address the systematic error of quenching, which appears to be
small compared to the other errors. Our results suggest that the representative
value for the low energy constants from the nucleon to vacuum matrix elements
are given as |alpha| simeq |beta| simeq 0.01 GeV^3. For a more reliable
estimate of the physical low energy matrix elements, it is better to use the
relevant form factors calculated in the direct method. The direct method tends
to give smaller value of the form factors, compared to the indirect one, thus
enhancing the proton life-time; indeed for the pi^0 final state the difference
between the two methods is quite appreciable.


title:
Once more on the interrelation between Abelian monopoles and P-vortices
  in SU(2) LGT

abstract:
  We study the properties of configurations from which P-vortices on one hand
or Abelian monopoles on the other hand have been removed. We confirm the loss
of confinement in both cases and investigate in what respect the modified
ensembles differ from the confining ones from the point of view of the
complementary confinement scenario.


title: Multiparticle States and the Hadron Spectrum on the Lattice

abstract:
  The Clebsch-Gordan decomposition is calculated for direct products of the
irreducible representations of the cubic space group. These results are used to
identify multiparticle states which appear in the hadron spectrum on the
lattice. Consideration of the cubic space group indicates how combinations of
both zero momentum and non-zero momentum multiparticle states contribute to the
spectrum.


title:
The Effect of Reduced Spatial Symmetries on Lattice States: Results for
  Non-zero Linear Momentum

abstract:
  The irreducible representations of the cubic space group are described and
used to determine the mapping of continuum states to lattice states with
non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from
the character table for the cubic space group. These results are used to
identify multiparticle states which appear in the hadron spectrum on the
lattice.


title: Rationale for UV-filtered clover fermions

abstract:
  We study the contributions Sigma_0 and Sigma_1, proportional to a^0 and a^1,
to the fermion self-energy in Wilson's formulation of lattice QCD with
UV-filtering in the fermion action. We derive results for m_{crit} and the
renormalization factors Z_S, Z_P, Z_V, Z_A to 1-loop order in perturbation
theory for several filtering recipes (APE, HYP, EXP, HEX), both with and
without a clover term. The perturbative series is much better behaved with
filtering, in particular tadpole resummation proves irrelevant. Our
non-perturbative data for m_{crit} and Z_A/(Z_m*Z_P) show that the combination
of filtering and clover improvement efficiently reduces the amount of chiral
symmetry breaking -- we find residual masses am_{res}=O(10^{-2}).


title:
Renormalization-group analysis of the validity of staggered-fermion QCD
  with the fourth-root recipe

abstract:
  I develop a renormalization-group blocking framework for lattice QCD with
staggered fermions. Under plausible, and testable, assumptions, I then argue
that the fourth-root recipe used in numerical simulations is valid in the
continuum limit. The taste-symmetry violating terms, which give rise to
non-local effects in the fourth-root theory when the lattice spacing is
non-zero, vanish in the continuum limit. A key role is played by reweighted
theories that are local and renormalizable on the one hand, and that
approximate the fourth-root theory better and better as the continuum limit is
approached on the other hand.


title: Calculation of the nucleon axial charge in lattice QCD

abstract:
  Protons and neutrons have a rich structure in terms of their constituents,
the quarks and gluons. Understanding this structure requires solving Quantum
Chromodynamics (QCD). However QCD is extremely complicated, so we must
numerically solve the equations of QCD using a method known as lattice QCD.
Here we describe a typical lattice QCD calculation by examining our recent
computation of the nucleon axial charge.


title: Nonperturbative determination of the QCD potential at O(1/m)

abstract:
  The relativistic correction to the QCD static inter-quark potential at O(1/m)
is investigated nonperturbatively for the first time by using lattice Monte
Carlo QCD simulations. The correction is found to be comparable with the
Coulombic term of the static potential when applied to charmonium, and amounts
to one-fourth of the Coulombic term for bottomonium.


title: Twisted supersymmetric sigma model on the lattice

abstract:
  In this paper we conduct a numerical study of the supersymmetric O(3)
non-linear sigma model. The lattice formulation we employ was derived in
\cite{sigma1} and corresponds to a discretization of a {\it twisted} form of
the continuum action. The twisting process exposes a {\it nilpotent}
supercharge $Q$ and allows the action to be rewritten in $Q$-exact form. These
properties may be maintained on the lattice. We show how to deform the theory
by the addition of potential terms which preserve the supersymmetry. A Wilson
mass operator may be introduced in this way with a minimal breaking of
supersymmetry. We additionally show how to rewrite the theory in the language
of K\"{a}hler-Dirac fields and explain why this avenue does not provide a good
route to discretization. Our numerical results provide strong evidence for a
restoration of full supersymmetry in the continuum limit {\it without} fine
tuning. We also observe a non-vanishing chiral condensate as expected from
continuum instanton calculations.


title: Predictions with Lattice QCD

abstract:
  In recent years, we used lattice QCD to calculate some quantities that were
unknown or poorly known. They are the $q^2$ dependence of the form factor in
semileptonic $D\to Kl\nu$ decay, the leptonic decay constants of the $D^+$ and
$D_s$ mesons, and the mass of the $B_c$ meson. In this paper, we summarize
these calculations, with emphasis on their (subsequent) confirmation by
measurements in $e^+e^-$, $\gamma p$ and $\bar{p}p$ collisions.


title: Meson spectral functions at nonzero momentum in hot QCD

abstract:
  We present preliminary results for meson spectral functions at nonzero
momentum, obtained from quenched lattice QCD simulations at finite temperature
using the Maximal Entropy Method. Twisted boundary conditions are used to have
access to many momenta p~T. For light quarks, we observe a drastic modification
when heating the system from below to above Tc. In particular, for the vector
spectral density we find a nonzero spectral weight at all energies.


title:
Spontaneous breaking of remnant gauge symmetries in zero-temperature
  SU(2) lattice gauge theory

abstract:
  The 4-d SU(2) lattice gauge theory is simulated in the minimal Coulomb gauge
which aims to maximize the traces of all links in three directions.
Fourth-direction links are interpreted as spins in a Heisenberg-like model with
varying interactions. These spins magnetize in 3-d hyperlayers at weak
coupling, breaking a remnant gauge symmetry, as well as the Polyakov-loop
symmetry. They demagnetize at a phase transition around $\beta = 2.5$ on the
infinite lattice, as determined by Binder cumulant crossings. Because $N$
symmetries are breaking on an $N^4$ lattice, the transition is unusually broad,
encompassing most of the crossover region on typical lattices.


title: Dual superconductivity and vacuum properties in Yang--Mills theories

abstract:
  We address, within the dual superconductivity model for color confinement,
the question whether the Yang-Mills vacuum behaves as a superconductor of type
I or type II. In order to do that we compare, for the theory with gauge group
SU(2), the determination of the field penetration depth $\lambda$ with that of
the superconductor correlation length $\xi$. The latter is obtained by
measuring the temporal correlator of a disorder parameter developed by the Pisa
group to detect dual superconductivity. The comparison places the vacuum close
to the border between type I and type II and marginally on the type II side. We
also check our results against the study of directly measurable effects such as
the interaction between two parallel flux tubes, obtaining consistent
indications for a weak repulsive behaviour. Future strategies to improve our
investigation are discussed.


title: Static forces in d=2+1 SU(N) gauge theories

abstract:
  Using a three-level algorithm we perform a high-precision lattice computation
of the static force up to 1fm in the 2+1 dimensional SU(5) gauge theory.
Discretization errors and the continuum limit are discussed in detail. By
comparison with existing SU(2) and SU(3) data it is found that \sigma
r_0^2=1.65-\pi/24 holds at an accuracy of 1% for all N>=2, where r_0 is the
Sommer reference scale. The effective central charge c_{eff}(r) is obtained and
an intermediate distance r_s is defined via the property c_{eff}(r_s)=\pi/24.
It separates in a natural way the short-distance regime governed by
perturbation theory from the long-distance regime described by an effective
string theory. The ratio r_s/r_0 decreases significantly from SU(2) to SU(3) to
SU(5), where r_s < r_0. We give a preliminary estimate of its value in the
large-N limit. The static force in the smallest representation of N-ality 2,
which tends to the k=2 string tension as r->oo, is also computed up to 0.7fm.
The deviation from Casimir scaling is positive and grows from 0.1% to 1% in
that range.


title: Applications of Chiral Perturbation theory to lattice QCD

abstract:
  These lectures describe the use of effective field theories to extrapolate
results from the parameter region where numerical simulations of lattice QCD
are possible to the physical parameters (physical quark masses, infinite
volume, vanishing lattice spacing, etc.). After a brief introduction and
overview, I discuss three topics: 1) Chiral perturbation theory in the
continuum; 2) The inclusion of discretization effects into chiral perturbation
theory, focusing on the application to Wilson and twisted-mass lattice
fermions; 3) Extending chiral perturbation theory to describe partially
quenched QCD.


title:
The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon
  density

abstract:
  We present numerical results for the location of the chiral critical line at
finite temperature and zero and non-zero baryon density for QCD with N_f=2+1
flavours of staggered fermions on lattices with temporal extent N_t=4. For
degenerate quark masses, we compare our results obtained with the exact RHMC
algorithm with earlier, inexact R-algorithm results and find a reduction of 25%
in the critical quark mass, for which the first order phase transition changes
to a smooth crossover. Extending our analysis to non-degenerate quark masses,
we map out the chiral critical line up to the neighbourhood of the physical
point, which we confirm to be in the crossover region. Our data are consistent
with a tricritical point at a strange quark mass of ~500 MeV. Finally, we
investigate the shift of the critical line with finite baryon density, by
simulating with an imaginary chemical potential for which there is no sign
problem. We observe this shift to be very small or, conversely, the critical
endpoint \mu^c(m_{u,d},m_s) to be extremely quark mass sensitive. Moreover, the
sign of this shift is opposite to standard expectations. If confirmed on a
finer lattice, it implies the absence of a critical endpoint or phase
transition for chemical potentials \mu_B < 500 MeV. We thus argue that finer
lattices are required to settle even the qualitative features of the QCD phase
diagram.


title:
A Lattice Computation of the First Moment of the Kaon's Distribution
  Amplitude

abstract:
  We present a lattice computation of the first moment of the kaon's
leading-twist distribution amplitude. The results were computed using ensembles
with 2+1 dynamical flavours with the domain wall fermion action and Iwasaki
gauge action from the RBC and UKQCD joint dataset. The first moment is non-zero
because of SU(3)-breaking effects, and we find that we are able to measure
these effects very clearly. We observe the expected chiral behaviour and
finally obtain <\xi>(2GeV) = 3/5*a_K^1(2GeV) = 0.032(3), which agrees very well
with results obtained using sum-rules, but with a significantly smaller error.


title: Flavor Twisted Boundary Conditions and Isovector Form Factors

abstract:
  We use vector flavor symmetry to relate form factors of isospin changing
operators to isovector form factors. Flavor twisted boundary conditions in
lattice QCD thus allow isovector form factors of twist-two operators, e.g, to
be computed at continuous values of the momentum transfer. These twisted
boundary conditions, moreover, are implemented only in the valence sector.
Effects of the finite volume must be addressed to extract isovector moments and
radii at zero lattice momentum. As an example, we use chiral perturbation
theory to assess the volume effects in extracting the isovector magnetic moment
of the nucleon from simulations with twisted boundary conditions.


title: Lattice gauge action suppressing near-zero modes of H_W

abstract:
  We propose a lattice action including unphysical Wilson fermions with a
negative mass m_0 of the order of the inverse lattice spacing. With this
action, the exact zero mode of the hermitian Wilson-Dirac operator H_W(m_0)
cannot appear and near-zero modes are strongly suppressed. By measuring the
spectral density rho(lambda_W), we find a gap near lambda_W=0 on the
configurations generated with the standard and improved gauge actions. This gap
provides a necessary condition for the proof of the exponential locality of the
overlap-Dirac operator by Hernandez, Jansen, and Luescher. Since the number of
near-zero modes is small, the numerical cost to calculate the matrix sign
function of H_W(m_0) is significantly reduced, and the simulation including
dynamical overlap fermions becomes feasible. We also introduce a pair of
twisted mass pseudo-fermions to cancel the unwanted higher mode effects of the
Wilson fermions. The gauge coupling renormalization due to the additional
fields is then minimized. The topological charge measured through the index of
the overlap-Dirac operator is conserved during continuous evolutions of gauge
field variables.


title: Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices

abstract:
  We formulate the massive domain wall fermions on anisotropic lattices.
  For the massive domain wall fermion, we find that the dispersion relation
assumes the usual form in the low momentum region when 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. For
light domain wall fermions, we verified that the chiral mode is stable against
quantum fluctuations on anisotropic lattices. This calculation serves as a
guidance for the tuning of the parameters in the quark action in future
numerical simulations.


title: Determining F_pi from spectral sum rules

abstract:
  We derive spectral sum rules for a system with two quarks coupled to an
imaginary isospin chemical potential in the \epsilon regime. The sum rules show
an explicit dependence on the pion decay constant which should make it possible
to measure F_pi from the eigenvalue spectrum of this particular Dirac operator.


title:
Doubly Heavy Baryons and Quark-Diquark Symmetry in Quenched and
  Partially Quenched Chiral Perturbation Theory

abstract:
  We extend the chiral Lagrangian with heavy quark-diquark symmetry to quenched
and partially quenched theories. These theories are used to derive formulae for
the chiral extrapolation of masses and hyperfine splittings of doubly heavy
baryons in lattice QCD simulations. A quark-diquark symmetry prediction for the
hyperfine splittings of heavy mesons and doubly heavy baryons is rather
insensitive to chiral corrections in both quenched and partially quenched QCD.
Extrapolation formulae for the doubly heavy baryon electromagnetic transition
moments are also determined for the partially quenched theory.


title:
Hadron spectrum, quark masses and decay constants from light overlap
  fermions on large lattices

abstract:
  We present results from a simulation of quenched overlap fermions with
L\"uscher-Weisz gauge field action on lattices up to $24^3 48$ and for pion
masses down to $\approx 250$ MeV. Among the quantities we study are the pion,
rho and nucleon masses, the light and strange quark masses, and the pion decay
constant. The renormalization of the scalar and axial vector currents is done
nonperturbatively in the $RI-MOM$ scheme. The simulations are performed at two
different lattice spacings, $a \approx 0.1$ fm and $\approx 0.15$ fm, and on
two different physical volumes, to test the scaling properties of our action
and to study finite volume effects. We compare our results with the predictions
of chiral perturbation theory and compute several of its low-energy constants.
The pion mass is computed in sectors of fixed topology as well.


title: A new lattice measurement for potentials between static SU(3) sources

abstract:
  In this article, a new calculation of static potentials between sources of
different representations in SU(3) gauge group is presented. The results of
author's previous study \cite{Deld00} at the smallest lattice spacing
$a_{s}\simeq0.11$~ fm are shown to have been affected by finite volume effects.
Within statistical errors, the new results obtained here are still in agreement
with both, Casimir scaling and flux tube counting. There is also no
contradiction to the results obtained in Ref.~ \cite{Bali00} which however
exclude flux counting.


title: Small Instantons in $CP^1$ and $CP^2$ Sigma Models

abstract:
  The anomalous scaling behavior of the topological susceptibility $\chi_t$ in
two-dimensional $CP^{N-1}$ sigma models for $N\leq 3$ is studied using the
overlap Dirac operator construction of the lattice topological charge density.
The divergence of $\chi_t$ in these models is traced to the presence of small
instantons with a radius of order $a$ (= lattice spacing), which are directly
observed on the lattice. The observation of these small instantons provides
detailed confirmation of L\"{u}scher's argument that such short-distance
excitations, with quantized topological charge, should be the dominant
topological fluctuations in $CP^1$ and $CP^2$, leading to a divergent
topological susceptibility in the continuum limit. For the $\CP$ models with
$N>3$ the topological susceptibility is observed to scale properly with the
mass gap. These larger $N$ models are not dominated by instantons, but rather
by coherent, one-dimensional regions of topological charge which can be
interpreted as domain wall or Wilson line excitations and are analogous to
D-brane or ``Wilson bag'' excitations in QCD. In Lorentz gauge, the small
instantons and Wilson line excitations can be described, respectively, in terms
of poles and cuts of an analytic gauge potential.


title: Probing the chiral weak Hamiltonian at finite volumes

abstract:
  Non-leptonic kaon decays are often described through an effective chiral weak
Hamiltonian, whose couplings ("low-energy constants") encode all
non-perturbative QCD physics. It has recently been suggested that these
low-energy constants could be determined at finite volumes by matching the
non-perturbatively measured three-point correlation functions between the weak
Hamiltonian and two left-handed flavour currents, to analytic predictions
following from chiral perturbation theory. Here we complete the analytic side
in two respects: by inspecting how small ("epsilon-regime") and intermediate or
large ("p-regime") quark masses connect to each other, and by including in the
discussion the two leading Delta I = 1/2 operators. We show that the
epsilon-regime offers a straightforward strategy for disentangling the
coefficients of the Delta I = 1/2 operators, and that in the p-regime
finite-volume effects are significant in these observables once the
pseudoscalar mass M and the box length L are in the regime ML \lsim 5.0.


title:
Non-perturbative renormalisation of left-left four-fermion operators
  with Neuberger fermions

abstract:
  We outline a general strategy for the non-perturbative renormalisation of
composite operators in discretisations based on Neuberger fermions, via a
matching to results obtained with Wilson-type fermions. As an application, we
consider the renormalisation of the four-quark operators entering the Delta S=1
and Delta S=2 effective Hamiltonians. Our results are an essential ingredient
for the determination of the low-energy constants governing non-leptonic kaon
decays.


title: Domain decomposition improvement of quark propagator estimation

abstract:
  Applying domain decomposition to the lattice Dirac operator and the
associated quark propagator, we arrive at expressions which, with the proper
insertion of random sources therein, can provide improvement to the estimation
of the propagator. Schemes are presented for both open and closed (or loop)
propagators. In the end, our technique for improving open contributions is
similar to the ``maximal variance reduction'' approach of Michael and Peisa,
but contains the advantage, especially for improved actions, of dealing
directly with the Dirac operator. Using these improved open propagators for the
Chirally Improved operator, we present preliminary results for the static-light
meson spectrum. The improvement of closed propagators is modest: on some
configurations there are signs of significant noise reduction of disconnected
correlators; on others, the improvement amounts to a smoothening of the same
correlators.


title: The axial N to Delta transition form factors from Lattice QCD

abstract:
  We evaluate the N to Delta axial transition form factors in lattice QCD in
the quenched theory, with two degenerate flavors of dynamical Wilson fermions
and using domain wall valence fermions with staggered sea quark configurations.
We predict the ratio $C_5^A(q^2)/C_3^V(q^2)$ relevant to the parity violating
asymmetry and check the validity of the off-diagonal Goldberger-Treiman
relation.


title:
A Framework for Systematic Study of QCD Vacuum Structure II: Coherent
  Lattice QCD

abstract:
  We propose the formulation of lattice QCD wherein all elements of the theory
(gauge action, fermionic action, theta-term, and all operators) are constructed
from a single object, namely the lattice Dirac operator D with exact chiral
symmetry. Several regularizations of this type are suggested via constructing
scalar densities (gauge actions) that are explicit functions of D. The simplest
of these is based on the proposition that classical limit of density associated
with Tr D is (up to an additive constant) proportional to FF, while the
corresponding operator is local. The possibilities of explicit interrelations
between gauge and fermionic aspects of the theory are emphasized together with
the utility of such formulations for exploring the QCD vacuum structure.


title: The decay constant of the first excited pion from lattice QCD

abstract:
  We review the theory that predicts that the decay constant of the excited
light pseudo-scalar mesons are suppressed in the chiral limit relative to the
pion decay constant. We compute the decay constant of the first excited pion
($\pi^\prime$) using unquenched QCD at a fixed lattice spacing with sea quarks
of mass as low as a third the mass of the strange quark. The final result is
very sensitive to the improvement conditions. We obtain $f_{\pi^\prime} /
f_{\pi}$ = 0.078(93) in the chiral limit.


title:
The 4-D Layer Phase as a Gauge Field Localization: Extensive Study of
  the 5-D Anisotropic U(1) Gauge Model on the Lattice

abstract:
  We study a 4+1 dimensional pure Abelian Gauge model on the lattice with two
anisotropic couplings independent of each other and of the coordinates. A first
exploration of the phase diagram using mean field approximation and monte carlo
techniques has demonstrated the existence of a new phase, the so called Layer
phase, in which the forces in the 4-D subspace are Coulomb-like while in the
transverse direction (fifth dimension) the force is confining. This allows the
possibility of a gauge field localization scheme. In this work the use of
bigger lattice volumes and higher statistics confirms the existence of the
Layer phase and furthermore clarifies the issue of the phase transitions'
order. We show that the Layer phase is separated from the strongly coupled
phase by a weak first order phase transition. Also we provide evidence that the
Layer phase is separated by the five-dimensional Coulomb phase with a second
order phase transition and we give a first estimation of the critical
exponents.


title: Ergodic SO(3), monopole condensation and vortex free energy

abstract:
  We study the continuum limit of adjoint SU(2) LGT by means of a suppression
term for Z2 monopoles. High barriers for tunnelling among different twist
sectors are overcome through parallel tempering. Monopole condensation is used
to study the deconfinement transition and the properties of the confined phase.
Ergodicity in summing over all twist sectors allows an unbiased measure of the
't Hooft vortices free energy. Its behaviour in the SO(3) confined phase hints
at differences from what conjectured for semi-integer discretizations.


title: Charm as a domain wall fermion in quenched lattice QCD

abstract:
  We report a study describing the charm quark by a domain-wall fermion (DWF)
in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge
ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of
$a^{-1} \sim 3$ GeV. We calculate masses of heavy-light (charmed) and
heavy-heavy (charmonium) mesons with spin-parity $J^P = 0^\mp$ and $1^\mp$,
leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$),
and the $D^0$-$\bar{D^0}$ mixing parameter. The charm quark mass is found to be
$m^{\bar{\rm MS}}_{c}(m_{c})=1.24(1)(18)$ GeV. The mass splittings in
charmed-meson parity partners $\Delta_{q,J=0}$ and $\Delta_{q, J=1}$ are
degenerate within statistical errors, in accord with experiment, and they
satisfy a relation $\Delta_{q=ud, J} > \Delta_{q=s, J}$, also consistent with
experiment. A C-odd axial vector charmonium state, $h_c), lies 22(11) MeV above
the $\chi_{c1}$ meson, or $m_{h_{c}} = 3533(11)_{\rm stat.}$ MeV using the
experimental $\chi_{c1}) mass. However, in this regard, we emphasize
significant discrepancies in the calculation of hyperfine splittings on the
lattice. The leptonic decay constants of $D$ and $D_s$ mesons are found to be
$f_D=232(7)_{\rm stat.}(^{+6}_{-0})_{\rm chiral}(11)_{\rm syst.}$ MeV and
$f_{D_s}/f_{D} = 1.05(2)_{\rm stat.}(^{+0}_{-2})_{\rm chiral}(2)_{\rm syst.}$,
where the first error is statistical, the second a systematic due to chiral
extrapolation and the third error combination of other known systematics. The
$D^0$-$\bar{D^0}$ mixing bag parameter, which enters the $\Delta C = 2$
transition amplitude, is found to be $B_D(2{GeV})=0.845(24)_{\rm
stat.}(^{+24}_{-6})_{\rm chiral}(105)_{\rm syst.}$.


title: Pi-K Scattering in Full QCD with Domain-Wall Valence Quarks

abstract:
  We calculate the pi+ K+ scattering length in fully-dynamical lattice QCD with
domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at
a lattice spacing of b=0.125 fm, lattice spatial size of L =2.5 fm and at pion
masses of m_pi=290, 350, 490 and 600 MeV. The lattice data, analyzed at
next-to-leading order in chiral perturbation theory, allows an extraction of
the full pi K scattering amplitude at threshold. Extrapolating to the physical
point gives m_pi a_3/2 = -0.0574 (+- 0.0016)(+0.0024 -0.0058) and m_pi a_1/2 =
0.1725 (+- 0.0017)(+0.0023 -0.0156) for the I=3/2 and I=1/2 scattering lengths,
respectively, where the first error is statistical and the second error is an
estimate of the systematic due to truncation of the chiral expansion.


title: Non-perturbative study of QCD correlators

abstract:
  This PhD dissertation is devoted to a non-perturbative study of QCD
correlators. The main tool that we use is lattice QCD. We concentrated our
efforts on the study of the main correlators of the pure Yang - Mills theory in
the Landau gauge, namely the ghost and the gluon propagators. We are
particularly interested in determining the $\Lqcd$ parameter. It is extracted
by means of perturbative predictions available up to NNNLO. The related topic
is the influence of non-perturbative effects that show up as appearance of
power-corrections to the low-momentum behaviour of the Green functions. A new
method of removing these power corrections allows a better estimate of $\Lqcd$.
Our result is $\Lambda^{n_f=0}_{\ms} = 269(5)^{+12}_{-9}$ MeV. Another question
that we address is the infrared behaviour of Green functions, at momenta of
order and below $\Lqcd$. At low energy the momentum dependence of the
propagators changes considerably, and this is probably related to confinement.
The lattice approach allows to check the predictions of analytical methods
because it gives access to non-perturbative correlators. According to our
analysis the gluon propagator is finite and non-zero at vanishing momentum, and
the power-law behaviour of the ghost propagator is the same as in the free
case.


title: Algorithms for Dynamical Fermions

abstract:
  This is the write-up of three lectures on algorithms for dynamical fermions
that were given at the ILFTN workshop 'Perspectives in Lattice QCD' in Nara
during November 2005. The first lecture is on the fundamentals of Markov Chain
Monte Carlo methods and introduces the Hybrid Monte Carlo (HMC) algorithm and
symplectic integrators; the second lecture covers topics in approximation
theory and thereby introduces the Rational Hybrid Monte Carlo (RHMC) algorithm
and ways of evading integrator instabilities by means of multiple pseudofermion
fields; the third lecture introduces on-shell chiral (Ginsparg-Wilson) lattice
fermions and discusses five-dimensional formulations for computing fermion
propagators for such fermions.


title: Chiral corrections to the Roper mass

abstract:
  We analyze the quark mass dependence of the Roper mass to one-loop order in
relativistic baryon chiral perturbation theory. The loop integrals are
evaluated using infrared regularization which preserves chiral symmetry and
establishes a chiral counting scheme. The derived chiral expansion of the Roper
mass may prove useful for chiral extrapolations of lattice data. For couplings
of natural size the quark mass dependence of the Roper mass is similar to the
one of the nucleon.


title: Convergence of the chiral expansion for the nucleon mass

abstract:
  A number of papers recently have used fourth-order chiral perturbation theory
to extrapolate lattice data for the nucleon mass; the process seems
surprisingly successful even for large pion masses. This paper shows that the
inclusion of the fifth-order terms spoils the agreement.


title:
Lattice Simulations of the Thermodynamics of Strongly Interacting
  Elementary Particles and the Exploration of New Phases of Matter in
  Relativistic Heavy Ion Collisions

abstract:
  At high temperatures or densities matter formed by strongly interacting
elementary particles (hadronic matter) is expected to undergo a transition to a
new form of matter - the quark gluon plasma - in which elementary particles
(quarks and gluons) are no longer confined inside hadrons but are free to
propagate in a thermal medium much larger in extent than the typical size of a
hadron. The transition to this new form of matter as well as properties of the
plasma phase are studied in large scale numerical calculations based on the
theory of strong interactions - Quantum Chromo Dynamics (QCD). Experimentally
properties of hot and dense elementary particle matter are studied in
relativistic heavy ion collisions such as those currently performed at the
relativistic heavy ion collider (RHIC) at BNL. We review here recent results
from studies of thermodynamic properties of strongly interacting elementary
particle matter performed on Teraflops-Computer. We present results on the QCD
equation of state and discuss the status of studies of the phase diagram at
non-vanishing baryon number density.


title: Charmonia from Lattice QCD

abstract:
  Recent lattice QCD results on charmonium properties are reviewed. I comment
on molecules and hybrid states as well as on future studies of states near
strong decay thresholds.


title: Non-perturbatively Determined Relativistic Heavy Quark Action

abstract:
  We present a method to non-perturbatively determine the parameters of the
on-shell, $O(a)$-improved relativistic heavy quark action. These three
parameters, $m_0$, $\zeta$, and $c_B=c_E$ are obtained by matching
finite-volume, heavy-heavy and heavy-light meson masses to the exact
relativistic spectrum through a finite-volume, step-scaling recursion
procedure. We demonstrate that accuracy on the level of a few percent can be
achieved by carrying out this matching on a pair of lattices with equal
physical spatial volumes but quite different lattice spacings. A fine lattice
with inverse lattice spacing $1/a=5.4$ GeV and $24^3 \times 48$ sites and a
coarse, $1/a=3.6$ GeV, $16^3 \times 32$ lattice are used together with a heavy
quark mass $m$ approximately that of the charm quark. This approach is unable
to determine the initially expected, four heavy-quark parameters: $m_0$,
$\zeta$, $c_B$ and $c_E$. This apparent non-uniqueness of these four parameters
motivated the analytic result, presented in a companion paper, that this set is
redundant and that the restriction $c_E=c_B$ is permitted through order $a|\vec
p|$ and to all orders in $m a$ where $\vec p$ is the heavy quark's spatial
momenta.


title: Relativistic Heavy Quark Effective Action

abstract:
  We study the fermion action needed to accurately describe the low energy
physics of systems including heavy quarks in lattice QCD even when the heavy
fermion mass $m$ is on the order of, or larger than, the inverse lattice
spacing: $m \ge 1/a$. We carry out an expansion through first order in $|\vec
p| a$ (where $\vec p$ is the heavy quark momentum) and all orders in $ma$,
refining the analysis of the Fermilab and Tsukuba groups. We demonstrate that
the spectrum of heavy quark bound states can be determined accurately through
$|\vec p| a$ and $(ma)^n$ for arbitrary exponent $n$ by using a lattice action
containing only three unknown coefficients: $m_0$, $\zeta$ and $c_P$ (a
generalization of $c_{SW}$), which are functions of $ma$. In a companion paper,
we show how these three coefficients can be precisely determined using
non-perturbative techniques.


title: Anomalous superfluidity in 2+1 dimensional two-color lattice QCD

abstract:
  We study thermodynamics of strongly coupled lattice QCD with $two$ colors of
staggered fermions in $(2+1)$ dimensions. The partition function of this model
can be written elegantly as a statistical mechanics of dimers and baryonloops.
The model is invariant under an $SO(3)\times U(1)$ symmetry. At low
temperatures we find evidence for superfluidity in the U(1) symmetry sector
while the SO(3) symmetry remains unbroken. The finite temperature phase
transition appears to belong to the Kosterlitz-Thouless universality class, but
the superfluid density jump $\rho_s(T_c)$ at the critical temperature $T_c$ is
anomalously higher than the normal value of $2 T_c/\pi$. We show that by adding
a small SO(3) symmetry breaking term to the model, the superfluid density jump
returns to its normal value implying that the extra symmetry causes anomalous
superfluid behavior. Our results may be of interest to researchers studying
superfluidity in spin-1 systems.


title: Fixed twist dynamics of SO(3) gauge theory

abstract:
  We perform a throughout study of 3+1 dim. SO(3) LGT for any fixed-twist
background. We concentrate in particular on the physically significant trivial
and 1-twist sectors. Introducing a Z(2) monopole chemical potential the 1st
order bulk transition is moved down in the strong coupling region and weakened
to 2nd order in the 4-dim Ising model universality class. In this extended
phase diagram we gain access to a confined phase in every fixed twist sector of
the theory. The Pisa disorder operator is employed together with the Polyakov
loop to study the confinement-deconfinement transition in each sector. Due to
the specific properties of both operators, most results can be used to gain
insight in the ergodic theory, where all twist sectors should be summed upon.
An explicit mapping of each fixed twist theory to effective positive plaquette
models with fixed twisted boundary conditions is applied to better establish
their properties in the different phases.


title: Charmonium spectral functions in two-flavour QCD

abstract:
  We compute charmonium spectral functions in 2-flavour QCD using the maximum
entropy method and anisotropic lattices. We find that the S-waves (J/psi and
eta_c) survive up to temperatures close to 2T_c, while the P-waves (chi_c0 and
chi_c1) melt away below 1.3T_c.


title: Topics in Effective Field Theory for Lattice QCD

abstract:
  In this work, we extend and apply effective field theory techniques to
systematically understand a subset of lattice artifacts which pollute the
lattice correlation functions for a few processes of physical interest. Where
possible, we compare to existing lattice QCD calculations. In particular, we
extend the heavy baryon Lagrangian to the next order in partially quenched
chiral perturbation theory and use it to compute the masses of the lightest
spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then
construct the twisted mass chiral Lagrangian for baryons and apply it to
compute the lattice spacing corrections to the baryon masses simulated with
twisted mass lattice QCD.
  We extend computations of the nucleon electromagnetic structure to account
for finite volume effects, as these observables are particularly sensitive to
the finite extent of the lattice. We resolve subtle peculiarities for lattice
QCD simulations of polarizabilities and we show that using background field
techniques, one can make predictions for the 4 spin-dependent nucleon
polarizabilities, quantities which are difficult to access experimentally.
  We then discuss the two-pion system in finite volume, determining the
exponentially small volume corrections necessary for lattice determinations of
the scattering parameters. We also determine the lattice spacing artifacts that
arise for a mixed-action lattice simulation of the two-pion system with
Ginsparg-Wilson valence quarks and staggered sea quarks. We show that the
isospin 2 scattering length has a near continuum like behavior, differing from
the chiral perturbation theory calculation by a computable difference.


title:
Calculating the hadronic vacuum polarization and leading hadronic
  contribution to the muon anomalous magnetic moment with improved staggered
  quarks

abstract:
  We present a lattice calculation of the hadronic vacuum polarization and the
lowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu
= (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to
the low-q^2 region of the vacuum polarization is necessary to accurately
extract the muon g-2. To obtain this fit, we use staggered chiral perturbation
theory, including the vector particles as resonances, and compare these to
polynomial fits to the lattice data. We discuss the fit results and associated
systematic uncertainties, paying particular attention to the relative
contributions of the pions and vector mesons. Using a single lattice spacing
ensemble (a=0.086 fm), light quark masses as small as roughly one-tenth the
strange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} =
(713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the error
is statistical only and the two values correspond to linear and quadratic
extrapolations in the light quark mass, respectively. Considering systematic
uncertainties not eliminated in this study, we view this as agreement with the
current best calculations using the experimental cross section for e^+e^-
annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including the
experimental decay rate of the tau lepton to hadrons, 711.0 (5.0)
(0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the current
lattice calculation.


title: The spectrum of lattice QCD with staggered fermions at strong coupling

abstract:
  Using 4 flavors of staggered fermions at infinite gauge coupling, we compare
various analytic results for the hadron spectrum with exact Monte Carlo
simulations. Agreement with Ref. \cite{Martin_etal} is very good, at the level
of a few percent.
  Our results give credence to a discrepancy between the baryon mass and the
critical chemical potential, for which baryons fill the lattice at zero
temperature and infinite gauge coupling. Independent determinations of the
latter set it at about 30% less than the baryon mass. One possible explanation
is that the nuclear attraction becomes strong at infinite gauge coupling.


title: The transition temperature in QCD

abstract:
  We present a detailed calculation of the transition temperature in QCD with
two light and one heavier (strange) quark mass on lattices with temporal extent
N_t =4 and 6. Calculations with improved staggered fermions have been performed
for various light to strange quark mass ratios in the range, 0.05 <= m_l/m_s <=
0.5, and with a strange quark mass fixed close to its physical value. From a
combined extrapolation to the chiral (m_l -> 0) and continuum (aT = 1/N_t -> 0)
limits we find for the transition temperature at the physical point T_c r_0 =
0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as
the distance in the static quark potential at which the slope takes on the
value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2. Using the currently best known value
for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV. The
transition temperature in the chiral limit is about 3% smaller. We discuss
current ambiguities in the determination of T_c in physical units and also
comment on the universal scaling behavior of thermodynamic quantities in the
chiral limit.


title:
Polyakov loop in different representations of SU(3) at finite
  temperature

abstract:
  We investigate the Polyakov loop in different representations of SU(3) in
pure gauge at finite $T$. We discuss Casimir scaling for the Polyakov loop in
the deconfined phase and test and generalize the renormalization procedure for
the Polyakov loop from \cite{Kaczmarek:2002mc} to arbitrary representations. In
the confined phase we extract the renormalized adjoint Polyakov loop, which is
finite in the thermodynamic limit. For our numerical calculations we used the
tree-level improved Symanzik action on $32^3\times 4,6,8$ lattices.


title:
Accelerating Dynamical Fermion Computations using the Rational Hybrid
  Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields

abstract:
  There has been much recent progress in the understanding and reduction of the
computational cost of the Hybrid Monte Carlo algorithm for Lattice QCD as the
quark mass parameter is reduced. In this letter we present a new solution to
this problem, where we represent the fermionic determinant using (n)
pseudofermion fields, each with an (\nth) root kernel. We implement this within
the framework of the Rational Hybrid Monte Carlo (RHMC) algorithm. We compare
this algorithm with other recent methods in this area and find it is
competitive with them.


title: Testing Algorithms for Finite Temperature Lattice QCD

abstract:
  We discuss recent algorithmic improvements in simulating finite temperature
QCD on a lattice. In particular, the Rational Hybrid Monte Carlo(RHMC)
algorithm is employed to generate lattice configurations for 2+1 flavor QCD.
Unlike the Hybrid R Algorithm, RHMC is reversible, admitting a Metropolis
accept/reject step that eliminates the $\mathcal{O}(\delta t^2)$ errors
inherent in the R Algorithm. We also employ several algorithmic speed-ups,
including multiple time scales, the use of a more efficient numerical
integrator, and Hasenbusch pre-conditioning of the fermion force.


title: The RHMC algorithm for theories with unknown spectral bounds

abstract:
  The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte
Carlo algorithm for lattice QCD simulations to situations involving fractional
powers of the determinant of the quadratic Dirac operator. This avoids the
updating increment ($dt$) dependence of observables which plagues the Hybrid
Molecular-dynamics (HMD) method. The RHMC algorithm uses rational
approximations to fractional powers of the quadratic Dirac operator. Such
approximations are only available when positive upper and lower bounds to the
operator's spectrum are known. We apply the RHMC algorithm to simulations of 2
theories for which a positive lower spectral bound is unknown: lattice QCD with
staggered quarks at finite isospin chemical potential and lattice QCD with
massless staggered quarks and chiral 4-fermion interactions ($\chi$QCD). A
choice of lower bound is made in each case, and the properties of the RHMC
simulations these define are studied. Justification of our choices of lower
bounds is made by comparing measurements with those from HMD simulations, and
by comparing different choices of lower bounds.


title:
Precision lattice QCD calculations and predictions of fundamental
  physics in heavy quark systems

abstract:
  I describe the recent success in performing accurate calculations of the
effects of the strong force on particles containing bottom and charm quarks.
Since quarks are never seen in isolation, and so cannot be studied directly,
numerical simulations are key to understanding the properties of these
particles and extracting information about the quarks. The results have direct
impact on the worldwide experimental programme that is aiming to determine the
parameters of the Standard Model of particle physics precisely and thereby
uncover or constrain the possibilities for physics beyond the Standard Model.
The numerical simulation of the strong force is a huge computational task and
the recent success is the result of international collaboration in developing
techniques that are fast enough to do the calculations on powerful
supercomputers.


title: Quark condensate in two-flavor QCD

abstract:
  We compute the condensate in QCD with two flavors of dynamical fermions using
numerical simulation. The simulations use overlap fermions, and the condensate
is extracted by fitting the distribution of low lying eigenvalues of the Dirac
operator in sectors of fixed topological charge to the predictions of Random
Matrix Theory.


title: Diseases with rooted staggered quarks

abstract:
  Calculations using staggered quarks augmented with a root of the fermion
determinant to reduce doubling give a qualitatively incorrect behavior in the
small quark mass region. Attempts to circumvent this problem for the continuum
limit involve an unproven combination of unphysical states, a loss of
unitarity, and a rather peculiar non-commutation of limits.


title: The pion form factor from lattice QCD with two dynamical flavours

abstract:
  We compute the electromagnetic form factor of the pion using
non-perturbatively O(a) improved Wilson fermions. The calculations are done for
a wide range of pion masses and lattice spacings. We check for finite size
effects by repeating some of the measurements on smaller lattices. The large
number of lattice parameters we use allows us to extrapolate to the physical
point. For the square of the charge radius we find <r^2>=0.441(20) fm^2, in
good agreement with experiment.


title: The critical end point in QCD

abstract:
  In this talk I present the logic behind, and examine the reliability of,
estimates of the critical end point (CEP) of QCD using the Taylor expansion
method.


title: Strong-Isospin Breaking in the Neutron-Proton Mass Difference

abstract:
  We determine the strong-isospin violating component of the neutron-proton
mass difference from fully-dynamical lattice QCD and partially-quenched QCD
calculations of the nucleon mass, constrained by partially-quenched chiral
perturbation theory at one-loop level. The lattice calculations were performed
with domain-wall valence quarks on MILC lattices with rooted staggered
sea-quarks at a lattice spacing of b ~ 0.125 fm, lattice spatial size of L~2.5
fm and pion masses ranging from m_pi~290 MeV to ~350 MeV. At the physical value
of the pion mass, we predict M_n - M_p |(d-u) = 2.26 +- 0.57 +- 0.42 +- 0.10
MeV where the first error is statistical, the second error is due to the
uncertainty in the ratio of light-quark masses, eta=m_u/m_d, determined by
MILC, and the third error is an estimate of the systematic due to chiral
extrapolation.


title: String-like behaviour of 4d SU(3) Yang-Mills flux tubes

abstract:
  We present here results on the fine structure of the static q\bar q potential
in d=4 SU(3) Yang-Mills theory. The potential is obtained from Polyakov loop
correlators having separations between 0.3 and 1.2 fermi. Measurements were
carried out on lattices of spatial extents of about 4 and 5.4 fermi. The
temporal extent was 5.4 fermi in both cases. The results are analyzed in terms
of the force between a q\bar q pair as well as in terms of a scaled second
derivative of the potential. The data is accurate enough to distinguish between
different effective string models and it seems to favour the expression for
ground state energy of a Nambu-Goto string.


title: Hadron Deformation and Form Factors from Lattice QCD

abstract:
  We review the current status of lattice QCD studies of the nucleon system. In
particular, we focus on the determination of the shape of the nucleon by
probing its wave function as well as by evaluating the N to Delta transition
form factors.


title: A lattice study of the masses of singlet 0++ mesons

abstract:
  We compute the masses of the flavour singlet 0++ mesons using (n_f=2)
unquenched lattice QCD with the Iwasaki and Wilson gauge actions. Both
fermionic and glueball interpolating operators are used to create the states.
The mass of the lightest 0++ meson is suppressed relative to the mass of the
0++ glueball in quenched QCD at an equivalent lattice spacing. We discuss two
possible physical reasons for this.


title: Probing Nucleon Structure on the Lattice

abstract:
  The QCDSF/UKQCD collaboration has an ongoing program to calculate nucleon
matrix elements with two flavours of dynamical O(a) improved Wilson fermions.
Here we present recent results on the electromagnetic form factors, the quark
momentum fraction <x> and the first three moments of the nucleon's
spin-averaged and spin-dependent generalised parton distributions, including
preliminary results with pion masses as low as 320 MeV.


title:
Leptonic widths of heavy quarkonia: QCD/NRQCD matching for the
  electromagnetic current at O(\alpha_s v^2)

abstract:
  We construct the S-wave part of the electromagnetic vector annihilation
current to $O(\alpha_s v^2)$, where $v$ is the non-relativistic quark velocity,
for heavy quarks whose dynamics are described by the NRQCD action on the
lattice. The NRQCD vector current for $Q\bar{Q}$ annihilation is expressed as a
linear combination of lattice operators with quantum numbers L=0, $J^P=1^-$,
and the coefficients are determined by matching to the corresponding continuum
current in QCD to$O(v^2)$ at one-loop. The annihilation channel gives a complex
amplitude with Coulomb-exchange and infrared singularities, making a careful
choice for the contours of integration and infrared subtraction functions in
the numerical integration necessary. An automated vertex generation program
written in Python is employed, allowing us to use a realistic NRQCD action and
an improved gluon lattice action; a change in the definition of either action
is easily accommodated in this procedure. The final result is applicable to
simulations of electromagnetic decays of heavy quarkonia, notably the
$\Upsilon$ meson.


title:
Dynamical overlap fermion simulations with a preconditioned Hybrid Monte
  Carlo force

abstract:
  We present simulation results for the 2-flavour Schwinger model with
dynamical Ginsparg-Wilson fermions. Our Dirac operator is constructed by
inserting an approximately chiral hypercube operator into the overlap formula,
which yields the overlap hypercube operator. Due to the similarity with the
hypercubic kernel, a low polynomial of this kernel can be used as a numerically
cheap way to evaluate the fermionic part of the Hybrid Monte Carlo force. We
verify algorithmic requirements like area conservation and reversibility, and
we discuss the viability of this approach in view of the acceptance rate. Next
we confirm a high level of locality for this formulation. Finally we evaluate
the chiral condensate at light fermion masses, based on the density of low
lying Dirac eigenvalues in different topological sectors. The results represent
one of the first measurements with dynamical overlap fermions, and they agree
very well with analytic predictions at weak coupling.


title: Evidence for diquarks in lattice QCD

abstract:
  Diquarks may play an important role in hadron spectroscopy, baryon decays and
color superconductivity. We investigate the existence of diquark correlations
in lattice QCD by considering systematically all the lowest energy diquark
channels in a color gauge-invariant setup. We measure mass differences between
the various channels and show that the positive parity scalar diquark is the
lightest. Quark-quark correlations inside the diquark are clearly seen in this
channel, and yield a diquark size of order 1 fm.


title: The non-perturbative part of the plaquette in quenched QCD

abstract:
  We define the non-perturbative part of a quantity as the difference between
its numerical value and the perturbative series truncated by dropping the order
of minimal contribution and the higher orders. For the anharmonic oscillator,
the double-well potential and the single plaquette gauge theory, the
non-perturbative part can be parametrized as A (lambda)^B exp{-C/lambda} and
the coefficients can be calculated analytically. For lattice QCD in the
quenched approximation, the perturbative series for the average plaquette is
dominated at low order by a singularity in the complex coupling plane and the
asymptotic behavior can only be reached by using extrapolations of the existing
series. We discuss two extrapolations that provide a consistent description of
the series up to order 20-25. These extrapolations favor the idea that the
non-perturbative part scales like (a/r_0)^4 with a/r_0 defined with the force
method. We discuss the large uncertainties associated with this statement. We
propose a parametrization of ln((a/r_0)) as the two-loop universal terms plus a
constant and exponential corrections. These corrections are consistent with
a_{1-loop}^2 and play an important role when beta<6. We briefly discuss the
possibility of calculating them semi-classically at large beta.


title: Critical Exponents for U(1) Lattice Gauge Theory at Finite Temperature

abstract:
  For compact U(1) lattice gauge theory (LGT) we have performed a finite size
scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed and
$N_s\to\infty$, approaching the phase transition from the confined phase. For
$N_{\tau}=4$, 5 and 6 our data contradict the expected scenario that this
transition is either first order or in the universality class of the 3d XY
model. If there are no conceptional flaws in applying the argument that the
Gaussian fixed point in 3d is unstable to our systems, estimates of the
critical exponents $\alpha/\nu$, $\gamma/\nu$, $(1-\beta)/\nu$ and $2-\eta$
indicate the existence of a new, non-trivial renormalization group fixed point
for second order phase transitions in 3d. Such a fixed point would be of
importance for renormalization group theory and statistical physics.


title: Sum Rules and Cutoff Effects in Wilson Lattice QCD

abstract:
  We use the transfer matrix formalism to derive non-perturbative sum rules in
Wilson's lattice QCD with N_f flavours of quarks. The discretization errors on
these identities are treated in detail. As an application, it is shown how the
sum rules can be exploited to give improved estimates of the continuum spectrum
and static potential.


title: Hadronic decays from the lattice

abstract:
  I review the lattice QCD approach to determining hadronic decay transitions.
Examples considered include rho to pi pi; b_1 to pi omega; hybrid meson decays
and scalar meson decays. I discuss what lattices can provide to help understand
the composition of hadrons.


title: The Kaon B-parameter in Mixed Action Chiral Perturbation Theory

abstract:
  We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a
partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and
staggered sea quarks. We find that the resulting expression is similar to that
in the continuum, and in fact has only two additional unknown parameters. At
one-loop order, taste-symmetry violations in the staggered sea sector only
contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the
masses of taste-singlet sea-sea mesons. Lattice discretization errors also give
rise to an analytic term which shifts the tree-level value of B_K by an amount
of O(a^2). This term, however, is not strictly due to taste-breaking, and is
therefore also present in the expression for B_K for pure G-W lattice fermions.
We also present a numerical study of the mixed B_K expression in order to
demonstrate that both discretization errors and finite volume effects are small
and under control on the MILC improved staggered lattices.


title: Mass spectrum of 1-+ exotic mesons from lattice QCD

abstract:
  Time correlation functions of a hybrid exotic meson operator, with JPC=1-+,
generated in quenched lattice QCD are subjected to a (Bayesian) maximum entropy
analysis. Five distinct spectral levels are uncovered. Their extrapolation into
the physical pion mass region suggests a possible relationship to
experimentally known states pi1(1400) and pi1(1600), and also to a state in the
2 GeV region carrying the same quantum numbers.


title: Improvement of quark propagator estimation through domain decomposition

abstract:
  Applying domain decomposition to the lattice Dirac operator and the
associated quark propagator, we arrive at expressions which, with the proper
insertion of random sources therein, can provide improvement to the estimation
of the propagator. Schemes are considered for both open and closed (or loop)
propagators. In the end, our technique for improving open contributions is
similar to the ``maximal variance reduction'' approach of Michael and Peisa,
but contains the advantage, especially for improved actions, of dealing
directly with the Dirac operator. Using these improved open propagators for the
Chirally Improved operator, we present preliminary results for the static-light
meson spectrum.


title: Status Report on ILDG activities

abstract:
  A status report about the International Lattice Data Grid (ILDG) is given.
Different countries participating in the ILDG have created regional lattice
data grid solutions that are implemented, working and used. The remaining task
and the focus of present activities is the development of the interoperability
of these regional grids. A first, successful step in this direction is a
metadata catalogue service which is already working interoperable.


title: Quarkonium Spectral Function from Anisotropic Lattice

abstract:
  We discuss the behavior of charmonia and bottomonia correlators and spectral
functions above the deconfinement temperature and determine melting
temperatures for different mesonic states.


title: Excited mesons from $N_f=2$ dynamical Clover Wilson lattices

abstract:
  We study mesons on the lattice with a special focus on excited states. For
that purpose we construct several quark sources with different spatial
smearings, including p-waves. These quark sources are then combined with the
appropiate Dirac structures to form meson interpolators of definite spin. We
use these operators to construct a cross correlation matrix from which we
extract ground and excited meson states using the variational method. For the
calculations we use gauge configurations with $N_f=2$ dynamical Clover Wilson
fermions provided by the CP-PACS collaboration. We show preliminary results for
pseudoscalar, scalar, vector and pseudovector mesons.


title:
Plaquette expectation value and lattice free energy of three-dimensional
  SU(N) gauge theory

abstract:
  We use high precision lattice simulations to calculate the plaquette
expectation value in three-dimensional SU(N) gauge theory for N=2,3,4,5,8.
Using these results, we study the N-dependence of the first non-perturbative
coefficient in the weak-coupling expansion of hot QCD. We demonstrate that, in
the limit of large N, the functional form of the plaquette expectation value
with ultraviolet divergences subtracted is 15.9(2)-44(2)/N^2.


title: The infrared behavior of lattice QCD Green's functions

abstract:
  We investigate different aspects of lattice QCD in Landau gauge using Monte
Carlo simulations. In particular, we focus on the low momentum behavior of
gluon and ghost propagators. The gauge group is SU(3). Different systematic
effects on the gluon and ghost propagators are studied, e.g. the dependence on
the choice of Gribov copies or the influence of dynamical Wilson fermions. We
compare our data with results from studies of Dyson-Schwinger equations for the
gluon and ghost propagators. We demonstrate that the infrared behavior of both
propagators, as found in this thesis, is consistent with different criteria for
confinement. However, the running coupling constant, given as a
renormalization-group-invariant combination of the gluon and ghost dressing
functions, does not expose a finite infrared fixed point. We also report on a
first nonperturbative computation of the SU(3) ghost-gluon-vertex
renormalization constant and on an investigation of the spectral properties of
the Faddeev-Popov operator.


title:
Topology, chiral and screening transitions at finite density in two
  colour QCD

abstract:
  The behaviour of the topological susceptibility in QCD with two colours and 8
flavours of quarks is studied at nonzero temperature on the lattice across the
finite density transition. It is shown that its signal drops at a
(pseudo-)critical chemical potential mu_c. The Polyakov loop and the chiral
condensate undergo their transitions at the same value. Pauli blocking
supervenes at a value of the chemical potential larger than mu_c.


title: Direct numerical computation of disorder parameters

abstract:
  In the framework of various statistical models as well as of mechanisms for
color confinement, disorder parameters can be developed which are generally
expressed as ratios of partition functions and whose numerical determination is
usually challenging. We develop an efficient method for their computation and
apply it to the study of dual superconductivity in 4d compact U(1) gauge
theory.


title: Quantum Operator Design for Lattice Baryon Spectroscopy

abstract:
  A previously-proposed method of constructing spatially-extended
gauge-invariant three-quark operators for use in Monte Carlo lattice QCD
calculations is tested, and a methodology for using these operators to extract
the energies of a large number of baryon states is developed. This work is part
of a long-term project undertaken by the Lattice Hadron Physics Collaboration
to carry out a first-principles calculation of the low-lying spectrum of QCD.
  These techniques are then applied in the construction of nucleon operators.
Correlation matrix elements between these operators are estimated using 200
configurations on a $12^3 \times 48$ anisotropic lattice in the quenched
approximation with unphysically heavy u, d quark masses (the pion mass is
approximately 700 MeV). After a change of basis operators using a variational
method is applied, the energies of up to eight states are extracted in each
symmetry channel.
  Although comparison with experiment is not justified, the pattern of levels
obtained qualitatively agrees with the observed spectrum. A comparison with
quark model predictions is also made; the quark model predicts more low-lying
even-parity states than this study yields, but both the quark model and this
study predict more odd-parity states near 2 GeV than currently observed in
experiments.


title:
Nonzero chemical potential in the overlap Dirac operator and comparison
  to random matrix theory

abstract:
  In this talk we present the results published recently in Ref. [1], where we
showed how to introduce a quark chemical potential in the overlap Dirac
operator. The resulting operator satisfies a Ginsparg-Wilson relation and has
exact zero modes. It is no longer gamma_5-Hermitian, but its nonreal
eigenvalues still occur in pairs. We compute the spectral density of the
operator on the lattice and show that, for small eigenvalues, the data agree
with analytical predictions of non-Hermitian chiral random matrix theory for
both trivial and nontrivial topology. We also explain an observed change in the
number of zero modes as a function of chemical potential.


title:
Trajectory Length and Autocorrelation Times -- Nf=2 simulations in the
  Schroedinger functional

abstract:
  A status report is presented on the large-volume simulations in the
Schroedinger functional with two flavours of O(a) improved Wilson quarks
performed by the ALPHA collaboration. The physics goal is to set the scale for
the computation of the fundamental parameters of QCD. In this talk the emphasis
is on aspects of the Hybrid Monte-Carlo algorithm, which we use with
(symmetric) even-odd and Hasenbusch preconditioning. We study the dependence of
aucorrelation times on the trajectory length. The latter is found to be
significant for fermionic correlators, the trajectories longer than unity
performing better than the shorter ones.


title: Gross-Neveu model as a laboratory for fermion discretization

abstract:
  We introduce a finite volume renormalization scheme for the
N-Majorana-component O(N) invariant Gross-Neveu model. Universal observables
are defined that are accessible to precise numerical simulation in various
discretizations and allow for an extrapolation to the continuum limit. Here
first numerical results with Wilson fermions are reported. For N=2 they
reproduce exact finite volume continuum results in the massless Thirring model.
Our N=8 data are ready for comparison for instance with staggered results in
the future.


title: Iterative methods for overlap and twisted mass fermions

abstract:
  We present a comparison of a number of iterative solvers of linear systems of
equations for obtaining the fermion propagator in lattice QCD. In particular,
we consider chirally invariant overlap and chirally improved Wilson (maximally)
twisted mass fermions. The comparison of both formulations of lattice QCD is
performed at four fixed values of the pion mass between 230MeV and 720MeV. For
overlap fermions we address adaptive precision and low mode preconditioning
while for twisted mass fermions we discuss even/odd preconditioning. Taking the
best available algorithms in each case we find that calculations with the
overlap operator are by a factor of 30-120 more expensive than with the twisted
mass operator.


title: Correlation of the ghost and the quark in the lattice Landau gauge QCD

abstract:
  Effects of the quark field on the ghost propagator of the lattice Landau
gauge are investigated by using the quenched gauge configuration of SU(2) first
copy and the parallel tempering (PT) gauge fixed samples, quenched SU(3) $56^4$
configuration and unquenched SU(3) configurations produced by the MILC
collaboration.
  We measure color symmetric and color antisymmetric ghost propagator and the
Binder cumulant of $l^1$ norm and $l^2$ norm of color antisymmetric ghost
propagator and investigate deviation from that of Gaussian distribution.
  The dynamical quarks make color antisymmetric ghost propagator closer to
Gaussian distribution and Kugo-Ojima color confinement parameter $c$ closer to
1.


title:
Rotational Symmetry and A Light Mode in Two-Dimensional Staggered
  Fermions

abstract:
  To obtain a light mode in two-dimensional staggered fermions, we introduce
four new local operators keeping the rotational invariance for a staggered
Dirac operator. To split masses of tastes, three cases are considered. The mass
matrix and the propagator for free theories are analyzed. We find that one of
three cases is a good candidate for taking a single mode by the mass splitting.
In the case, it is possible that a heavy mode obtains infinite mass on even
sites or odd sites.


title:
Perturbative chiral violations for domain-wall QCD with improved gauge
  actions

abstract:
  We investigate, in the framework of perturbation theory at finite $N_s$, the
effectiveness of improved gauge actions in suppressing the chiral violations of
domain-wall fermions. Our calculations show substantial reductions of the
residual mass when it is compared at the same value of the gauge coupling, the
largest suppression being obtained when the DBW2 action is used. Similar
effects can also be observed for a power-divergent mixing coefficient which is
chirally suppressed. No significant reduction instead can be seen in the case
of the difference between the vector and axial-vector renormalization constants
when improved gauge actions are used in place of the plaquette action. We also
find that one-loop perturbation theory is not an adequate tool to carry out
comparisons at the same energy scale (of about 2 GeV), and in fact in this case
even an enhancement of the chiral violations is frequently obtained.


title:
Infrared Gluon and Ghost Propagators from Lattice QCD. Results from
  large asymmetric lattices

abstract:
  We report on the infrared limit of the quenched lattice Landau gauge gluon
and ghost propagators as well as the strong coupling constant computed from
large asymmetric lattices. The infrared lattice propagators are compared with
the pure power law solutions from Dyson-Schwinger equations (DSE). For the
gluon propagator, the lattice data is compatible with the DSE solution. The
preferred measured gluon exponent being $\sim 0.52$, favouring a null zero
momentum propagator. The lattice ghost propagator shows finite volume effects
and, for the volumes considered, the propagator does not follow a pure power
law. Furthermore, the strong coupling constant is computed and its infrared
behaviour investigated.


title:
Investigation of the overlap of excited bottomonium states with hybrid
  operators

abstract:
  We analyze the overlap of color-octet meson operators with the $\Upsilon$ and
the $\eta_b$ and their 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:
Dynamical simulations of QCD at finite temperature with a truncated
  perfect action

abstract:
  The Hypercube operator determines a variant of the approximate, truncated
perfect fermion action. In this pilot study we are going to report on first
experiences in dynamical QCD simulations with the Hypercube fermions. We apply
this formulation in an investigation of the finite temperature transition for
two flavours. On lattices of size $8^3\times 4$ we explore the phase diagram.
Physical scales are estimated from pseudoscalar and vector meson masses
obtained on $8^3\times 16$ lattices. We observe the presence of a metastability
region but do not find evidence for an Aoki phase. The Hypercube operator
allows us to simulate at ratios of pseudoscalar to vector meson masses at least
as small as 0.8 at the thermal crossover at $N_t=4$, which renders this
formulation cheaper than the Wilson like fermions.


title: The rooted staggered determinant in the Schwinger model

abstract:
  We investigate the continuum limit of the rooted staggered action in the
2-dimensional Schwinger model. We match both the unrooted and rooted staggered
determinants with an overlap fermion determinant of two (one) flavors and a
local pure gauge effective action by fitting the coefficients of the effective
action and the mass of the overlap operator. The residue of this fit measures
the difference of the staggered and overlap fermion actions. We show that this
residue scales at least as O(a^2), implying that any difference, be it local or
non-local, between the staggered and overlap actions becomes irrelevant in the
continuum limit. For the model under consideration here, this observation
justifies the rooting procedure for the staggered sea quark action.


title: The one-flavor quark condensate and related problems

abstract:
  I describe a recent calculation (by me, Hoffmann, Liu, and Schaefer) of the
chiral condensate in one-flavor QCD using numerical simulations with overlap
fermions. The condensate is extracted by fitting the distribution of low lying
eigenmodes of the Dirac operator in sectors of fixed topological charge to the
predictions of Random Matrix Theory. Our results are in excellent agreement
with estimates from the orientifold large-N expansion. Much interesting physics
surrounds this calculation, which I will highlight.


title: Thermodynamics of (2+1)-flavor QCD

abstract:
  We report on the status of our QCD thermodynamics project. It is performed on
the QCDOC machine at Brookhaven National Laboratory and the APEnext machine at
Bielefeld University. Using a 2+1 flavor formulation of QCD at almost realistic
quark masses we calculated several thermodynamical quantities. In this
proceeding we show the susceptibilites of the chiral condensate and the
Polyakov loop, the static quark potential and the spatial string tension.


title: Simulation of Lattice Gauge Action from the Overlap Operator

abstract:
  We show the result of the lattice gauge field tensor which is derived from
the classical continuum limit of the overlap Dirac operator. By analogous
construction, it was recently proposed that the gauge action can be obtained
from the overlap operator as well which is proportional to Tr a D_{ov}. We
discuss how to carry out Monte Carlo simulations of such a gauge action
together with the overlap fermion.


title:
On the Locality and Scaling of Overlap Fermions at Coarse Lattice
  Spacings

abstract:
  The overlap fermion offers the considerable advantage of exact chiral
symmetry on the lattice, but is numerically intensive. This can be made
affordable while still providing large lattice volumes, by using coarse lattice
spacing, given that good scaling and localization properties are established.
Here, using overlap fermions on quenched Iwasaki gauge configurations, we
demonstrate directly that, with appropriate choice of negative Wilson's mass,
the overlap Dirac operator's range is comfortably small in lattice units for
each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero
in physical units in the continuum limit). In particular, our direct results
contradict recent speculation that an inverse lattice spacing of 1 GeV is too
low to have satisfactory localization. Furthermore, hadronic masses (available
on the two coarser lattices) scale very well.


title: Lattice Results for the QCD Phase Transition

abstract:
  We discuss recent results for the phase transition in finite-temperature QCD
from numerical (Monte Carlo) simulations of the lattice-regularized theory.
Emphasis is given to the case of two degenerate light-quark flavors. The order
of the transition in this case, which could have cosmological implications, has
not yet been established.


title:
Exploring the infrared 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. The lattice data favours $\kappa \sim 0.52$, which would imply a
vanishing zero momentum gluon propagator as predicted by the Kugo-Ojima
confinement mechanism and the Zwanziger horizon condition. Results for the
ghost propagator and for the running coupling constant are shown.


title: Avoiding the boson sign problem at finite chemical potential

abstract:
  The usual path integral formulation for scalar particles at finite density
involves a sign problem, making numerical simulation impractical. We present
alternative methods free of this difficulty. We apply these approaches to phi^4
theory in 2+1 dimensions, presenting preliminary numerical results for physical
quantities in the vicinity of the phase transition in the T-mu plane.


title:
Baryon correlators containing different diquarks from lattice
  simulations

abstract:
  Point to point vacuum correlators containing diquarks in the color
anti-triplet representation are computed both in the quenched approximation and
dynamical overlap simulations with two flavors. The scalar, pseudoscalar and
axial vector diquarks are combined with light quarks to form color singlets.
The scalar ("good") diquark channel shows a stronger attraction than the axial
vector ("bad") channel in the quenched data set. The pseudoscalar diquark
channel shows a finite volume zero mode artifact: the correlator becomes
negative at large distance when the quark mass is small. By separating
configurations without zero modes from those with zero modes, we found that the
zero modes have an important contribution in both the attraction in the scalar
channel and the repulsion in the pseudoscalar channel. In the axial vector
diquark channel, we did not find apparent zero mode effects.


title: Overlap fermions on a twisted mass sea

abstract:
  We present first results of a mixed action project. We analyze gauge
configurations generated with two flavors of dynamical twisted mass fermions.
Neuberger's overlap Dirac operator is used for the valence sector. The various
choices in the setup of the simulation are discussed. We employ chiral
perturbation theory to describe the effects of using different actions in the
sea and valence sector at non-zero lattice spacing.


title: Lattice QCD at finite temperature

abstract:
  I discuss recent developments in finite temperature lattice QCD, including
the calculation of the transition temperature, equation of state, color
screening and meson spectral functions.


title:
Searching for the elusive critical endpoint at finite temperature and
  isospin density

abstract:
  We consider 3-flavour lattice QCD with a finite chemical potential mu_I for
isospin, close to the finite temperature transition from hadronic matter to a
quark-gluon plasma. In this region one can argue that the position and probably
the nature of this transition mimic those at finite quark-number chemical
potential mu. The quark mass is chosen to be close to the critical mass at zero
chemical potentials. Since the Binder cumulants used to determine the nature of
this transition in HMD(R) simulations are very sensitive to the updating
increment dt, we have switched to the newer exact RHMC algorithm for our
simulations. Preliminary results indicate that there is no critical endpoint in
the small mu_I regime, at least none connected with the critical point at zero
chemical potentials.


title:
Multi-Step stochastic correction in dynamical fermion updating
  algorithms

abstract:
  The advantages of using Multi-Step corrections for simulations of lattice
gauge theories with dynamical fermions will be discussed. This technique is
suited for algorithms based on the Multi-Boson representation of the dynamical
fermions as well as for the Hybrid Monte-Carlo (HMC) algorithm and variants of
the latter, like the Polynomial-HMC. Especially the latter has the power to
deal with an odd number of fermion fields--an essential feature necessary for
realistic QCD-simulations with up-, down-, and strange-quarks. In particular,
we will discuss the application of the multi-step (actually two-step)
correction technique to a PHMC updating algorithm for twisted-mass Wilson
fermions with non-degenerate fermion masses, as it was used in recent dynamical
simulations for N_f=2+1+1 fermion flavors.


title: Landau Gauge Gluon and Ghost Propagators from Lattice QCD

abstract:
  We report on recent numerical computations of the Landau gauge gluon and
ghost propagators as well as of the ghost-gluon vertex function in pure SU(3)
Yang-Mills theory and in full QCD on the lattice. Special emphasis is paid to
the low momentum region. In particular, we present new data for the gluon
propagator at momenta below 300 MeV. We also discuss different systematic
effects as there are finite-size, lattice discretization and Gribov copy but
also unquenching effects. A MOM-scheme running coupling \alpha_s(q^2) based on
the ghost-gluon vertex is calculated and found to decrease for momenta below
550 MeV, even though the renormalization constant of the vertex deviates only
weakly from being constant.


title:
Exploring the chiral singularities of two color lattice QCD at strong
  coupling

abstract:
  We use a modified directed path algorithm to study the finite temperature
chiral singularities of two color lattice QCD with staggered fermions at strong
coupling. Our lattice calculations are done at a fixed finite temperature in
the broken phase with a variety of different quark masses. We find that to the
lowest order, the behavior of our observables, namely the condensates and the
decay constants are all consistent with the predictions of the low energy
effective theory of our model. We further notice that in order to see
consistency, the quark masses used in our lattice calculations need to be quite
small than typically used.


title:
Lattice Gauge Theory Approach to Spontaneous Symmetry Breaking from an
  Extra Dimension

abstract:
  We present lattice simulation results corresponding to an SU(2) pure gauge
theory defined on the orbifold space E_4 x I_1, where E_4 is the
four-dimensional Euclidean space and I_1 is an interval, with the gauge
symmetry broken to a U(1) subgroup at the two ends of the interval by
appropriate boundary conditions. We demonstrate that the U(1) gauge boson
acquires a mass from a Higgs mechanism. The mechanism is driven by two of the
extra-dimensional components of the five-dimensional gauge field which play
respectively the role of the longitudinal component of the gauge boson and a
massive real physical scalar, the Higgs particle. Despite the
non-renormalizable nature of the theory, we observe only a mild cut-off
dependence of the physical observables. We also show evidence that there is a
region in the parameter space where the system behaves in a way consistent with
dimensional reduction.


title: GW Meson Scattering on a Staggered Sea

abstract:
  We discuss the structure of the NLO corrections to the chiral formulae for
mesonic scattering processes in mixed action simulations using Ginsparg-Wilson
valence quarks and staggered sea quarks. In particular, we show that the
analytic contribution of the NLO chiral Lagrangian is the same as in QCD. We
also comment on how this result restricts the dependence of the amplitudes on
the unknown parameter C_Mix appearing in the chiral theory appropriate for
these systems. We conclude with some comments on the explicit scattering
lengths.


title: RG decimation study of SU(2) gauge theory

abstract:
  We report on numerical studies of RG decimations in SU(2) gauge theory. We
study in particular a class of plaquette actions involving sums of group
representations. We measure a number of observables representative of different
length scales in order to investigate the transformation of the system under
different choices of spin blocking, and examine the flow of the effective
action couplings. A need for a projection to some class of effective actions on
the configurations resulting from the adopted numerical decimation procedures
is demonstrated. A numerical decimation procedure resulting in the effective
single plaquette Lagrangian tailored to reproduce different medium/large scale
physics is devised.


title: Renormalization of infrared contributions to the QCD pressure

abstract:
  Thanks to dimensional reduction, the infrared contributions to the QCD
pressure can be obtained from two different three-dimensional effective field
theories, called the Electrostatic QCD (Yang-Mills plus adjoint Higgs) and the
Magnetostatic QCD (pure Yang-Mills theory). Lattice measurements have been
carried out within these theories, but a proper interpretation of the results
requires renormalization, and in some cases also improvement, i.e. the removal
of terms of O(a) or O(a^2). We discuss how these computations can be
implemented and carried out up to 4-loop level with the help of Numerical
Stochastic Perturbation Theory.


title: Monopole condensation in two-flavour Adjoint QCD

abstract:
  Two distinct phase transitions occur at different temperatures in QCD with
adjoint fermions (aQCD): deconfinement and chiral symmetry restoration. In this
model, quarks do no explicitely break the center Z(3) symmetry and therefore
the Polyakov loop is a good order parameter for the deconfinement transition.
We study monopole condensation by inspecting the expectation value of an
operator which creates a monopole. Such a quantity is expected to be an order
parameter for the deconfinement transition as in the case of fundamental
fermions.


title:
Color Screening, Casimir Scaling, and Domain Structure in G(2) and SU(N)
  Gauge Theories

abstract:
  We argue that screening of higher-representation color charges by gluons
implies a domain structure in the vacuum state of non-abelian gauge theories,
with the color magnetic flux in each domain quantized in units corresponding to
the gauge group center. Casimir scaling of string tensions at intermediate
distances results from random spatial variations in the color magnetic flux
within each domain. The exceptional G(2) gauge group is an example rather than
an exception to this picture, although for G(2) there is only one type of
vacuum domain, corresponding to the single element of the gauge group center.
We present some numerical results for G(2) intermediate string tensions and
Polyakov lines, as well as results for certain gauge-dependent projected
quantities. In this context, we discuss critically the idea of projecting link
variables to a subgroup of the gauge group. It is argued that such projections
are useful only when the representation-dependence of the string tension, at
some distance scale, is given by the representation of the subgroup.


title: Why (staggered fermions)^{1/4} fail at finite density

abstract:
  Because the staggered fermion determinant is complex at nonzero mu, taking
its fourth root leads to phase ambiguities. These unphysical effects cause the
measure to become discontinuous; the problem becomes acute when Re mu exceeds
approximately half the pion mass (when T>0 this rough bound probably moves
towards larger mu). We show how to overcome the problem, but only very close to
the continuum limit. This regime may be beyond reach with current resources.


title:
Lattice QCD determination of states with spin 5/2 or higher in the
  spectrum of nucleons

abstract:
  Energies for excited isospin 1/2 states that include the nucleon are computed
using quenched, anisotropic lattices. Baryon interpolating field operators that
are used include nonlocal operators that provide $G_2$ irreducible
representations of the octahedral group. The decomposition of spin 5/2 or
higher states is realized for the first time in a lattice QCD calculation. We
observe patterns of degenerate energies in the irreducible representations of
the octahedral group that correspond to the subduction of the continuum spin
5/2 or higher.


title: Update on the physics of light pseudoscalar mesons

abstract:
  We present an update of the MILC investigation of the properties of light
pseudoscalar mesons using three flavors of improved staggered quarks. Results
are presented for the $\pi$ and $K$ leptonic decay constants, the CKM matrix
element $V_{us}$, the up, down and strange quark masses, and the coefficients
of the $O(p^4)$ chiral lagrangian. We have new data for lattice spacing $a
\approx 0.15$ fm with several values of the light quark mass down to one-tenth
the strange quark mass, higher statistics for $a \approx 0.09$ fm with the
light quark mass equal to one-tenth the strange quark mass, and initial results
for our smallest lattice spacing, $a \approx 0.06$ fm with light quark mass
two-fifths of the strange quark mass.


title: Field theoretic study of a cold Fermi gas in the unitary limit

abstract:
  Trapped and cooled gases of alkali atoms can be manipulated to exhibit a
variety of interesting phenomena. For example, dilute gases of fermionic atoms,
in 2 hyperfine states, can be cooled to temperatures where they become
superfluid. An external field can be applied to tune the scattering length a.
When |a| exceeds the interparticle spacing, nonperturbative tools are needed to
study the system theoretically. The unitary limit, |a|\to\infty, is
particularly interesting due to its universality and symmetry. Lattice field
theory and effective field theory can be used to systematically calculate
properties of this system. Results are presented for the finite temperature
phase transition and for behavior near zero temperature.


title: Quantum fluctuations of k-strings: A case study

abstract:
  K strings in Yang-Mills theory can be considered as bound states of k
elementary confining strings carrying one unit of colour flux. Current
estimates of k-string tension sigma_k are very sensitive to the leading
corrections due to quantum fluctuations of the string. In this study we address
this problem by comparing Polyakov-Polyakov correlators in the fundamental
representation (k=1) with the corresponding ones with k=2 in the confining
phase of a Z_4 gauge theory in three dimensions. Highly efficient simulation
techniques are available in this case. Although the k=1 Polyakov-Polyakov
correlator matches nicely with the expected bosonic string effects up to the
Next-to-Leading-Order, the k=2 Polyakov-Polyakov correlators show large
deviations. This is an important source of potential systematic errors in the
current estimates of sigma_k.


title: An Analysis of the Hadronic Spectrum from Lattice QCD

abstract:
  I begin by discussing the basic ideas of quantum field theory (QFT). I
provide a review of symmetries in physics and then move on to discuss the quark
model. I then review lattice gauge theory with particular attention paid to
lattice QCD and some of the associated problems. I discuss gauge fields on the
lattice along with free lattice fermions. I follow this with a definition of
the lattice QCD action and discuss how to reproduce the correct continuum
physics. I include a discussion of the basic numerical techniques employed in
lattice simulations. I review methods for putting particles onto the lattice
and describe how to fit the resulting data. The symmetries of the QCD
Lagrangian are reviewed along with various forms of symmetry breaking in
physics, the PCAC relation, the Goldberger-Treiman relation and the spontaneous
breakdown of the axial symmetry. I move on to discuss sigma models and finally
arrive at a basic chiral perturbation theory. I present research completed with
my supervisor C. Allton and collaborators A.W. Thomas, D.B. Leinweber and R.
Young in the final three chapters. This work involves making lattice
predictions for the Hadronic mass spectrum using extrapolation techniques based
on the predictions of chiral perturbation theory which have been developed by
the Adelaide group.


title: Confining properties of 2-color QCD at finite density

abstract:
  We study the confining properties of QCD with two colors across the finite
density phase transition. A disorder parameter detecting dual superconductivity
of the QCD vacuum is used as a probe for the confinement/deconfinement phase
transition.


title: Lattice simulations of real-time quantum fields

abstract:
  We investigate lattice simulations of scalar and nonabelian gauge fields in
Minkowski space-time. For SU(2) gauge-theory expectation values of link
variables in 3+1 dimensions are constructed by a stochastic process in an
additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and
the use of a tilted real-time contour leads to converging results in general.
All fixed point solutions are shown to fulfil the infinite hierarchy of
Dyson-Schwinger identities, however, they are not unique without further
constraints. For the nonabelian gauge theory the thermal equilibrium fixed
point is only approached at intermediate Langevin-times. It becomes more stable
if the complex time path is deformed towards Euclidean space-time. We analyze
this behavior further using the real-time evolution of a quantum anharmonic
oscillator, which is alternatively solved by diagonalizing its Hamiltonian.
Without further optimization stochastic quantization can give accurate
descriptions if the real-time extend of the lattice is small on the scale of
the inverse temperature.


title: Testing UV-filtered ("fat-link") clover fermions

abstract:
  We investigate filtered clover fermions, built from fat gauge links, both in
one-loop perturbation theory and in numerical simulations. We use a variety of
filtering recipes (APE, HYP, EXP, HEX), some of which are suitable for a HMC
with dynamical fermions. A generic filtering together with a (fat-link) clover
term yields fermions with much reduced chiral symmetry breaking.


title:
Broadening of the confining flux tube joining higher-representation
  sources

abstract:
  In the context of confining gauge theories we study the flux tube generated
by a pair of static sources belonging to higher rank representations of the
gauge group. Using a simple geometric approach based on minimal surfaces
describing the world-sheet of the underlying k-string, we infer logarithmic
broadening of the flux tube as a function of source separation. It turns out
that the coefficient of the logarithm does not depend on the specific
representation of the source nor on its N-ality and is universal. Numerical
results on a Z_4 gauge theory in three dimensions with static sources carrying
two units of elementary flux compare very favourably with these predictions.