title:
Lattice Gauge Fixing as Quenching and the Violation of Spectral
  Positivity

abstract:
  Lattice Landau gauge and other related lattice gauge fixing schemes are known
to violate spectral positivity. The most direct sign of the violation is the
rise of the effective mass as a function of distance. The origin of this
phenomenon lies in the quenched character of the auxiliary field $g$ used to
implement lattice gauge fixing, and is similar to quenched QCD in this respect.
This is best studied using the PJLZ formalism, leading to a class of covariant
gauges similar to the one-parameter class of covariant gauges commonly used in
continuum gauge theories. Soluble models are used to illustrate the origin of
the violation of spectral positivity. The phase diagram of the lattice theory,
as a function of the gauge coupling $\beta$ and the gauge-fixing parameter
$\alpha$, is similar to that of the unquenched theory, a Higgs model of a type
first studied by Fradkin and Shenker. The gluon propagator is interpreted as
yielding bound states in the confined phase, and a mixture of fundamental
particles in the Higgs phase, but lattice simulation shows the two phases are
connected. Gauge field propagators from the simulation of an SU(2) lattice
gauge theory on a $20^4$ lattice are well described by a quenched mass-mixing
model. The mass of the lightest state, which we interpret as the gluon mass,
appears to be independent of $\alpha$ for sufficiently large $\alpha$.


title:
Monopole Chains in the Compact Abelian Higgs Model with doubly-charged
  Matter Field

abstract:
  We study the properties of topological defects in the lattice compact Abelian
Higgs Model with charge Q=2 matter field. We find that monopoles and
antimonopoles form chain-like structures which are dense in the
confinement/symmetric phase. In this phase the mentioned structures explain
both the confinement of single-charged and the breaking of strings spanned
between doubly-charged test particles. This observation helps to understand how
the non-diagonal gluons, once taken into consideration in the Abelian
projection of gluodynamics, could reproduce in this framework the string
breaking for adjoint charges.


title: N(N*) and Delta(Delta*) on the lattice

abstract:
  We investigate the mass spectrum of Nucleon and Delta (and its counterparts
with strange and charm), and their excited states, in quenched lattice QCD with
exact chiral symmetry. For each light baryon, we use 23 masses to determine the
coefficients of the mass formula in quenched chiral perturbation theory. By
chiral extrapolation to m_\pi=135 MeV, we obtain M_N=958(26) MeV,
M_{N*}=1553(42) MeV, M_{Delta}=1216(32) MeV and M_{Delta*}=1611(17) MeV, which
are identified with N(939)P_{11},N(1535)S_{11}, Delta(1232)P_{33} and
Delta(1620)S_{31} respectively. Further, we directly measure the masses of
Omega^{-}, M_{Omega}=1648(60) MeV, and its excited state, M_{Omega*}=1935(48)
MeV; as well as the triply charmed baryon Omega_{ccc}^{++},
M_{Omega_{ccc}^{++}}=4931(22) MeV, and its excited state,
M_{{\Omega^{++}_{ccc}}^*}=5185(35) MeV.


title:
The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially
  Quenched $\chi$PT

abstract:
  This paper presents a first study of the pseudoscalar meson masses to two
loops, or NNLO, within the supersymmetric formulation of partially quenched
chiral perturbation theory (PQ$\chi$PT). The expression for the pseudoscalar
meson mass in the case of three valence and three sea quarks with equal masses,
but different from each other, is given to ${\cal O}(p^6)$, along with a
numerical analysis.


title: Zero Lattice Sound

abstract:
  We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon
chemical potential mu, using both analytical and numerical methods. In
particular, we study the self-consistent Boltzmann equation in the Fermi liquid
framework using the quasiparticle interaction calculated to O(1/N_f), and find
solutions for zero sound propagation for almost all mu > mu_c, the critical
chemical potential for chiral symmetry restoration. Next we present results of
a numerical lattice simulation, examining temporal correlation functions of
mesons defined using a point-split interpolating operator, and finding evidence
for phonon-like behaviour characterised by a linear dispersion relation in the
long wavelength limit. We argue that our results provide the first evidence for
a collective excitation in a lattice simulation.


title:
Non-perturbative renormalization of lattice operators in coordinate
  space

abstract:
  We present the first numerical implementation of a non-perturbative
renormalization method for lattice operators, based on the study of correlation
functions in coordinate space at short Euclidean distance. The method is
applied to compute the renormalization constants of bilinear quark operators
for the non-perturbative O(a)-improved Wilson action in the quenched
approximation. The matching with perturbative schemes, such as MS-bar, is
computed at the next-to-leading order in continuum perturbation theory. A
feasibility study of this technique with Neuberger fermions is also presented.


title: Positivity violation for the lattice Landau gluon propagator

abstract:
  We present explicit numerical evidence of reflection-positivity violation for
the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge
theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3)
and for three different lattice couplings in the scaling region (beta = 4.2,
5.0, 6.0). In particular, we observe a clear oscillatory pattern in the
real-space propagator C(t). We also verify that the (real-space) data show good
scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form.
The violation of positivity is in contradiction with a stable-particle
interpretation of the associated field theory and may be viewed as a
manifestation of confinement.


title: Improvement and Taste Symmetry Breaking for Staggered Quarks

abstract:
  We compare several improved actions for staggered quarks. We study the effect
of improvement on the taste changing interactions by calculating the splitting
in the pion spectrum. We investigate the effect of the improvement on some
topological properties.


title:
Center vortex model for the infrared sector of SU(3) Yang-Mills theory
  -- baryonic potential

abstract:
  The baryonic potential in the framework of the SU(3) random vortex
world-surface model is evaluated for a variety of static color source
geometries. For comparison, carefully taking into consideration the string
tension anisotropy engendered by the hypercubic lattice description, also the
Delta and Y law predictions for the baryonic potential are given. Only the Y
law predictions are consistent with the baryonic potentials measured.


title:
The critical equation of state of the three-dimensional O(N)
  universality class: N>4

abstract:
  We determine the scaling equation of state of the three-dimensional O(N)
universality class, for N=5, 6, 32, 64. The N=5 model is relevant for the SO(5)
theory of high-T_c superconductivity, while the N=6 model is relevant for the
chiral phase transition in two-color QCD with two flavors. We first obtain the
critical exponents and the small-field, high-temperature, expansion of the
effective potential (Helmholtz free energy) by analyzing the available
perturbative series, in both fixed-dimension and epsilon-expansion schemes.
Then, we determine the critical equation of state by using a systematic
approximation scheme, based on polynomial representations valid in the whole
critical region, which satisfy the known analytical properties of the equation
of state, take into account the Goldstone singularities at the coexistence
curve and match the small-field, high-temperature, expansion of the effective
potential. This allows us also to determine several universal amplitude ratios.
We also compare our approximate solutions with those obtained in the large-N
expansion, up to order 1/N, finding good agreement for N\gtrsim 32.


title: Propagators in Coulomb gauge from SU(2) lattice gauge theory

abstract:
  A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is
performed using large scale lattice simulations. The (equal-time) transverse
gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul}
(p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator
decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator
is weakly momentum dependent. The small momentum behavior of the Coulomb
potential is consistent with linear confinement. We find that the inequality
\sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide
evidence that the ghost form factor d(p) and f(p) acquire IR singularities,
i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out
that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare
ghost form factor d_0(p) is finite and therefore renormalization group
invariant.


title: Quenching Effects in the Hadron Spectrum

abstract:
  Lattice QCD has generated a wealth of data in hadronic physics over the last
two decades. Until relatively recently, most of this information has been
within the "quenched approximation" where virtual quark--anti-quark pairs are
neglected. This review presents a descriptive discussion of the effects of
removing this approximation in the calculation of hadronic masses.


title: Majorana and Majorana-Weyl fermions in lattice gauge theory

abstract:
  In various dimensional Euclidean lattice gauge theories, we examine a
compatibility of the Majorana decomposition and the charge conjugation property
of lattice Dirac operators. In $8n$ and $1+8n$ dimensions, we find a difficulty
to decompose a classical lattice action of the Dirac fermion into a system of
the Majorana fermion and thus to obtain a factorized form of the Dirac
determinant. Similarly, in $2+8n$ dimensions, there is a difficulty to
decompose a classical lattice action of the Weyl fermion into a system of the
Majorana--Weyl fermion and thus to obtain a factrized form of the Weyl
determinant. Prescriptions based on the overlap formalism do not remove these
difficulties. We argue that these difficulties are reflections of the global
gauge anomaly associated to the real Weyl fermion in $8n$ dimensions. For this
reason (besides other well-known reasons), a lattice formulation of the N=1
super Yang--Mills theory in these dimensions is expected to be extremely
difficult to find.


title: Staggered eigenvalue mimicry

abstract:
  We study the infrared part of the spectrum for UV-filtered staggered Dirac
operators and compare them to the overlap counterpart. With sufficient
filtering and at small enough lattice spacing the staggered spectra manage to
``mimic'' the overlap version. They show a 4-fold near-degeneracy, and a clear
separation between would-be zero modes and non-zero modes. This suggests an
approximate index theorem for filtered staggered fermions and a correct
sensitivity to the topology of QCD. Moreover, it supports square-rooting the
staggered determinant to obtain dynamical ensembles with $N_f=2$.


title:
Non-perturbative O(a)-improvement of Wilson quark action in three-flavor
  QCD with plaquette gauge action

abstract:
  We perform a non-perturbative determination of the O(a)-improvement
coefficient c_SW for the Wilson quark action in three-flavor QCD with the
plaquette gauge action. Numerical simulations are carried out in a range of
\beta=12.0-5.2 on a single lattice size of 8^3x16 employing the Schr\"odinger
functional setup of lattice QCD. As our main result, we obtain an interpolation
formula for c_SW and the critical hopping parameter K_c as a function of the
bare coupling. This enables us to remove O(a) scaling violation from physical
observables in future numerical simulation in the wide range of \beta. Our
analysis with a perturbatively modified improvement condition for c_SW suggests
that finite volume effects in c_SW are not large on the 8^3x16 lattice. We
investigate N_f dependence of c_SW by additional simulations for N_f=4, 2 and 0
at \beta=9.6. As a preparatory step for this study, we also determine c_SW in
two-flavor QCD at \beta=5.2. At this \beta, several groups carried out
large-scale calculations of the hadron spectrum, while no systematic
determination of c_SW has been performed.


title: Twisted Superspace on a Lattice

abstract:
  We propose a new formulation which realizes exact twisted supersymmetry for
all the supercharges on a lattice by twisted superspace formalism. We show
explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino
models in two dimensions. We introduce mild lattice noncommutativity to
preserve Leibniz rule on the lattice. The formulation is based on the twisted
superspace formalism for N=D=2 supersymmetry which was proposed recently. From
the consistency condition of the noncommutativity of superspace, we find an
unexpected three-dimensional lattice structure which may reduce into two
dimensional lattice where the superspace describes semilocally scattered
fermions and bosons within a double size square lattice.


title: The locality of the square-root method for improved staggered quarks

abstract:
  We study the effects of improvement on the locality of square-rooted
staggered Dirac operators in lattice QCD simulations. We find the localisation
lengths of the improved operators (FAT7TAD and ASQTAD) to be very similar to
that of the one-link operator studied by Bunk et al., being at least the
Compton wavelength of the lightest particle in the theory, even in the
continuum limit. We conclude that improvement has no effect. We discuss the
implications of this result for the locality of the nth-rooted fermion
determinant used to reduce the number of sea quark flavours, and for possible
staggered valence quark formulations.


title: Lattice measurement of the Isgur-Wise functions tau_1/2 and tau_3/2

abstract:
  We propose a method to compute the Isgur-Wise form factors tau_1/2(1) and
tau_3/2(1) for the decay of B mesons into orbitally excited (P wave) D**
charmed mesons on the lattice in the static limit. We also present the result
of an exploratory numerical simulation which shows that the signal/noise ratio
allows for a more dedicated computation. We find tau_1/2(1)=0.38(5) and
tau_3/2(1)= 0.53(8), with yet unknown systematic errors. These preliminary
numbers agree fairly well with theoretical expectation.


title:
Topological susceptibility in staggered fermion chiral perturbation
  theory

abstract:
  The topological susceptibility of the vacuum in quantum chromodynamics has
been simulated numerically using the Asqtad improved staggered fermion
formalism. At nonzero lattice spacing the residual fermion doublers (fermion
``tastes'') in the staggered fermion formalism give contributions to the
susceptibility that deviate from conventional continuum chiral perturbation
theory. In this brief report we estimate the taste-breaking artifact and
compare it with results of recent simulations, finding that it accounts for
roughly half of the scaling violation.


title: Chiral symmetry on the lattice

abstract:
  As a non-perturbative and gauge invariant regularization the lattice provides
a tool for deeper understanding of the celebrated Yang-Mills theory, QCD and
chiral gauge theories. For illustration, I discuss some analytic developments
on the lattice related to chiral symmetry, chiral fermions and improvement
programs. Chiral symmetry on the lattice has an amazing history, and it might
influence our perception of a symmetry beyond this example.


title: On the finite size mass shift formula for stable particles

abstract:
  Luescher's finite size mass shift formula in a periodic finite volume,
involving forward scattering amplitudes in the infinite volume, is revisited
for the two stable distinguishable particle system. The generalized mass shift
formulae for the boson and fermion are derived in the boson-boson and
fermion-boson systems, respectively. The nucleon mass shift formula is given in
the nucleon-pion system and the relation to the computation within chiral
perturbation theory is discussed.


title:
Updated tests of scaling and universality for the spin-spin correlations
  in the 2D and 3D spin-S Ising models using high-temperature expansions

abstract:
  We have extended, from order 12 through order 25, the high-temperature series
expansions (in zero magnetic field) for the spin-spin correlations of the
spin-S Ising models on the square, simple-cubic and body-centered-cubic
lattices. On the basis of this large set of data, we confirm accurately the
validity of the scaling and universality hypotheses by resuming several tests
which involve the correlation function, its moments and the exponential or the
second-moment correlation-lengths.


title:
Static quark anti-quark free energy and the running coupling at finite
  temperature

abstract:
  We analyze the free energy of a static quark anti-quark pair in quenched QCD
at short and large distances. From this we deduce running couplings, g^2(r,T),
and determine the length scale that separates at high temperature the short
distance perturbative regime from the large distance non-perturbative regime in
the QCD plasma phase. Ambiguities in the definition of a coupling beyond the
perturbative regime are discussed in their relation to phenomenological
considerations on heavy quark bound states in the quark gluon plasma. Our
analysis suggests that it is more appropriate to characterize the
non-perturbative properties of the QCD plasma phase close to T_c in terms
remnants of the confinement part of the QCD force rather than a strong
Coulombic force.


title: Continuum limit of the spectrum of the hadronic string

abstract:
  We look at the continuum limit of the two universal predictions of the
hadronic string theory namely the Luescher term and the energy difference
between successive energy states in three dimensional SU(2) lattice gauge
theory using Wilson loops and Polyakov loop correlators. We also compare our
simulation data with the theoretical predictions in hep-th/0406205.


title: Heavy $qq$ interaction at finite temperature

abstract:
  The first lattice QCD numerical study of heavy quark-quark potentials at
finite temperature is reported. Using the quenched approximation, we evaluate
the color anti-symmetric and symmetric potentials.


title: Twisted mass quarks and the phase structure of lattice QCD

abstract:
  The phase structure of zero temperature twisted mass lattice QCD is
investigated. We find strong metastabilities in the plaquette observable when
the untwisted quark mass assumes positive or negative values. We provide
interpretations of this phenomenon in terms of chiral symmetry breaking and the
effective potential model of Sharpe and Singleton.


title:
Study of CP(N-1) \theta-Vacua by Cluster-Simulation of SU(N) Quantum
  Spin Ladders

abstract:
  D-theory provides an alternative lattice regularization of the (1+1)-d
CP(N-1) quantum field theory. In this formulation the continuous classical
CP(N-1) fields emerge from the dimensional reduction of discrete SU(N) quantum
spins. In analogy to Haldane's conjecture, ladders consisting of an even number
of transversely coupled spin chains lead to a CP(N-1) model with vacuum angle
\theta = 0, while an odd number of chains yields \theta = \pi. In contrast to
Wilson's formulation of lattice field theory, in D-theory no sign problem
arises at \theta = \pi, and an efficient cluster algorithm is used to
investigate the \theta-vacuum effects. At \theta = \pi there is a first order
phase transition with spontaneous breaking of charge conjugation symmetry for
CP(N-1) models with N>2.


title:
Some new results on an old controversy: is perturbation theory the
  correct asymptotic expansion in nonabelian models?

abstract:
  Several years ago it was found that perturbation theory for two-dimensional
O(N) models depends on boundary conditions even after the infinite volume limit
has been taken termwise, provided $N>2$. There ensued a discussion whether the
boundary conditions introduced to show this phenomenon were somehow anomalous
and there was a class of `reasonable' boundary conditions not suffering from
this ambiguity. Here we present the results of some computations that may be
interpreted as giving some support for the correctness of perturbation theory
with conventional boundary conditions; however the fundamental underlying
question of the correctness of perturbation theory in these models and in
particular the perturbative $\beta$ function remain challenging problems of
mathematical physics.


title: First Study for the Pentaquark Potential in SU(3) Lattice QCD

abstract:
  The static penta-quark (5Q) potential $V_{\rm 5Q}$ is studied in SU(3)
lattice QCD with $16^3\times 32$ and $\beta$=6.0 at the quenched level. From
the 5Q Wilson loop, $V_{\rm 5Q}$ is calculated in a gauge-invariant manner,
with the smearing method to enhance the ground-state component. $V_{\rm 5Q}$ is
well described by the OGE plus multi-Y Ansatz: a sum of the OGE Coulomb term
and the multi-Y-type linear term proportional to the minimal total length of
the flux-tube linking the five quarks. Comparing with ${\rm Q \bar Q}$ and 3Q
potentials, we find a universality of the string tension, $\sigma_{\rm Q \bar
Q} \simeq \sigma_{\rm 3Q} \simeq \sigma_{\rm 5Q}$, and the OGE result for
Coulomb coefficients.


title: Chirally improving Wilson fermions II. Four-quark operators

abstract:
  In this paper we discuss how the peculiar properties of twisted lattice QCD
at maximal twist can be employed to set up a consistent computational scheme in
which, despite the explicit breaking of chiral symmetry induced by the presence
of the Wilson and mass terms in the action, it is possible to completely bypass
the problem of wrong chirality and parity mixings in the computation of the
CP-conserving matrix elements of the $\Delta S=1,2$ effective weak Hamiltonian
and at the same time have a positive determinant for non-degenerate quarks as
well as full O($a$) improvement in on-shell quantities with no need of
improving the lattice action and the operators.


title: Topology and Staggered Fermion Action Improvement

abstract:
  It is conventional wisdom that staggered fermions do not feel gauge field
topology. However, the response of staggered fermion eigenmodes to the topology
of the gauge field can depend quite sensitively on the way in which the
staggered fermion action is improved. We study this issue using a variety of
improved staggered quark actions. We observe that the separation between the
``would be'' zero modes and the non-chiral modes increases with the level of
improvement. This enables the ``zero modes'' to be identified unambiguously.
The distribution of the remaining non-chiral modes is compared with the
predictions of Random Matrix Theory. Satisfactory agreement is obtained.


title: BK from the lattice with Wilson quarks

abstract:
  We report our results for the bag-parameter BK obtained from the quenched
simulations on the lattice with Wilson fermions at three values of the lattice
spacing. We implemented the method by which no subtraction of the mixing with
other four-fermion dS=2 operators is needed. Our final result, in terms of the
renormalisation group invariant bag-parameter, is BK = 0.96 +/- 0.10.


title: The static tetraquark and pentaquark potentials

abstract:
  We evaluate the static $qq\bar{q}\bar{q}$ and $qqqq\bar{q}$ potentials in the
quenched theory at $\beta=5.8$ and $\beta=6.0$ on a lattice of size $16^3\times
32$. We compare the static potentials to the sum of two meson potentials for
the tetraquark system and to the sum of the baryonic and mesonic potentials for
the pentaquark state, as well as, with the confining potential obtained in the
strong coupling expansion.


title: On the phase structure of twisted mass lattice QCD

abstract:
  The introduction of a chirally twisted mass term has been proposed as an
attractive approach to O(a) improvement of Quantum Chromodynamics with Wilson
fermions on a lattice. For numerical simulation projects it is important to
know the phase structure of the theory in the region of small quark masses. We
study this question in the framework of chiral perturbation theory.
Generalizing the analysis of Sharpe and Singleton we find extensions of normal
and Aoki phase scenarios and a possible new phase with spontaneous breakdown of
chiral symmetry to a discrete $Z_2$.


title:
A strategy to study the role of the charm quark in explaining the
  Delta{I}=1/2 rule

abstract:
  We present a strategy designed to separate several possible origins of the
well-known enhancement of the Delta{I}=1/2 amplitude in non-leptonic kaon
decays. In particular, we seek to disentangle the contribution of physics at
the typical QCD scale (soft-gluon exchange) from the effects at the scale of
the charm quark mass. This is achieved by considering QCD with an unphysically
light charm quark, so that the theory possesses an approximate SU(4)_L x
SU(4)_R chiral symmetry. By computing the relevant operator matrix elements and
monitoring their values as the charm quark mass departs from the
SU(4)-symmetric situation, the role of the charm quark can be assessed. We
study the influence of the charm quark mass in Chiral Perturbation Theory.
First results from lattice simulations in the SU(4)-symmetric limit are also
discussed.


title: Nucleon Properties at Finite Volume: the Epsilon Prime Regime

abstract:
  We study the properties of the nucleon in highly asymmetric volumes where the
spatial dimensions are small but the time dimension is large in comparison to
the inverse pion mass. To facilitate power-counting at the level of Feynman
diagrams, we introduce $\epsilon^\prime$-power-counting which is a special case
of Leutwyler's $\delta$-power-counting. Pion zero-modes enter the
$\epsilon^\prime$-counting perturbatively, in contrast to both the $\epsilon$-
and $\delta$-power-countings, since $m_q < q\bar{q}> V$ remains large. However,
these modes are enhanced over those with non-zero momenta and enter at lower
orders in the $\epsilon^\prime$-expansion than they would in large volume
chiral perturbation theory. We discuss an application of
$\epsilon^\prime$-counting by determining the nucleon mass, magnetic moment and
axial matrix element at the first nontrivial order in the
$\epsilon^\prime$-expansion.


title: A nucleon in a tiny box

abstract:
  We use Chiral Perturbation Theory to compute the nucleon mass-shift due to
finite volume and temperature effects. Our results are valid up to
next-to-leading order in the "\eps-regime" (mL ~ m\beta << 1) as well as in the
"p-regime" (mL ~ m\beta >> 1). Based on the two leading orders, we discuss the
convergence of the expansion as a function of the lattice size and quark
masses. This result can be used to extrapolate lattice results obtained from
lattice sizes smaller than the pion cloud, avoiding the numerical simulation of
physics under theoretical control. An extraction of the low-energy coefficient
c_3 of the chiral Lagrangean from lattice simulations at small volumes and a
``magic'' ratio \beta=1.22262 L might be possible.


title: A no-go theorem for the Majorana fermion on a lattice

abstract:
  A variant of the Nielsen--Ninomiya no-go theorem is formulated. This theorem
states that, under several assumptions, it is impossible to write down a
doubler-free Euclidean lattice action of a single Majorana fermion in $8k$ and
$8k+1$ dimensions.


title:
Y-type Flux-Tube Formation and Gluonic Excitations in Baryons: From QCD
  to Quark Model

abstract:
  Using SU(3) lattice QCD, we perform the first systematic study for the
ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st
excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, {\it i.e.}, the energies of
the ground state and the 1st excited state of the gluon field in the presence
of the static three quarks. From the accurate and thorough calculation for more
than 300 different patterns of 3Q systems, the static ground-state 3Q potential
$V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus
Y-type linear potential, {\it i.e.}, Y-Ansatz, within 1%-level deviation. As a
clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on
the lattice in maximally-Abelian projected QCD. For more than 100 patterns of
3Q systems, we calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm
e.s.}$ in quenched lattice QCD, and find the gluonic excitation energy $\Delta
E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ to be about 1
GeV. This large gluonic-excitation energy is conjectured to ensure the success
of the quark model for the low-lying hadrons even without gluonic excitations.


title:
Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t
  Hooft Picture for Color Confinement

abstract:
  We study the Nambu-'t Hooft picture for color confinement in terms of the
abelianization of QCD and monopole condensation in the maximally abelian (MA)
gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon
amplitude is strongly suppressed, and then the off-diagonal gluon phase shows
strong randomness, which leads to rapid reduction of the off-diagonal gluon
correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian
Landau gauge, the Euclidean gluon propagator indicates a large effective mass
of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the
intermediate distance as $0.2{\rm fm} \le r \le 0.8{\rm fm}$. Due to the
infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized
like nonabelian Higgs theories in the MA gauge. We investigate the
inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and
find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared
region, which indicates the dual Higgs mechanism by monopole condensation. We
define the ``gluonic Higgs scalar field'' providing the MA projection, and find
the correspondence between its hedgehog singularity and the monopole location
in lattice QCD.


title:
Gluonic Higgs Scalar, Abelianization and Monopoles in QCD -- Similarity
  and Difference between QCD in the MA Gauge and the NAH Theory

abstract:
  We study the similarity and the difference between QCD in the maximally
abelian (MA) gauge and the nonabelian Higgs (NAH) theory by introducing the
``gluonic Higgs scalar field'' $\vec \phi(x)$ corresponding to the
``color-direction'' of the nonabelian gauge connection. The infrared-relevant
gluonic mode in QCD can be extracted by the projection along the
color-direction $\vec \phi(x)$ like the NAH theory. This projection is
manifestly gauge-invariant, and is mathematically equivalent to the ordinary MA
projection. Since $\vec \phi(x)$ obeys the adjoint gauge transformation and is
diagonalized in the MA gauge, $\vec \phi(x)$ behaves as the Higgs scalar in the
NAH theory, and its hedgehog singularity provides the magnetic monopole in the
MA gauge like the NAH theory. We observe this direct correspondence between the
monopole appearing in the MA gauge and the hedgehog singularity of $\vec
\phi(x)$ in lattice QCD, when the gluon field is continuous as in the SU($N_c$)
Landau gauge. In spite of several similarities, QCD in the MA gauge largely
differs from the NAH theory in the two points: one is infrared monopole
condensation, and the other is infrared enhancement of the abelian correlation
due to monopole condensation.


title: Study of Quark Confinement in Baryons with Lattice QCD

abstract:
  In SU(3) lattice QCD, we perform the detailed study for the ground-state
three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q
potential $V_{\rm 3Q}^{\rm e.s.}$, i.e., the energies of the ground state and
the 1st excited state of the gluon field in the presence of the static three
quarks. From the accurate calculation for more than 300 different patterns of
3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is
found to be well described by the Coulomb plus Y-type linear potential
(Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type
flux-tube formation is actually observed on the lattice in maximally-Abelian
projected QCD. For about 100 patterns of 3Q systems, we calculate the 1st
excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, and find a large
gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm
e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of
the success of the quark model even without gluonic excitations. We present
also the first study for the penta-quark potential $V_{\rm 5Q}$ in lattice QCD,
and find that $V_{\rm 5Q}$ is well described by the sum of the OGE Coulomb plus
multi-Y type linear potential.


title:
Infrared Abelian Dominance and Dual Higgs Mechanism in Maximally Abelian
  Gauge

abstract:
  We study infrared abelian dominance and the dual Higgs mechanism in the
maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. In
the MA gauge, the off-diagonal gluon phase tends to be random, and the
off-diagonal gluon $A_\mu^\pm$ acquires the effective mass as $M_{\rm off}
\simeq$ 1.2 GeV. From the monopole current in the MA gauge, we extract the dual
gluon field $B_\mu$ and estimate the dual gluon mass as $m_B \simeq $ 0.5 GeV.
The QCD-monopole structure is also investigated in terms of off-diagonal
gluons. From the lattice QCD in the MA gauge, the dual Ginzburg-Landau (DGL)
theory can be constructed as a realistic infrared effective theory based on
QCD.


title:
Strong randomness of off-diagonal gluon phases and off-diagonal gluon
  mass in the maximally abelian gauge in QCD

abstract:
  We study abelianization of QCD in the maximally abelian (MA) gauge. In the MA
gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the
off-diagonal gluon phase shows strong randomness, which leads to a large
off-diagonal gluon mass. Using lattice QCD, we find a large effective
off-diagonal gluon mass in the MA gauge: $M_{\rm off} \simeq 1.2 {\rm GeV}$ in
SU(2) QCD, $M_{\rm off} \simeq 1.1 {\rm GeV}$ in SU(3) QCD. Due to the large
off-diagonal gluon mass in the MA gauge, infrared QCD is well abelianized like
nonabelian Higgs theories. We investigate the inter-monopole potential and the
dual gluon field $B_\mu$ in the MA gauge, and find longitudinal magnetic
screening with $m_B \simeq$ 0.5 GeV in the infrared region, which indicates the
dual Higgs mechanism by monopole condensation. We propose a gauge invariant
description of the MA projection by introducing the ``gluonic Higgs scalar
field''.


title: Quark Confinement Physics from Quantum Chromodynamics

abstract:
  We show the construction of the dual superconducting theory for the
confinement mechanism from QCD in the maximally abelian (MA) gauge using the
lattice QCD Monte Carlo simulation. We find that essence of infrared abelian
dominance is naturally understood with the off-diagonal gluon mass $m_{\rm off}
\simeq 1.2 {\rm GeV}$ induced by the MA gauge fixing. In the MA gauge, the
off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon
phase tends to be random. As the mathematical origin of abelian dominance for
confinement, we demonstrate that the strong randomness of the off-diagonal
gluon phase leads to abelian dominance for the string tension. In the MA gauge,
there appears the macroscopic network of the monopole world-line covering the
whole system. We investigate the monopole-current system in the MA gauge by
analyzing the dual gluon field $B_\mu$. We evaluate the dual gluon mass as $m_B
= 0.4 \sim$ 0.5GeV in the infrared region, which is the lattice-QCD evidence of
the dual Higgs mechanism by monopole condensation. Owing to infrared abelian
dominance and infrared monopole condensation, QCD in the MA gauge is
describable with the dual Ginzburg-Landau theory.


title: Dense baryonic matter in strong coupling lattice gauge theory

abstract:
  We investigate the strong coupling limit of lattice QCD in the Hamiltonian
formulation for systems with non-zero baryon density. In leading order the
Hamiltonian looks like an antiferromagnet that is invariant under global
U(N_f)xU(N_f) and local SU(N_c). Physically it describes meson dynamics with a
fixed background of baryon density. We study this Hamiltonian with several
baryon number distributions, and concentrate on the global symmetries of the
ground state and on the properties of low lying excitations. In particular, for
uniform non-zero baryon density we write the partition function as a path
integral that is tractable in the limit of large N_c. We find that the ground
state spontaneously breaks chiral symmetry as well as discrete lattice
rotations in a way that depends on N_f and the density. The low energy
excitations include type I and type II Goldstone bosons. The energies of the
latter are of order 1/N_c, and are quadratic in momentum. Bosons of either type
can develop anisotropic dispersion relations.


title:
Deconfinement in Yang-Mills: a conjecture for a general gauge Lie group
  G

abstract:
  Svetitsky and Yaffe have argued that -- if the deconfinement phase transition
of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order --
it should be in the universality class of a d-dimensional scalar model
symmetric under the center C(G) of G. These arguments have been investigated
numerically only considering Yang-Mills theory with gauge symmetry in the
G=SU(N) branch, where C(G)=Z(N). The symplectic groups Sp(N) provide another
extension of SU(2)=Sp(1) to general N and they all have the same center Z(2).
Hence, in contrast to the SU(N) case, Sp(N) Yang-Mills theory allows to study
the relevance of the group size on the order of the deconfinement phase
transition keeping the available universality class fixed. Using lattice
simulations, we present numerical results for the deconfinement phase
transition in Sp(2) and Sp(3) Yang-Mills theories both in (2+1)d and (3+1)d. We
then make a conjecture on the order of the deconfinement phase transition in
Yang-Mills theories with general Lie groups SU(N), SO(N), Sp(N) and with
exceptional groups G(2), F(4), E(6), E(7), E(8). Numerical results for G(2)
Yang-Mills theory at finite temperature in (3+1)d are also presented.


title: Quark Confinement Physics from Lattice QCD

abstract:
  We study quark confinement physics using lattice QCD. In the maximally
abelian (MA) gauge, the off-diagonal gluon amplitude is strongly suppressed,
and then the off-diagonal gluon phase shows strong randomness, which leads to a
large effective off-diagonal gluon mass, M_off=1.2GeV. Due to the large
off-diagonal gluon mass in the MA gauge, low-energy QCD is abelianized like
nonabelian Higgs theories. In the MA gauge, there appears a macroscopic network
of the monopole world-line covering the whole system. We extract and analyze
the dual gluon field B_mu from the monopole-current system in the MA gauge, and
evaluate the dual gluon mass as m_B = 0.4-0.5GeV in the infrared region, which
is a lattice-QCD evidence of the dual Higgs mechanism by monopole condensation.
Even without explicit use of gauge fixing, we can define the maximal abelian
projection by introducing a ``gluonic Higgs field'' phi(x), whose hedgehog
singularities lead to monopoles. From infrared abelian dominance and infrared
monopole condensation, infrared QCD is describable with the dual
Ginzburg-Landau theory. In relation to the color-flux-tube picture for baryons,
we study the three-quark (3Q) ground-state potential V_3Q in SU(3) lattice QCD
at the quenched level, with the smearing technique for enhancement of the
ground-state component. With accuracy better than a few %, V_3Q is well
described by a sum of the two-body Coulomb part and the three-body linear
confinement part sigma_3Q L_min, where L_min denotes the minimal value of the
total length of the color flux tube linking the three quarks. Comparing with
the Q-barQ potential, we find a universal feature of the string tension and the
OGE result for the Coulomb coefficient.


title: Mobility edge in lattice QCD

abstract:
  We determine the location $\lambda_c$ of the mobility edge in the spectrum of
the hermitian Wilson operator on quenched ensembles. We confirm a theoretical
picture of localization proposed for the Aoki phase diagram. When $\lambda_c>0$
we also determine some key properties of the localized eigenmodes with
eigenvalues $|\lambda|<\lambda_c$. Our results lead to simple tests for the
validity of simulations with overlap and domain-wall fermions.


title: Remnant Symmetry and the Confinement Phase in Coulomb Gauge

abstract:
  We report on connections between the confining color Coulomb potential,
center vortices, and the unbroken realization of remnant gauge symmetry in
Coulomb gauge.


title: Pion mass splitting and phase structure in Twisted Mass QCD

abstract:
  In the framework of Wilson Chiral Perturbation Theory, we study the effect
induced by a twisted Wilson term, as it appears in Twisted Mass QCD (with 2
degenerate quarks). In particular we consider the vacuum orientation and the
pion masses. The computations are done to NLO both in the mass and in the
lattice spacing (i.e. to O(a^2)). There are no restrictions on the relative
size of lattice artifacts with respect to the physical mass, thus allowing, in
principle, to bridge between the physical regime and the unphysical one, where
lattice artifacts tend to dominate. The inclusion of O(a^2) lattice artifacts
can account for the splitting of degeneracy of the three pion masses. Moreover
O(a^2) terms are necessary to model non trivial behaviors of the vacuum
orientation such as possible Aoki phases. It turns out that these last two
phenomena are determined by the same constant.


title:
Large logarithmic rescaling of the scalar condensate: new lattice
  evidences

abstract:
  Using two different methods, we have determined the rescaling of the scalar
condensate $Z\equiv Z_\phi$ near the critical line of a 4D Ising model. Our
lattice data, in agreement with previous numerical indications, support the
behavior $Z_\phi\sim \ln ({\Lambda})$, $\Lambda$ being the ultraviolet cutoff.
This result is predicted in an alternative description of symmetry breaking
where there are no upper bounds on the Higgs boson mass from `triviality'.


title: The phase diagram of twisted mass lattice QCD

abstract:
  We use the effective chiral Lagrangian to analyze the phase diagram of
two-flavor twisted mass lattice QCD as a function of the normal and twisted
masses, generalizing previous work for the untwisted theory. We first determine
the chiral Lagrangian including discretization effects up to next-to-leading
order (NLO) in a combined expansion in which m_\pi^2/(4\pi f_\pi)^2 ~ a \Lambda
(a being the lattice spacing, and \Lambda = \Lambda_{QCD}). We then focus on
the region where m_\pi^2/(4\pi f_\pi)^2 ~ (a \Lambda)^2, in which case
competition between leading and NLO terms can lead to phase transitions. As for
untwisted Wilson fermions, we find two possible phase diagrams, depending on
the sign of a coefficient in the chiral Lagrangian. For one sign, there is an
Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is
washed out into a crossover if the twisted mass is non-vanishing. For the other
sign, there is a first order transition for pure Wilson fermions, and we find
that this transition extends into the twisted mass plane, ending with two
symmetrical second order points at which the mass of the neutral pion vanishes.
We provide graphs of the condensate and pion masses for both scenarios, and
note a simple mathematical relation between them. These results may be of
importance to numerical simulations.


title: Random Lattice QCD and chiral effective theories

abstract:
  Resent developments in the Random Matrix and Random Lattice Theories give a
possibility to find low-energy theorems for many physical models in the
Born-Infeld form. In our approach that based on the Random Lattice
regularization of QCD we try to used the similar ideas in the low-energy baryon
physics for finding of the low-energy theory for the chiral fields in the
strong-coupling regime.


title:
The finite temperature transition for 2-flavour lattice QCD at finite
  isospin density

abstract:
  We simulate 2-flavour lattice QCD at finite isospin chemical potential mu_I,
for temperatures close to the finite temperature transition from hadronic
matter to a quark-gluon plasma. The mu_I dependence of the transition coupling
is observed and used to estimate the decrease in the transition temperature
with increasing mu_I. These simulations are performed on an 8^3 times 4 lattice
at 3 different quark masses. Our estimate of the magnitude of the fluctuations
of the phase of the fermion determinant at small quark-number chemical
potential mu, suggest that the position of the small mu and small mu_I
transitions should be the same for mu_I=2mu, and we argue that the nature of
these transitions should be the same. For all mu_I < m_pi the smoothness of
these transitions and the values of the Binder cumulant B_4, indicate that
these transitions are mere crossovers, and show no sign of the expected
critical endpoint. For mu_I > m_pi and a small isospin (I_3) breaking term
lambda, we do find evidence of a critical endpoint which would indicate that,
for lambda=0, there is a tricritical point on the phase boundary where the pion
condensate evaporates, where this phase transition changes from second to first
order.


title:
Light pseudoscalar decay constants, quark masses, and low energy
  constants from three-flavor lattice QCD

abstract:
  As part of our program of lattice simulations of three flavor QCD with
improved staggered quarks, we have calculated pseudoscalar meson masses and
decay constants for a range of valence quark masses and sea quark masses on
lattices with lattice spacings of about 0.125 fm and 0.09 fm. We fit the
lattice data to forms computed with staggered chiral perturbation theory. Our
results provide a sensitive test of the lattice simulations, and especially of
the chiral behavior, including the effects of chiral logarithms. We find:
f_\pi=129.5(0.9)(3.5)MeV, f_K=156.6(1.0)(3.6)MeV, and f_K/f_\pi=1.210(4)(13),
where the errors are statistical and systematic. Following a recent paper by
Marciano, our value of f_K/f_\pi implies |V_{us}|=0.2219(26). Further, we
obtain m_u/m_d= 0.43(0)(1)(8), where the errors are from statistics, simulation
systematics, and electromagnetic effects, respectively. The data can also be
used to determine several of the constants of the low energy effective
Lagrangian: in particular we find 2L_8-L_5=-0.2(1)(2) 10^{-3} at chiral scale
m_\eta. This provides an alternative (though not independent) way of estimating
m_u; 2L_8-L_5 is far outside the range that would allow m_u=0. Results for
m_s^\msbar, \hat m^\msbar, and m_s/\hat m can be obtained from the same lattice
data and chiral fits, and have been presented previously in joint work with the
HPQCD and UKQCD collaborations. Using the perturbative mass renormalization
reported in that work, we obtain m_u^\msbar=1.7(0)(1)(2)(2)MeV and
m_d^\msbar=3.9(0)(1)(4)(2)MeV at scale 2 GeV, with errors from statistics,
simulation, perturbation theory, and electromagnetic effects, respectively.


title: QED in 2+1 Dimensions with Fermi and Gap Anisotropies

abstract:
  QED in 2+1 dimensions has long been studied as a model field theory which
exhibits both asymptotic freedom and non-trivial IR behaviour. There is also a
trend towards viewing it as a candidate low energy effective theory for the
pseudogap phase of high temperature superconductors. One feature of these
theories is their lack of isotropy in the x and y directions (a common feature
of Dirac theories in condensed matter systems). A model motivated by this work
is outlined, and tentative evidence presented for chiral symmetry restoration
as the relative anisotropy is increased.


title: Decuplet Baryon Masses in Partially Quenched Chiral Perturbation Theory

abstract:
  The masses of the spin-3/2 baryons are calculated to next-to-next-to-leading
order in heavy baryon chiral perturbation theory and partially quenched heavy
baryon chiral perturbation theory. The calculation is performed for three light
flavors in the isospin limit. These results are necessary for extrapolating QCD
and partially quenched QCD lattice calculations of the decuplet baryon masses.


title:
Perturbative determination of mass dependent renormalization and
  improvement coefficients for the heavy-light vector and axial-vector currents
  with relativistic heavy and domain-wall light quarks

abstract:
  We determine the mass dependent renormalization as well as improvement
coefficients for the heavy-light vector and axial-vector currents consisting of
the relativistic heavy and the domain-wall light quarks through the standard
matching procedure. The calculation is carried out perturbatively at the one
loop level to remove the systematic error of $O(\alpha_s (am_Q)^n a\p)$ as well
as $O(\alpha_s (am_Q)^n)$ ($n\ge$0), where $\p$ is a typical momentum scale in
the heavy-light system. We point out that renormalization and improvement
coefficients of the heavy-light vector current agree with those of the
axial-vector current, thanks to the exact chiral symmetry for the light quark.
The results obtained with three different gauge actions, plaquette, Iwasaki and
DBW2, are presented as a function of heavy quark mass and domain-wall height.


title: Center Vortices and the Gribov Horizon

abstract:
  We show how the infinite color-Coulomb energy of color-charged states is
related to enhanced density of near-zero modes of the Faddeev-Popov operator,
and calculate this density numerically for both pure Yang-Mills and gauge-Higgs
systems at zero temperature, and for pure gauge theory in the deconfined phase.
We find that the enhancement of the eigenvalue density is tied to the presence
of percolating center vortex configurations, and that this property disappears
when center vortices are either removed from the lattice configurations, or
cease to percolate. We further demonstrate that thin center vortices have a
special geometrical status in gauge-field configuration space: Thin vortices
are located at conical or wedge singularities on the Gribov horizon. We show
that the Gribov region is itself a convex manifold in lattice configuration
space. The Coulomb gauge condition also has a special status; it is shown to be
an attractive fixed point of a more general gauge condition, interpolating
between the Coulomb and Landau gauges.


title: The status of pentaquark spectroscopy on the lattice

abstract:
  The present work is a summary of the status of lattice pentaquark
calculations. After a pedagogic introduction to the basics of lattice hadron
spectroscopy we give a critical comparison of results presently available in
the literature. Special emphasis is put on presenting some of the possible
pitfalls of these calculations. In particular we discuss at length the choice
of the hadronic operators and the separation of genuine five-quark states from
meson-baryon scattering states.


title: The Lattice NJL Model at Non-zero Baryon and Isospin Densities

abstract:
  We present initial results of a numerical investigation of the chiral
symmetry restoring transition in the (3+1)-dimensional Nambu -- Jona-Lasinio
model with both non-zero baryon chemical potential (mu_B) and isospin chemical
potential (mu_I). With non-zero isospin chemical potential, the model suffers
from a sign problem. We proceed in two ways: (i) We perform ``partially
quenched'' simulations in which mu_I is made non-zero only during the
measurement of chiral observables; (ii) We perform full simulations with
imaginary isospin chemical potential with the aim to analytically continue
results to real mu_I.


title: Applying chiral perturbation to twisted mass Lattice QCD

abstract:
  We have explored twisted mass LQCD (tmLQCD) analytically using chiral
perturbation theory, including discretization effects up to O(a^2), and working
at next-to-leading (NLO) order in the chiral expansion. In particular we have
studied the vacuum structure, and calculated the dependence of pion masses and
decay constants on the quark mass, twisting angle and lattice spacing. We give
explicit examples for quantities that both are and are not automatically
improved at maximal twisting.


title:
The low-lying mass spectrum of the N=1 SU(2) SUSY Yang-Mills theory with
  Wilson fermions

abstract:
  We analyze the low energy spectrum of bound states of the N=1 SU(2) SUSY
Yang-Mills Theory (SYM). This work continues the investigation of the
non-perturbative properties of SYM by Monte Carlo simulations in the Wilson
discretization with dynamical gluinos. The dynamics of the gluinos is included
by the Two-Step Multi-Bosonic Algorithm (TSMB) for dynamical fermions. A new
set of configurations has been generated on a 16^3x32 lattice at beta=2.3 and
kappa=0.194. The analysis also includes sets of configurations previously
generated on a smaller (12^3x24) lattice at kappa=0.1925, 0.194 and 0.1955.
Guided by predictions from low energy Lagrangians, we consider spin-1/2, scalar
and pseudoscalar particles. The spectrum of SYM is a challenging subject of
investigation because of the extremely noisy correlators. In particular,
meson-like correlators contain disconnected contributions. The larger
time-extention of the 16^3x32 lattice allows to observe two-state signals in
the effective mass. Finite-volume effects are monitored by comparing results
from the two lattice sizes.


title:
Scalar meson in dynamical and partially quenched two-flavor QCD: lattice
  results and chiral loops

abstract:
  This is an exploratory study of the lightest non-singlet scalar $q\bar q$
state on the lattice with two dynamical quarks. Domain Wall fermions are used
for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice
spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the
exponential time-dependence of the dynamical correlators with $m_{val}=m_{sea}$
and N_f=2. Since this statistical error-bar from dynamical correlators is
rather large, we analyze also the partially quenched lattice correlators with
$m_{val}$ not equal $m_{sea}$. They are positive for $m_{val}>=m_{sea}$ and
negative for $m_{val}<m_{sea}$. In order to understand this striking effect of
partial quenching, we derive the scalar correlator within the Partially
Quenched ChPT and find it describes lattice correlators well. The leading
unphysical contribution in Partially Quenched ChPT comes from the exchange of
the two pseudoscalar fields and is also positive for $m_{val}>=m_{sea}$ and
negative for $m_{val}<m_{sea}$ at large t. After the subtraction of this
unphysical contribution from the partially quenched lattice correlators, the
correlators are positive and exponentially falling. The resulting scalar meson
mass 1.51(19) GeV from the partially quenched correlators is consistent with
the dynamical result and has appreciably smaller error-bar.


title: Detecting chiral singularities in lattice QCD at strong coupling

abstract:
  We study the difficulties associated with detecting chiral singularities in
strongly coupled lattice QCD at fixed nonzero tempearture. We show that the
behavior of the chiral condensate, the pion mass and the pion decay constant,
for small masses, are all consistent with the predictions of Chiral
Perturbation Theory. However, the values of the quark masses that we need to
demonstrate this are much smaller than those being used in dynamical QCD
simulations.


title: Hadron Properties with FLIC Fermions

abstract:
  The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of
nonperturbative O(a)-improvement in lattice fermion actions offering near
continuum results at finite lattice spacing. It provides computationally
inexpensive access to the light quark mass regime of QCD where chiral
nonanalytic behaviour associated with Goldstone bosons is revealed. The
motivation and formulation of FLIC fermions, its excellent scaling properties
and its low-lying hadron mass phenomenology are presented.


title: Monopole gas in three dimensional SU(2) gluodynamics

abstract:
  We study properties of the Abelian monopoles in the Maximal Abelian
projection of the three dimensional pure SU(2) gauge model. We match the
lattice monopole dynamics with the continuum Coulomb gas model using a method
of blocking from continuum. We obtain the Debye screening length and the
monopole density in continuum using numerical results for the lattice density
of the (squared) monopole charges and for the monopole action. The monopoles
treated within our blocking method provide about 75% contribution to the
non--Abelian Debye screening length. We also find that monopoles form a Coulomb
plasma which is not dilute.


title:
The finite temperature transition for 3-flavour lattice QCD at finite
  isospin density

abstract:
  We simulate 3-flavour lattice QCD with a small chemical potential $\mu_I$ for
isospin, at temperatures close to the finite temperature transition. Using
quark masses just above the critical mass for zero chemical potential, we
determine the position of the transition from hadronic matter to a quark-gluon
plasma as a function of $\mu_I$. We see evidence for a critical endpoint where
the transition changes from a crossover to a first-order transition as $\mu_I$
is increased. We argue that QCD at finite $\mu_I$ and QCD at finite
quark-numberchemical potential $\mu$ should behave similarly in this region.


title:
The Polyakov Loop and its Relation to Static Quark Potentials and Free
  Energies

abstract:
  It appears well accepted in the literature that the correlator of Polyakov
loops in a finite temperature system decays with the "average" free energy of
the static quark-antiquark system, and can be decomposed into singlet and
adjoint (or octet for QCD) contributions. By fixing a gauge respecting the
transfer matrix, attempts have been made to extract those contributions
separately. In this paper we point out that the "average" and "adjoint"
channels of Polyakov loop correlators are misconceptions. We show analytically
that all channels receive contributions from singlet states only, and give a
corrected definition of the singlet free energy. We verify this finding by
simulations of the 3d SU(2) pure gauge theory in the zero temperature limit,
which allows to cleanly extract the ground state exponents and the non-trivial
matrix elements. The latter account for the difference between the channels
observed in previous simulations.


title: Numerical Study of Lattice Landau Gauge QCD and the Gribov Copy Problem

abstract:
  The infrared properties of lattice Landau gauge QCD of SU(3) are studied by
measuring gluon propagator, ghost propagator, QCD running coupling and
Kugo-Ojima parameter of $\beta=6.0, 16^4,24^4,32^4$ and $\beta=6.4, 32^4, 48^4,
56^4$ lattices. By the larger lattice measurements, we observe that the
runnning coupling measured by the product of the gluon dressing function and
the ghost dressing function squared rescaled to the perturbative QCD results
near the highest lattice momentum has the maximum of about 2.2 at around
$q=0.5$ GeV/c, and behaves either approaching constant or even decreasing as
$q$ approaches zero. The magnitude of the Kugo-Ojima parameter is getting
larger but staying around -0.83 in contrast to the expected value -1 in the
continuum theory. We observe, however, there is an exceptional sample which has
larger magnitude of the Kugo-Ojima parameter and stronger infrared singularity
of the ghost propagator. The reflection positivity of the 1-d Fourier transform
of the gluon propagator of the exceptional sample is manifestly violated.
  Gribov noise problem was studied by performing the fundamental modular gauge
(FMG) fixing with use of the parallel tempering method of $\beta=2.2, 16^4$
SU(2) configurations. Findings are that the gluon propagator almost does not
suffer noises, but the Kugo-Ojima parameter and the ghost propagator in the FMG
becomes $\sim 5$% less in the infrared region than those suffering noises. It
is expected that these qualitative aspects seen in SU(2) will reflect in the
infrared properties of SU(3) QCD as well.


title:
A numerical study of a confined $Q\bar{Q}$ system in compact U(1)
  lattice gauge theory in 4D

abstract:
  We present a numerical study about the confining regime of compact U(1)
lattice gauge theory in 4D. To address the problem, we exploit the duality
properties of the theory. The main features of this method are presented, and
its possible advantages and limits with respect to alternative techniques are
briefly discussed. In Monte Carlo simulations, we focus our attention onto the
case when a pair of static external charges is present. Some results are shown,
concerning different observables which are of interest in order to understand
the confinement mechanism, like the profile of the electric field induced by
the static charges, and the ratios between Polyakov loop correlation functions
at different distances.


title: Simulating lattice QCD at finite temperature and zero quark mass

abstract:
  We simulate lattice QCD with an irrelevant chiral 4-fermion interaction which
allows us to simulate at zero quark mass. This enables us to study the
finite-temperature chiral-symmetry-restoring phase transition for 2 massless
quark flavours, which is believed to be second order. In particular, it enables
us to estimate the critical exponents which characterize the universality class
of this transition. Our earlier simulations on $N_t=4$ and $N_t=6$ lattices
revealed that finite lattice-spacing artifacts on such coarse lattices affect
the nature of the transition. We are now simulating on $N_t=8$ lattices ($12^3
\times 8$, $16^3 \times 8$ and $24^3 \times 8$ lattices) where we expect to
expose the continuum behaviour of this transition.


title: Probing for Instanton Quarks with epsilon-Cooling

abstract:
  We use epsilon-cooling, adjusting at will the order a^2 corrections to the
lattice action, to study the parameter space of instantons in the background of
non-trivial holonomy and to determine the presence and nature of constituents
with fractional topological charge at finite and zero temperature for SU(2). As
an additional tool, zero temperature configurations were generated from those
at finite temperature with well-separated constituents. This is achieved by
"adiabatically" adjusting the anisotropic coupling used to implement finite
temperature on a symmetric lattice. The action and topological charge density,
as well as the Polyakov loop and chiral zero-modes are used to analyse these
configurations. We also show how cooling histories themselves can reveal the
presence of constituents with fractional topological charge. We comment on the
interpretation of recent fermion zero-mode studies for thermalized ensembles at
small temperatures.


title: On the degrees of freedom of lattice electrodynamics

abstract:
  Using Euler's formula for a network of polygons for 2D case (or polyhedra for
3D case), we show that the number of dynamic\textit{\}degrees of freedom of the
electric field equals the number of dynamic degrees of freedom of the magnetic
field for electrodynamics formulated on a lattice. Instrumental to this
identity is the use (at least implicitly) of a dual lattice and of a (spatial)
geometric discretization scheme based on discrete differential forms. As a
by-product, this analysis also unveils a physical interpretation for Euler's
formula and a geometric interpretation for the Hodge decomposition.


title: Improved Measure of Local Chirality

abstract:
  It is popular to probe the structure of the QCD vacuum indirectly by studying
individual fermion eigenmodes, because this provides a natural way to filter
out UV fluctuations. The double-peaking in the distribution of the local chiral
orientation parameter (X) has been offered as evidence, by some, in support of
a particular model of the vacuum. Here we caution that the X-distribution
peaking varies significantly with various versions of the definition of X.
Furthermore, each distribution varies little from that resulting from a random
reshuffling of the left-handed (and independently the right-handed) fields,
which destroys any QCD-induced left-right correlation; that is, the
double-peaking is mostly a phase-space effect. We propose a new universal
definition of the X parameter whose distribution is uniform for randomly
reshuffled fields. Any deviations from uniformity for actual data can then be
directly attributable to QCD-induced dynamics. We find that the familiar double
peak disappears.


title: Vector meson at non-zero baryon density and zero sound

abstract:
  We present simulation results of the (2+1)d four-fermion model with a baryon
chemical potential. We examine temporal correlation functions of the vector
meson, and find evidence of phonon-like behavior characterised by a linear
dispersion relation in the long wavelength limit. We also discuss the
consistency of our numerical results with analytical solutions to the Boltzmann
equation corresponding to zero sound. We argue that our results provide the
first evidence for a collective excitation in a lattice simulation.


title: The order of the chiral transition in N_f=2 QCD

abstract:
  A strategy is developed to investigate the order of the transition using
finite size scaling and its relation to color confinement. An in-depth
numerical investigation has been performed with KS fermions on lattices with
N_t=4 and N_s=12,16,20,24,32 and quark masses am_q ranging from 0.01335 to
0.35. The specific heat and a number of susceptibilities have been measured and
compared with the expectation of an O(4) second order and a first order phase
transition. A second order O(4) is excluded, whilst data are consistent with a
first order.


title: Chiral transition and deconfinement in N_f = 2 QCD

abstract:
  The transition is studied by means of a disorder parameter detecting
condensation of magnetic monopoles in the vacuum. The deconfining transition is
found to coincide with the chiral transition and the susceptibility \rho,
related to the disorder parameter, is consistent with a first order phase
transition.


title:
A scaling study of the step scaling function in SU(3) gauge theory with
  improved gauge actions

abstract:
  We study the scaling behavior of the step scaling function for SU(3) gauge
theory, employing the renormalization-group improved Iwasaki gauge action and
the perturbatively improved L\"uscher-Weisz gauge action. We confirm that the
step scaling functions from the improved gauge actions agree with that
previously obtained from the plaquette action within errors in the continuum
limit at both weak and strong coupling regions. We also investigate how
different choices of boundary counter terms for the improved gauge actions
affect the scaling behavior. In the extrapolation to the continuum limit, we
observe that the cut off dependence becomes moderate for the Iwasaki action, if
a perturbative reduction of scaling violations is applied to the simulation
results. We also measure the low energy scale ratio with the Iwasaki action,
and confirm its universality.


title: On the order of the deconfining transition in N_f=2 QCD

abstract:
  A careful study is made on the lattice of the phase diagram of QCD with two
staggered flavors, to investigate the order of the chiral transition of N_f=2
QCD. The specific heat and the susceptibility of the chiral condensate are
determined for different spatial sizes of the system, and a finite size scaling
analysis provides a determination of the (pseudo)critical indices. The result
is a strong indication that the chiral transition is first order.


title: On the nature and order of the deconfining transition in QCD

abstract:
  The determination of the parameters of the deconfining transition in N_f=2
QCD is discussed, and its relevance to the understanding of the mechanism of
color confinement.


title: Are magnetic monopoles hadrons?

abstract:
  The charges of magnetic monopoles are constrained to a multiple of $2\pi$
times the inverse of the elementary unit electric charge. In the standard
model, quarks have fractional charge, raising the question of whether the basic
magnetic monople unit is a multiple of $2 \pi/e$ or three times that. A simple
lattice construction shows how a magnetic monopole of the lower strength is
possible if it interacts with gluonic fields as well. Such a monopole is thus a
hadron. This is consistent with the construction of magnetic monopoles in grand
unified theories.


title: Three dimensional vacuum domains in four dimensional SU(2) gluodynamics

abstract:
  Performing lattice simulations of the four dimensional SU(2)gluodynamics we
find evidence for existence of three-dimensional domains whose total volume
scales in physical units. Technically, the domains are defined in terms of the
minimal density of negative links in Z(2) projection of gauge fields. The
volume can be viewed also as the minimal volume bound by the center vortices.
We argue that the three-dimensional domains are closely related to confinement.


title:
The Nf=2 residual mass in Perturbative Lattice-HQET for an improved
  determination of the (MS bar) b-quark mass

abstract:
  We determine to order alpha^3 the so-called residual mass in the lattice
regularisation of the Heavy Quark Effective Theory for Nf=2. Our
(gauge-invariant) strategy makes use of Numerical Stochastic Perturbation
Theory to compute the static interquark potential where the above mentioned
mass term appears as an additive contribution. We discuss how the new
coefficient we compute in the expansion of the residual mass can improve the
determination of the (MS bar) mass of the b-quark from lattice simulations of
the Heavy Quark Effective Theory.


title:
Density matrix renormalization group approach to a two-dimensional
  bosonic model

abstract:
  Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional
$\lambda\phi^4$ model to study spontaneous breakdown of discrete $Z_2$ symmetry
numerically. We obtain the critical coupling $(\lambda/\mu^2)_{\rm c}=59.89\pm
0.01$ and the critical exponent $\beta=0.1264\pm 0.0073$, which are consistent
with the Monte Carlo and the exact results, respectively. The results are based
on extrapolation to the continuum limit with lattice sizes $L=250,500$, and
1000. We show that the lattice size L=500 is sufficiently close to the the
limit $L\to\infty$ \cite{Sugihara:2004qr}.


title: Momentum dependence of the N to Delta transition form factors

abstract:
  We present a new method to determine the momentum dependence of the N to
Delta transition form factors and demonstrate its effectiveness in the quenched
theory at $\beta=6.0$ on a $32^3 \times 64$ lattice. We address a number of
technical issues such as the optimal combination of matrix elements and the
simultaneous overconstrained analysis of all lattice vector momenta
contributing to a given momentum transfer squared, $Q^2$.


title:
NLO anomalous dimension of multiplicatively renormalizable four-fermion
  operators in Schroedinger Functional schemes

abstract:
  Renormalization constants for multiplicatively renormalizable parity-odd
four-fermion operators are computed in various different Schroedinger
Functional (SF) schemes and lattice regularizations with Wilson quarks at
one-loop order in perturbation theory. Our results are used in the calculation
of their NLO anomalous dimensions, through matching to continuum schemes. They
also enable a comparison of the two-loop perturbative RG running to the
previously obtained nonperturbative one in the region of small renormalized
coupling.


title: Semileptonic B Decays with Nf=2+1 Dynamical Quarks

abstract:
  Semileptonic, B --> pi l,nu, decays are studied on the MILC dynamical
configurations using NRQCD heavy and Asqtad light quarks. We work with light
valence quark masses ranging between m_s and m_s/8. Preliminary simple linear
chiral extrapolations have been carried out for form factors f_para and f_perp
at fixed E_pi. The chirally extrapolated results for the form factors f_+(q^2)
and f_0(q^2) are then fit to the Becirevic-Kaidalov (BK) ansatz. Preliminary
estimates of the CKM matrix element |V_{ub}| are presented based on the
recently published branching fractions for B exclusive semileptonic decays by
the CLEO collaboration.


title: The Lattice Free Energy with Overlap Fermions: A Two-Loop Result

abstract:
  We calculate the 2-loop partition function of QCD on the lattice, using the
Wilson formulation for gluons and the overlap-Dirac operator for fermions.
Direct by-products of our result are the 2-loop free energy and average
plaquette. Our calculation serves also as a prototype for further higher loop
calculations in the overlap formalism. We present our results as a function of
a free parameter $M_0$ entering the overlap action; the dependence on the
number of colors $N$ and fermionic flavors $N_f$ is shown explicitly.


title: Numerical Study of the Ghost-Ghost-Gluon Vertex on the Lattice

abstract:
  It is well known that, in Landau gauge, the renormalization function of the
ghost-ghost-gluon vertex \widetilde{Z}_1(p^2) is finite and constant, at least
to all orders of perturbation theory. On the other hand, a direct
non-perturbative verification of this result using numerical simulations of
lattice QCD is still missing. Here we present a preliminary numerical study of
the ghost-ghost-gluon vertex and of its corresponding renormalization function
using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained
in 4 dimensions for lattice couplings beta = 2.2, 2.3, 2.4 and lattice sides N
= 4, 8, 16.


title: Temporal correlator in YM^2_3 and reflection-positivity violation

abstract:
  We consider numerical data for the lattice Landau gluon propagator obtained
at very large lattice volumes in three-dimensional pure SU(2) Yang-Mills gauge
theory (YM^2_3). We find that the temporal correlator C(t) shows an oscillatory
pattern and is negative for several values of t. This is an explicit violation
of reflection positivity and can be related to gluon confinement. We also
obtain a good fit for this quantity in the whole time interval using a sum of
Stingl-like propagators.


title:
Confinement and center vortices in Coulomb gauge: analytic and numerical
  results

abstract:
  We review the confinement scenario in Coulomb gauge. We show that when thin
center vortex configurations are gauge transformed to Coulomb gauge, they lie
on the common boundary of the fundamental modular region and the Gribov region.
This unifies elements of the Gribov confinement scenario in Coulomb gauge and
the center-vortex confinement scenario. We report on recent numerical studies
which support both of these scenarios.


title: Electric Polarizability of Neutral Hadrons from Lattice QCD

abstract:
  By simulating a uniform electric field on a lattice and measuring the change
in the rest mass, we calculate the electric polarizability of neutral mesons
and baryons using the methods of quenched lattice QCD. Specifically, we measure
the electric polarizability coefficient from the quadratic response to the
electric field for 10 particles: the vector mesons $\rho^0$ and $K^{*0}$; the
octet baryons n, $\Sigma^0$, $\Lambda_{o}^{0}$, $\Lambda_{s}^{0}$, and $\Xi^0$;
and the decouplet baryons $\Delta^0$, $\Sigma^{*0}$, and $\Xi^{*0}$.
Independent calculations using two fermion actions were done for consistency
and comparison purposes. One calculation uses Wilson fermions with a lattice
spacing of $a=0.10 $fm. The other uses tadpole improved L\"usher-Weiss gauge
fields and clover quark action with a lattice spacing $a=0.17 $fm. Our results
for neutron electric polarizability are compared to experiment.


title: An unquenched lattice QCD calculation of the mass of the bottom quark

abstract:
  We compute the b quark mass from dynamical lattice QCD with clover quarks.
The calculation is done at a fixed lattice spacing with sea quark masses as low
as half the strange quark mass. Our final result is m_b(m_b} = 4.25(2)(11) GeV,
where the first error is statistical and the last error is the systematic
uncertainty.


title:
A solution to the fermion doubling problem for supersymmetric theories
  on the transverse lattice

abstract:
  Species doubling is a problem that infects most numerical methods that use a
spatial lattice. An understanding of species doubling can be found in the
Nielsen-Ninomiya theorem which gives a set of conditions that require species
doubling. The transverse lattice approach to solving field theories, which has
at least one spatial lattice, fails one of the conditions of the
Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the
standard Lagrangian formulation of the transverse lattice. We will show that
the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the
transverse lattice does not have species doubling.


title: Nuclear Lattice Simulations with EFT

abstract:
  This proceedings article is a summary of results from work done in
collaboration with Bugra Borasoy and Thomas Schaefer. We study nuclear and
neutron matter by combining chiral effective field theory with non-perturbative
lattice methods. We present results for hot neutron matter at temperatures 20
to 40 MeV and densities below twice nuclear matter density.


title: Static potential and local color fields in unquenched lattice QCD$_3$

abstract:
  String breaking by dynamical quarks in three-dimensional lattice QCD is
analyzed through measurements of the potential and the local color-electric
field strength generated by a static quark-antiquark pair. Simulations were
done for unquenched SU(2) color with two flavors of staggered light quarks. An
improved gluon action was used, which allows simulations to be done on coarse
lattices, providing an extremely efficient means to access the large quark
separations and long propagation times at which string breaking occurs. The
static sources were generated using Wilson loop operators, hence no light
valence quarks are present in the resulting trial states. Results give
unambiguous evidence of string breaking. First the static potential is shown to
saturate at twice the heavy-light meson mass at large separations. Then it is
demonstrated that the local color-electric field strength in the region between
the heavy quarks tends towards vacuum values at large separations, the first
time that this most graphic effect of quark vacuum polarization on the
confining flux-tube has been realized in lattice QCD. Implications of these
results for unquenched simulations of four-dimensional QCD are drawn.


title:
Remarks on the hadronic matrix elements relevant to the SUSY K-Kbar
  mixing amplitude

abstract:
  We compute the 1-loop chiral corrections to the bag parameters which are
needed for the discussion of the SUSY K-Kbar mixing problem in both finite and
infinite volume. We then show how the bag parameters can be combined among
themselves and with some auxiliary quantities and thus sensibly reduce the
systematic errors due to chiral extrapolations as well as those due to finite
volume artefacts present in the results obtained from lattice QCD. We also show
that in some cases these advantages remain as such even after including the
2-loop chiral corrections. Similar discussion is also made for the K --> pi
electro-weak penguin operators.


title: Penta-quark baryon in anisotropic lattice QCD

abstract:
  The penta-quark(5Q) baryon is studied in anisotropic quenched lattice QCD
with renormalized anisotropy a_s/a_t=4 for a high-precision mass measurement.
The standard Wilson action at beta=5.75 and the O(a) improved Wilson quark
action with kappa=0.1210(0.0010)0.1240 are employed on a 12^3 \times 96
lattice. Contribution of excited states is suppressed by using a smeared
source. We investigate both the positive- and negative-parity 5Q baryons with
I=0 and spin J=1/2 using a non-NK-type interpolating field. After chiral
extrapolation, the lowest positive-parity state is found to have a mass,
m_{Theta}=2.25 GeV, which is much heavier than the experimentally observed
Theta^+(1540). The lowest negative-parity 5Q appears at m_{Theta}=1.75 GeV,
which is near the s-wave NK threshold. To distinguish spatially-localized 5Q
resonances from NK scattering states, we propose a new general method imposing
a ``Hybrid Boundary Condition (HBC)'', where the NK threshold is artificially
raised without affecting compact five-quark states. The study using the HBC
method shows that the negative-parity state observed on the lattice is not a
compact 5Q but an s-wave NK-scattering state.


title: Free energies of static three quark systems

abstract:
  We study the behaviour of free energies of baryonic systems composed of three
heavy quarks on the lattice in SU(3) pure gauge theory at finite temperature.
For all temperatures above $T_c$ we find that the connected part of the singlet
(decuplet) free energy of the three quark system is given by the sum of the
connected parts of the free energies of $qq$-triplets (-sextets). Using
renormalized free energies we can compare free energies in different colour
channels as well as those of $qq$- and $qqq$-systems on an unique energy scale.


title: Quark-gluon vertex in arbitrary kinematics

abstract:
  We compute the quark-gluon vertex in quenched lattice QCD, in the Landau
gauge using an off-shell mean-field O(a)-improved fermion action. The complete
vertex is computed in two specific kinematical limits, while the Dirac-vector
part is computed for arbitrary kinematics. We find a nontrivial and rich tensor
structure, including a substantial infrared enhancement of the interaction
strength regardless of kinematics.


title: Pion form factor with twisted mass QCD

abstract:
  The pion form factor is calculated using quenched twisted mass QCD with
beta=6.0 and maximal twisting angle omega=pi/2. Two pion masses and several
values of momentum transfer are considered. The momentum averaging procedure of
Frezzotti and Rossi is used to reduce lattice spacing errors, and numerical
results are consistent with the expected O(a) improvement.


title: Numerical Study of the Ghost-Gluon Vertex in Landau gauge

abstract:
  We present a numerical study of the ghost-gluon vertex and of the
corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau
gauge for SU(2) lattice gauge theory. Data were obtained for three different
lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta =
2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called
smeared gauge fixing. We also consider two different sets of momenta (orbits)
in order to check for possible effects due to the breaking of rotational
symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in
momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately
constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a
nonperturbative verification of the so-called nonrenormalization of the Landau
ghost-gluon vertex. Finally, we use our data to evaluate the running coupling
constant \alpha_s(p^2).


title:
Approximated seventh order calculation of vacuum wave function of 2+1
  dimensional SU(2) lattice gauge theory

abstract:
  Using the coupled cluster expansion with the random phase approximation, we
calculate the long wavelength vacuum wave function and the vacuum energy of 2+1
dimensional Hamiltonian SU(2) lattice gauge theory (LGT) up to the seventh
order. The coefficients $\mu_0$, $\mu_2$ of the vacuum wave function show good
scaling behavior and convergence in high order calculations.


title: Calorons with non-trivial holonomy on and off the lattice

abstract:
  We discuss recent solutions for SU(2) calorons with non-trivial holonomy at
higher charge, both through analytic means and using cooling, as well as
extensive lattice studies for SU(3).


title:
A model independent determination of $|V_{ub}|$ using the global $q^2$
  dependence of the dispersive bounds on the $B\to\pi l\nu$ form factors

abstract:
  We propose a method to determine the CKM matrix element $|V_{ub}|$ using the
global $q^2$ dependence of the dispersive bound on the form factors for $B\to
\pi l\nu$ decay. Since the lattice calculation of the $B\to \pi l\nu$ form
factor is limited to the large $q^2$ regime, only the experimental data in a
limited kinematic range can be used in a conventional method. In our new method
which exploits the statistical distributions of the dispersive bound proposed
by Lellouch, we can utilize the information of the global $q^2$ dependence for
all kinematic range. As a feasibility study we determine $|V_{ub}|$ by
combining the form factors from quenched lattice QCD, the dispersive bounds,
and the experimental data by CLEO. We show that the accuracy of $|V_{ub}|$ can
be improved by our method.


title:
Preliminary results of the heavy-light meson spectrum using chirally
  improved light quarks

abstract:
  Using a ``wall'' of quark point sources, we invert the chirally improved
Dirac operator to create an ``incoherent'' collection of quark propagators
which originate from all spatial points of the source time slice. The
lowest-order NRQCD approximation is used to create heavy-quark propagators from
the same wall source. However, since the numerical cost involved in computing
such heavy-quark propagators is low, we are able to use a number of source
gauge paths to establish coherence between the heavy and light quarks at
several spatial separations. The resulting collection of heavy-light meson
correlators is analyzed to extract the corresponding mass spectrum.


title:
A comparative study of overlap and staggered fermions in the Schwinger
  model

abstract:
  We investigate the validity of the square rooting procedure of the staggered
determinant in the context of the Schwinger model. We find some evidence that
at fixed physical quark mass the square root of the staggered determinant
becomes proportional to the overlap determinant in the continuum limit. We also
find that at fixed lattice spacing moderate smearing dramatically improves the
chiral behavior of staggered fermions.


title: Finite volume effects using lattice chiral perturbation theory

abstract:
  Lattice regularization is used to perform chiral perturbation theory
calculations in finite volume. The lattice spacing is chosen small enough to be
irrelevant, and numerical results are obtained from simple summations.


title: Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills

abstract:
  We investigate critical slowing down in the local updating continuous-time
Quantum Monte Carlo method by relating the finite size scaling of Fisher Zeroes
to the dynamically generated gap, through the scaling of their respective
critical exponents. As we comment, the nonlinear sigma model representation
derived through the hamiltonian of our lattice spin model can also be used to
give a effective treatment of planar anomalous dimensions in N=4 SYM. We
present scaling arguments from our FSS analysis to discuss quantum corrections
and recent 2-loop results, and further comment on the prospects of extending
this approach for calculating higher twist parton distributions.


title: Cold, dense matter via the lattice NJL model

abstract:
  We simulate the lattice Nambu--Jona-Lasinio (NJL) model in 3+1-dimensions at
non-zero baryon chemical potential (mu) and zero temperature (T) and treat the
results as phenomenologically relevant for cold, dense quark matter.
Measurements of the chiral condensate indicate a crossover in the thermodynamic
limit, whilst at high chemical potential and zero temperature we observe a
non-zero diquark condensate and a gap in the fermion dispersion relation, which
together provide evidence for BCS superfluidity. In particular, the size of gap
is found to be approximately 15% the value of the vacuum fermion mass and
roughly independent of mu in the chirally restored phase.


title:
Exploratory spectrum calculations using overlap valence quarks on a
  staggered sea

abstract:
  We present exploratory results for the hadron mass spectrum and pseudoscalar
meson decay constants using mixed actions. We use improved staggered sea quarks
and HYP-smeared overlap valence quarks. We obtain good signals on 10
configurations at one lattice spacing and two different sets of sea quark
masses.


title:
Amplitude ratios for the mass spectrum of the 2d Ising model in the
  high-T, H \neq 0 phase

abstract:
  We study the behaviour of the 2d Ising model in the symmetric high
temperature phase in presence of a small magnetic perturbation. We successfully
compare the quantum field theory predictions for the shift in the mass spectrum
of the theory with a set of high precision transfer matrix results. Our results
rule out a prediction for the same quantity obtained some years ago with strong
coupling methods.


title: Cutoff effects in meson spectral functions

abstract:
  We study the lattice spacing dependence of meson spectral functions
calculated in quenched QCD with domain wall fermions as well as clover Wilson
fermions in quenched and partially-quenched QCD. We conclude that for lattice
spacing $a \le 3$ GeV all excited states appearing in the spectral functions
are lattice artifacts.


title:
Numerical study of the equation of state for two flavor QCD at non-zero
  baryon density

abstract:
  We discuss the equation of state (EoS) for two flavor QCD at non-zero
temperature and density. Derivatives of $\ln Z$ with respect to quark chemical
potential $\mu_q$ are calculated up to sixth order. From this Taylor series,
the pressure, quark number density and associated susceptibilities are
estimated as functions of temperature and $\mu_q$. It is found that the
fluctuations in the quark number density increase in the vicinity of the phase
transition temperature and the susceptibilities start to develop a pronounced
peak as $\mu_q$ is increased. This suggests the presence of a critical endpoint
in the $(\mu_q, T)$ plane. Moreover, we comment on the hadron resonance gas
model, which explains well our simulation results below $T_c$.


title: Lattice Simulations with Chemical Potential

abstract:
  After giving an overview of recently invented methods for simulating lattice
QCD at small mu/T, we discuss some results for bulk thermodynamic quantities of
QCD matter coming from those methods. We focus on the transition line and the
critical endpoint in the QCD phase diagram.


title: The locality problem for two tastes of staggered fermions

abstract:
  We address the locality problem arising in simulations, which take the square
root of the staggered fermion determinant as a Boltzmann weight to reduce the
number of dynamical quark tastes from four to two. We study analytically and
numerically the square root of the staggered fermion operator as a candidate to
define a two taste theory from first principles. Although it has the correct
weight, this operator is non-local in the continuum limit. Our work serves as a
warning that fundamental properties of field theories might be violated when
employing blindly the square root trick. The question, whether a local operator
reproducing the square root of the staggered fermion determinant exists, is
left open.


title: On-shell improvement of the massive Wilson quark action

abstract:
  We review a relativistic approach to the heavy quark physics in lattice QCD
by applying a relativistic $O(a)$ improvement to the massive Wilson quark
action on the lattice. After explaining how power corrections of $m_Q a$ can be
avoided and remaining uncertainties are reduced to be of order $(a\Lambda_{\rm
QCD})^2$, we demonstrate a determination of four improvement coefficients in
the action up to one-loop level in a mass dependent way. We also show a
perturbative determination of mass dependent renormalization factors and $O(a)$
improvement coefficients for the vector and axial vector currents. Some
preliminary results of numerical simulations are also presented.


title: Finite size mass shift formula for stable particles revisited

abstract:
  Luescher's finite size mass shift formula in a periodic finite volume,
involving forward scattering amplitudes in the infinite volume, is revisited
for the two stable distinguishable particle system. The generalized mass shift
formulae for the boson and fermion are derived in the boson-boson and
fermion-boson systems, respectively. The nucleon mass shift is discussed in the
nucleon-pion system.


title: The Chroma Software System for Lattice QCD

abstract:
  We describe aspects of the Chroma software system for lattice QCD
calculations. Chroma is an open source C++ based software system developed
using the software infrastructure of the US SciDAC initiative. Chroma
interfaces with output from the BAGEL assembly generator for optimised lattice
fermion kernels on some architectures. It can be run on workstations, clusters
and the QCDOC supercomputer.


title: Unquenched simulations with N_f=2 light quark flavours

abstract:
  The quark mass dependence of meson masses and decay constants in N_f=2 QCD is
studied at a fixed gauge coupling with different dynamical quark masses.
Partially Quenched Wilson Chiral Perturbation Theory (PQWchiPT) is applied to
obtain the extrapolation to zero quark mass. It is shown, that in our analysis
NNLO-terms play a more important role than O(a)-terms, which can be neglected.
Also we compare our results with recent CP-PACS results.


title: Cutoff-effects in the spectrum of dynamical Wilson fermions

abstract:
  We investigate the low-lying eigenvalues of the improved Wilson-Dirac
operator in the Schroedinger functional with two dynamical quark flavors. At a
lattice spacing of approximately 0.1 fm we find more very small eigenvalues
than in the quenched case. These cause problems with HMC-type algorithms and in
the evaluation of fermionic correlation functions. Through a simulation at a
finer lattice spacing we are able to establish their nature as cutoff-effects


title: Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory

abstract:
  We point out a caveat in the proof for automatic O(a) improvement in twisted
mass lattice QCD at maximal twist angle. With the definition for the twist
angle previously given by Frezzotti and Rossi, automatic O(a) improvement can
fail unless the quark mass satisfies m_q >> a^2 Lambda_QCD^3. We propose a
different definition for the twist angle which does not require a restriction
on the quark mass for automatic O(a) improvement. In order to illustrate
explicitly automatic O(a) improvement we compute the pion mass in the
corresponding chiral effective theory. We consider different definitions for
maximal twist and show explicitly the absence or presence of the leading O(a)
effect, depending on the size of the quark mass.


title:
Are there Local Minima in the Magnetic Monopole Potential in Compact
  QED?

abstract:
  We investigate the influence of the granularity of the lattice on the
potential between monopoles. Using the flux definition of monopoles we
introduce their centers of mass and are able to realize continuous shifts of
the monopole positions. We find periodic deviations from the $1/r$-behavior of
the monopole-antimonopole potential leading to local extrema. We suppose that
these meta-stabilities may influence the order of the phase transition in
compact QED.


title: Next-to-Leading-Order Staggered Chiral Perturbation Theory

abstract:
  We have extended staggered chiral perturbation theory to O(a^2 p^2), O(a^4),
and O(a^2 m), the orders necessary for a full next-to-leading order calculation
of pseudo-Goldstone boson masses and decay constants including taste-symmetry
violations. We present predictions relating SO(4) taste-breaking splittings in
masses, pseudoscalar decay constants, and dispersion relations. These can be
used to test the fourth-root trick.


title: Singlet Free Energies of a Static Quark-Antiquark Pair

abstract:
  We study the singlet part of the free energy of a static quark anti-quark
pair at finite temperature in three flavor QCD with degenerate quark masses
using $N_{\tau}=4$ and 6 lattices with Asqtad staggered fermion action. We look
at thermodynamics of the system around phase transition and study its scaling
with lattice spacing and quark masses.


title: QCD Thermodynamics: Lattice Results confront Models

abstract:
  We show that lattice results on four flavor QCD at nonzero temperature and
baryon density compare well with the hadron resonance gas model up to T approx.
0.95 Tc, and approach a free field behaviour with a reduced effective number of
flavor for T \ge 1.5 Tc. Chiral symmetry and confinement are interrelated, and
we note analogies between the critical line of QCD and that of simple models
with the same global symmetries.


title: Extracting excited states from lattice QCD: the Roper resonance

abstract:
  We present a new method for extracting excited states from a single two-point
correlation function calculated on the lattice. Our method simply combines the
correlation function evaluated at different time slices so as to ``subtract''
the leading exponential decay (ground state) and to give access to the first
excited state. The method is applied to a quenched lattice study (volume = 24^3
x 64, beta = 6.2, 1/a = 2.55 GeV) of the first excited state of the nucleon
using the local interpolating operator O = [uT C gamma5 d] u. The results are
consistent with the identification of our extracted excited state with the
Roper resonance N'(1440). The switching of the level ordering with respect to
the negative-parity partner of the nucleon, N*(1535), is not seen at the
simulated quark masses and, basing on crude extrapolations, is tentatively
expected to occur close to the physical point.


title:
Wilson-like fermions and the static B_B parameter with no chirality
  breaking mixings

abstract:
  I consider the recent proposal by R. Frezzotti and G. Rossi to chirally
improve Wilson fermions in such a way that mixings among operators of different
chirality can be excluded. The method, which is based on the use of twisted
mass QCD with several replica of valence quarks, is extended here to
static-light systems. The operators relevant for the computation of the B_B
parameter (in the static approximation) are discussed. In this case the same
renormalization pattern as for Ginsparg-Wilson fermions is obtained by a simple
modification of the discretization of the action for valence quarks.