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CP invariance of chiral gauge theories and Majorana-Yukawa couplings on
the lattice: The construction of CP-invariant lattice chiral gauge theories and the
construction of lattice Majorana fermions with chiral Yukawa couplings is
subject to topological obstructions. In the present work we suggest lattice
extensions of charge and parity transformation for Weyl fermions. This enables
us to construct lattice chiral gauge theories that are CP invariant. For the
construction of Majorana-Yukawa couplings, we discuss two models with
symplectic Majorana fermions: a model with two symplectic doublets, and one
with an auxiliary doublet. | hep-lat |
Lattice Gauge Fixing, Gribov Copies and BRST Symmetry: We show that a modification of the BRST lattice quantization allows to
circumvent an old paradox, formulated by Neuberger, related to lattice Gribov
copies and non-perturbative BRST invariance. In the continuum limit the usual
BRST formulation is recovered. | hep-lat |
Lattice field theory results for hybrid static potentials at short
quark-antiquark separations and their parametrization: We present SU(3) lattice Yang-Mills data for hybrid static potentials from
five ensembles with different small lattice spacings and the corresponding
parametrizations for quark-antiquark separations $0.08\,\text{fm} \le r \le
1.12\,\text{fm}$. We remove lattice discretization errors at tree level of
perturbation theory and partly at order $a^2$ as well as the $a$-dependent self
energy. In particular the tree-level improvement of static potentials is
discussed in detail and two methods are compared. The resulting
parametrizations are expected to represent continuum limit results for hybrid
static potentials within statistical errors. | hep-lat |
Can axial U(1) anomaly disappear at high temperature?: In our recent study of two-flavor lattice QCD using chiral fermions, we find
strong suppression of axial U(1) anomaly above the critical temperature of
chiral phase transition. Our simulation data also indicate suppression of
topological susceptibility. In this talk, we present both of our theoretical
and numerical evidence for disappearance of axial U(1) anomaly, emphasizing the
importance of controlling lattice chiral symmetry violation, which is enhanced
at high temperature. | hep-lat |
String tensions of SU(N) gauge theories in 2+1 dimensions: We calculate the energy spectrum of closed strings in SU(N) gauge theories
with N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control
all systematic errors, and this allows us to perform a precise comparison with
different theoretical predictions.
When we study the dependence of the string mass on its length L we find that
the Nambu-Goto prediction is a very good approximation down to relatively short
lengths, where the Luscher term alone is insufficient. We then isolate the
corrections to the Luscher term, and compare them to recent theoretical
predictions, which indeed seem to be mildly preferred by the data.
When we take these corrections into account and extract string tensions from
the string masses, we find that their continuum limit is lower by 2%-1% from
the predictions of Karabli, Kim, and Nair. The discrepancy decreases with N,
but when we extrapolate our results to N=oo we still find a discrepancy of
0.88% which is a 4.5 sigma effect. | hep-lat |
Level spacings for weakly asymmetric real random matrices and
application to two-color QCD with chemical potential: We consider antisymmetric perturbations of real symmetric matrices in the
context of random matrix theory and two-color quantum chromodynamics. We
investigate the level spacing distributions of eigenvalues that remain real or
become complex conjugate pairs under the perturbation. We work out analytical
surmises from small matrices and show that they describe the level spacings of
large random matrices. As expected from symmetry arguments, these level
spacings also apply to the overlap Dirac operator for two-color QCD with
chemical potential. | hep-lat |
Thermodynamics of free Domain Wall fermions: Studying various thermodynamic quantities for the free domain wall fermions
for both finite and infinite fifth dimensional extent N_5, we find that the
lattice corrections are minimum for $N_T\geq10$ for both energy density and
susceptibility, for its irrelevant parameter M in the range 1.45-1.50. The
correction terms are, however, quite large for small lattice sizes of
$N_T\leq8$. We propose modifications of the domain wall operator, as well as
the overlap operator, to reduce the finite cut-off effects to within 10% of the
continuum results of the thermodynamic quantities for the currently used
N_T=6-8 lattices. Incorporating chemical potential, we show that \mu^2
divergences are absent for a large class of such domain wall fermion actions
although the chiral symmetry is broken for $\mu\neq0$. | hep-lat |
Matrix elements of (delta S=2) operators with Wilson fermions: We test the recent proposal of using the Ward identities to compute the
K0-K0bar mixing amplitude with Wilson fermions, without the problem of spurious
lattice subtractions. From our simulations, we observe no difference between
the results obtained with and without subtractions. In addition, from the
standard study of the complete set of (delta S=2) operators, we quote the
following (preliminary) results (in the MS(NDR) scheme): Bk(2 GeV)=0.70(10), <
O7^{3/2}>_{K->pi pi} = 0.10(2)(1) GeV^3, < O8^{3/2}>_{K->pi pi} = 0.49(6)(0)
GeV^3. | hep-lat |
Searching for continuous phase transitions in 5D SU(2) lattice gauge
theory: We study the phase diagram of 5-dimensional $SU(2)$ Yang-Mills theory on the
lattice. We consider two extensions of the fundamental plaquette Wilson action
in the search for the continuous phase transition suggested by the $4+\epsilon$
expansion. The extensions correspond to new terms in the action: i) a unit size
plaquette in the adjoint representation or ii) a two-unit sided square
plaquette in the fundamental representation. We use Monte Carlo to sample the
first and second derivative of the entropy near the confinement phase
transition, with lattices up to $12^{5}$. While we exclude the presence of a
second order phase transition in the parameter space we sampled for model i),
our data is not conclusive in some regions of the parameter space of model ii). | hep-lat |
What the Gribov copy tells on the confinment and the theory of dynamical
chiral symmetry breaking: We performed lattice Landau gauge QCD simulation on \beta=6.0, 16^4, 24^4,
32^4 and \beta=6.4, 32^4, 48^4 and 56^4 by adopting the gauge fixing that
minimizes the norm of the gauge field, and measured the running coupling by
using the gluon propagator and the ghost propagator. In view of ambiguity in
the vertex renormalization factor \tilde Z_1 in the lattice, we adjust the
normalization of the running coupling by the perturbative QCD results near the
highest momentum point. It has a maximum \alpha_s(q)~ 2.1(3) at around q=0.5
GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached
-0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is
\alpha_G=0.20 but there is an exceptional Gribov copy with \alpha_G=0.27. The
features of the exceptional Gribov copy are investigated by measuring four
one-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to
each lattice axis. We observe, in general, correlation between absolute value
of the Kugo-Ojima parameter and the degree of reflection positivity violation
in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov
copy has an axis whose gluon propagator manifestly violates reflection
positivity, and the average of the Cartan subalgebra components of the
Kugo-Ojima parameter along this axis is consistent to -1. The running coupling
of the enemble average shows a suppression at 0 momentum, but when the ghost
propagator of the exceptional Gribov copy is adopted, the suppression
disappears and the data implies presence of the infrared fixed point
\alpha_s(0)~ 2.5(5) and \kappa=0.5 suggested by the Dyson-Schwinger approach in
the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and
N_f=2 unquenched SU(3) QCD are also made. | hep-lat |
Stout-smearing, gradient flow and $c_{\text{SW}}$ at one loop order: The one-loop determination of the coefficient $c_\text{SW}$ of the Wilson
quark action has been useful to push the leading cut-off effects for on-shell
quantities to $\mathcal{O}(\alpha^2 a)$ and, in conjunction with
non-perturbative determinations of $c_\text{SW}$, to $\mathcal{O}(a^2)$, as
long as no link-smearing is employed. These days it is common practice to
include some overall link-smearing into the definition of the fermion action.
Unfortunately, in this situation only the tree-level value
$c_\text{SW}^{(0)}=1$ is known, and cut-off effects start at
$\mathcal{O}(\alpha a)$. We present some general techniques for calculating one
loop quantities in lattice perturbation theory which continue to be useful for
smeared-link fermion actions. Specifically, we discuss the application to the
1-loop improvement coefficient $c_\text{SW}^{(1)}$ for overall stout-smeared
Wilson fermions. | hep-lat |
Gauge Invariance and Lattice Monopoles: The number and the location of monopoles in Lattice configurations depend on
the choice of the gauge, in contrast to the obvious requirement that monopoles,
as physical objects, have a gauge-invariant status.
It is proved, starting from non-abelian Bianchi identities, that monopoles
are indeed gauge-invariant: the technique used to detect them has instead an
efficiency which depends on the choice of the abelian projection, in a known
and well understood way. | hep-lat |
Lyapunov Spectra in SU(2) Lattice Gauge Theory: We develop a method for calculating the Lyapunov characteristic exponents of
lattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is
obtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with
lattice size is found. | hep-lat |
The pion_0 to gamma gamma decay and the chiral anomaly in the
quark-composites approach to QCD: We evaluate the pion_0 into two gammas decay amplitude by an effective action
derived from QCD in the quark composites approach, getting the standard value.
We also verify that our effective action correctly reproduces the chiral
anomaly. | hep-lat |
Gradient Flow Coupling in the SU(2) gauge theory with two adjoint
fermions: We study SU(2) gauge theory with two fermion flavors in the adjoint
representation. Using a clover improved HEX smeared action and the gradient
flow running coupling allows us to simulate with larger lattice size than
before. We find an infrared fixed point after a continuum extrapolation in the
range $4.5 \lesssim g^{*2} \lesssim 5$. We also measure the mass anomalous
dimension and find the value $ 0.25 \lesssim \gamma^* \lesssim 0.28 $ at the
fixed point. | hep-lat |
Physical observables from boundary artifacts: scalar glueball in
Yang-Mills theory: By relating the functional averages of a generic scalar operator in
simulations with Open (O) and Periodic (P) boundary conditions (BCs)
respectively for $SU(3)$ lattice gauge theory, we show that the scalar glueball
mass and the glueball to vacuum matrix element can be extracted very
efficiently from the former. Numerical results are compared with those
extracted from the two point function of the time slice energy density (both
PBC and OBC). The scaling properties of the mass and the matrix element are
studied with the help of Wilson (gradient) flow. | hep-lat |
Controlling Residual Chiral Symmetry Breaking in Domain Wall Fermion
Simulations: At stronger gauge-field couplings, the domain wall fermion (DWF) residual
mass, a measure of chiral symmetry breaking, grows rapidly. This measure is
largely due to near zero fermion eigenmodes of logarithm of the 4D transfer
matrix along the fifth dimension, and these eigenmodes increase rapidly at
strong coupling. To suppress these eigenmodes, we have added to the DWF path
integral a multiplicative weighting factor consisting of a ratio of
determinants of Wilson-Dirac fermions having a chirally twisted mass with a
large negative real component and a small imaginary chiral component. Numerical
results show that this weighting factor with an appropriate choice of twisted
masses significantly suppresses the residual mass while allowing adequate
topological tunneling. | hep-lat |
Developing and testing the density of states FFA method in the SU(3)
spin model: The Density of States Functional Fit Approach (DoS FFA) is a recently
proposed modern density of states technique suitable for calculations in
lattice field theories with a complex action problem. In this article we
present an exploratory implementation of DoS FFA for the SU(3) spin system at
finite chemical potential $\mu$ - an effective theory for the Polyakov loop.
This model has a complex action problem similar to the one of QCD but also
allows for a dual simulation in terms of worldlines where the complex action
problem is solved. Thus we can compare the DoS FFA results to the reference
data from the dual simulation and assess the performance of the new approach.
We find that the method reproduces the observables from the dual simulation for
a large range of $\mu$ values, including also phase transitions, illustrating
that DoS FFA is an interesting approach for exploring phase diagrams of lattice
field theories with a complex action problem. | hep-lat |
Non-perturbative improvement of nHYP smeared Wilson fermions: Using Schroedinger functional techniques, we determine the coefficient of the
clover term necessary for non-perturbative O(a) improvement of hypercubic
smeared Wilson fermions on a quenched plaquette action background. Unlike for
unsmeared Wilson fermions, the resulting clover coefficients are close to the
tree-level value even at coarse lattice spacings, indicating the absence of
large cutoff effects. A number of exploratory tests are also performed with the
improved action. | hep-lat |
Excited states of massive fermions in a chiral gauge theory: It is shown numerically, in a chiral U(1) gauge Higgs theory in which the
left and right-handed fermion components have opposite U(1) charges, that the
spectrum of gauge and Higgs fields surrounding a static fermion contains both a
ground state and at least one stable excited state. To bypass the difficulties
associated with dynamical fermions in a lattice chiral gauge theory we consider
only static fermion sources in a quenched approximation, at fixed lattice
spacing and couplings, and with a lattice action along the lines suggested long
ago by Smit and Swift. | hep-lat |
Type of dual superconductivity for the $SU(2)$ Yang--Mills theory: We investigate the type of dual superconductivity responsible for quark
confinement. For this purpose, we solve the field equations of the $U(1)$
gauge-scalar model to obtain the static vortex solution in the whole range
without restricting to the long-distance region. Then we use the resulting
magnetic field of the vortex to fit the gauge-invariant chromoelectric field
connecting a pair of quark and antiquark which was measured by numerical
simulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves
the accuracy of the fitted value for the Ginzburg--Landau parameter to
reconfirm the type I dual superconductivity for quark confinement which was
claimed by preceding works based on a fitting using the Clem ansatz. Moreover,
we calculate the Maxwell stress tensor to obtain the distribution of the force
around the flux tube. This result suggests that the attractive force acts among
chromoelectric flux tubes, in agreement with the type I dual superconductivity. | hep-lat |
Critical Behavior of the Schwinger Model with Wilson Fermions: We present a detailed analysis, in the framework of the MFA approach, of the
critical behaviour of the lattice Schwinger model with Wilson fermions on
lattices up to $24^2$, through the study of the Lee-Yang zeros and the specific
heat. We find compelling evidence for a critical line ending at $\kappa = 0.25$
at large $\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2,
20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation
is verified in the explored $\beta$ region. | hep-lat |
Aharonov--Bohm Effect in 3D Abelian Higgs Theory: We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D
Abelian Higgs Model: the corresponding topological interaction is proportional
to the linking number of the vortex and the particle world trajectories. We
show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of
tested charged particles. | hep-lat |
Multicanonical simulation of 3D dynamical triangulation model and a new
phase structure: We apply the multicanonical technique to the three dimensional dynamical
triangulation model, which is known to exhibit a first order phase transition
with the Einstein-Hilbert action. We first clarify the first order nature of
the phase transition with the Einstein-Hilbert action in several ways including
a high precision finite size scaling analysis. We then add a new local term to
the action and confirm the conjecture made through the MCRG technique that the
line of the first order phase transition extends to the expanded phase diagram,
ending at a point. Fractal dimension at the end point is measured to be around
three up to the present size. | hep-lat |
Clock model interpolation and symmetry breaking in O(2) models: Motivated by recent attempts to quantum simulate lattice models with
continuous Abelian symmetries using discrete approximations, we define an
extended-O(2) model by adding a $\gamma \cos(q\varphi)$ term to the ordinary
O(2) model with angular values restricted to a $2\pi$ interval. In the $\gamma
\rightarrow \infty$ limit, the model becomes an extended $q$-state clock model
that reduces to the ordinary $q$-state clock model when $q$ is an integer and
otherwise is a continuation of the clock model for noninteger $q$. By shifting
the $2\pi$ integration interval, the number of angles selected can change
discontinuously and two cases need to be considered. What we call case $1$ has
one more angle than what we call case $2$. We investigate this class of clock
models in two space-time dimensions using Monte Carlo and tensor
renormalization group methods. Both the specific heat and the magnetic
susceptibility show a double-peak structure for fractional $q$. In case $1$,
the small-$\beta$ peak is associated with a crossover, and the large-$\beta$
peak is associated with an Ising critical point, while both peaks are
crossovers in case $2$. When $q$ is close to an integer by an amount $\Delta q$
and the system is close to the small-$\beta$ Berezinskii-Kosterlitz-Thouless
transition, the system has a magnetic susceptibility that scales as $\sim 1 /
(\Delta q)^{1 - 1/\delta'}$ with $\delta'$ estimates consistent with the
magnetic critical exponent $\delta = 15$. The crossover peak and the Ising
critical point move to Berezinskii-Kosterlitz-Thouless transition points with
the same power-law scaling. A phase diagram for this model in the $(\beta, q)$
plane is sketched. These results are possibly relevant for configurable
Rydberg-atom arrays where the interpolations among phases with discrete
symmetries can be achieved by varying continuously the distances among atoms
and the detuning frequency. | hep-lat |
Measurement of hadron masses in 2-color finite density QCD: We investigate hadron spectra in 2-color QCD using lattice simulation with
$N_{f}=2$ at low temperature and finite density in which there appears not only
the hadronic phase but also the superfluid phase. We first calculate the pion
and rho meson spectrum, which is well-known from previous works. The spectral
ordering of these mesons flips around the quark chemical potential
$\mu=m^{0}_{\pi}/2$ ($m^{0}_{\pi}$: the pion mass at $\mu=0$), where the phase
transition between the hadronic and superfluid phases occurs. For $\mu \gtrsim
m^{0}_{\pi}/2$, the effective mass for the pion linearly increases while the
one for the rho meson monotonically decreases. Furthermore, we measure hadron
spectra with the isospin $I=0$ and the angular momentum $J^{P}=0^{\pm}$. The
effective masses for the meson, diquark, and antidiquark with the same quantum
number become degenerate just below $\mu = m^{0}_{\pi}/2$, and the three
hadrons have the same mass in the superfluid phase. It suggests that mixing
occurs between spectra associating with mesons and baryons due to the
$U(1)_{B}$ symmetry breaking. This phenomenon can be explained in the linear
sigma model with the approximate $SU(4)$ Pauli-Gursey symmetry. | hep-lat |
Lambda(1405) and Negative-Parity Baryons in Lattice QCD: We review briefly recent studies of the Lambda(1405) spectrum in Lattice QCD.
Ordinary three-quark pictures of the Lambda(1405) in quenched Lattice QCD fail
to reproduce the mass of the experimental value, which seems to support the
penta-quark picture for the Lambda(1405) such as a Kbar-N molecule-like state.
It is also noted that the present results suffer from relatively large
systematic uncertainties coming from the finite volume effect, the chiral
extrapolation and the quenching effect. | hep-lat |
A Noisy Monte Carlo Algorithm: We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear
accept/reject algorithm which accommodates unbiased stochastic estimates of the
probability to an exact one. This is achieved by adopting the Metropolis
accept/reject steps for both the dynamical and noise configurations. We test it
on the five state model and obtain desirable results even for the case with
large noise. We also discuss its application to lattice QCD with stochastically
estimated fermion determinants. | hep-lat |
Non-perturbative results for the coefficients b_m and b_a-b_p in O(a)
improved lattice QCD: We determine the improvement coefficients b_m and b_a-bp in quenched lattice
QCD for a range of beta-values, which is relevant for current large scale
simulations. At fixed beta, the results are rather sensitive to the precise
choices of parameters. We therefore impose improvement conditions at constant
renormalized parameters, and the coefficients are then obtained as smooth
functions of g_0^2. Other improvement conditions yield a different functional
dependence, but the difference between the coefficients vanishes with a rate
proportional to the lattice spacing. We verify this theoretical expectation in
a few examples and are therefore confident that O(a) improvement is achieved
for physical quantities. As a byproduct of our analysis we also obtain the
finite renormalization constant which relates the subtracted bare quark mass to
the bare PCAC mass. | hep-lat |
Calculation of the pion charge radius from an improved model-independent
method: We propose a new improved model-independent method for calculating the pion
charge radius. In a recently-proposed model-independent method for the pion
charge radius, we find it difficult to compute the pion charge radius for small
pole mass $M_{\rm{pole}}^2$ and volume due to systematic errors coming from
finite volume effect and higher-order contamination of the Taylor expansion of
the form factor. We circumvent this difficulty by introducing a new appropriate
function and propose a modified method that can calculate the pion charge
radius with less systematic errors in the small $M_{\rm{pole}}^2$ and volume
cases. As preliminary results, we check that our improved model-independent
method works well on a mockup data and also an actual lattice QCD data at the
pion mass of 0.51 GeV. | hep-lat |
Inclusion of isospin breaking effects in lattice simulations: Isospin symmetry is explicitly broken in the Standard Model by the mass and
electric charge of the up and down quarks. These effects represent a
perturbation of hadronic amplitudes at the percent level. Although these
contributions are small, they play a crucial role in hadronic and nuclear
physics. Moreover, as lattice computations are becoming increasingly precise,
it is becoming more and more important to include these effects in numerical
simulations. We summarize here how to properly define QCD and QED on a finite
and discrete space-time so that isospin corrections to hadronic observables can
be computed ab-initio and we review the main results on the isospin corrections
to the hadron spectrum. We mainly focus on the recent work going beyond the
electro-quenched approximation. | hep-lat |
2+1 flavour Domain Wall Fermion simulations by the RBC and UKQCD
collaborations: We review simulations of dynamical domain wall fermions at a fixed inverse
lattice spacing of 1.73GeV and with pion masses as light as 330MeV and spatial
dimensions as large as 2.7fm performed by the RBC and UKQCD collaborations.
These results include pseudoscalar masses and decay constants and low energy
constants of the chiral effective lagrangian. We also review results for the
neutral kaon mixing amplitude $B_K$, the Kl3 form factor, pseudoscalar meson
structure, and vector meson decay constants. In the baryon sector we review
results for the spectrum, and nucleon form factors and structure functions.
Highlights of our programme include preliminary quark masses, and
determinations of $V_{us}$ from both $f_K/f_\pi$ and from Kl3, and an updated
result for $B_K$. We find significant finite volume effects in the nucleon
axial charge $g_A$ for our $m_\pi=330$ MeV ensemble on a $(2.7 {\rm fm})^3$
lattice, and highlight the importance of large physical volumes for non-trivial
nucleon physics. | hep-lat |
Upper Higgs boson mass bounds from a chirally invariant lattice
Higgs-Yukawa model: We establish the cutoff-dependent upper Higgs boson mass bound by means of
direct lattice computations in the framework of a chirally invariant lattice
Higgs-Yukawa model emulating the same chiral Yukawa coupling structure as in
the Higgs-fermion sector of the Standard Model. As expected from the triviality
picture of the Higgs sector, we observe the upper mass bound to decrease with
rising cutoff parameter $\Lambda$. Moreover, the strength of the fermionic
contribution to the upper mass bound is explored by comparing to the
corresponding analysis in the pure $\Phi^4$-theory. | hep-lat |
On the type of the temperature phase transition in phi-4 model: The temperature induced phase transition is investigated in the one-component
scalar field \phi^4 model on a lattice by using Monte Carlo simulations. Using
the GPGPU technology a huge amount of data is collected that gives a
possibility to determine the Linde-Weinberg low bound on the coupling constant
\lambda_0 and investigate the type of the phase transition for a wide interval
of coupling values. It is found that for the values of \lambda close to this
bound a weak-first-order phase transition happens. It converts into a second
order phase transition with the increase of \lambda. A comparison with analytic
calculations in continuum field theory and lattice simulations obtained by
other authors is given. | hep-lat |
Chiral symmetry restoration in QCD with many flavours: We discuss the phases of QCD in the parameter space spanned by the number of
light flavours and the temperature with respect to the realisation of chiral
and conformal symmetries. The intriguing interplay of these symmetries is best
studied by means of lattice simulations, and some selected results from our
recent work are presented here. | hep-lat |
Distributing the chiral and flavour components of Dirac-Kahler fermions
across multiple lattices: We use a specific implementation of discrete differential geometry to
describe Dirac-Kahler fermions in such a way that we can separate their chiral
and flavour components. The formulation introduces additional lattices so that
on each lattice there is a single field of definate chirality. Within this
framework, we define an non-compact Abelian gauge theory. | hep-lat |
Exotic phases of finite temperature SU(N) gauge theories with massive
fermions: F, Adj, A/S: The phase diagrams at high temperature of SU(N) gauge theories with massive
fermions are calculated by numerically minimizing the one-loop effective
potential. We consider fermions in the Fundamental (F), Adjoint (Adj),
Antisymmetric (AS), and Symmetric (S) representations, for N from 3 to 9, with
periodic and antiperiodic boundary conditions applied. For one flavour of AS/S
(Dirac) fermion with periodic boundary conditions the C-breaking phase is
favoured perturbatively for all values of the fermion mass. In the case of one
flavour of adjoint Majorana fermion, and periodic boundary conditons, the
deconfined phase is favoured for any fermion mass. For one or more adjoint
Dirac fermion (two or more Majorana fermions) we find partially-confining
phases as well as new phases with unusual properties. Our results for SU(3) and
SU(4) are consistent with our lattice simulations of a related model. | hep-lat |
From C to Parton Sea: Bjorken-x Dependence of the PDFs: Studying the structure of nucleons is not only important to understanding the
strong interactions of quarks and gluons, but also to improving the precision
of new-physics searches. Since a broad class of experiments, including the LHC
and dark-matter detection, require Standard-Model backgrounds with parton
distribution functions (PDFs) as inputs for disentangling SM contributions from
potential new physics. For a long time, lattice calculations of the PDFs (as
well as many hadron structures) has been limited to the first few moments. In
this talk, we present a first direct calculation of the Bjorken-x dependence of
the PDFs using Large-Momentum Effective Theory (LaMET). An exploratory study of
the antiquark/sea flavor asymmetry of these distributions will be discussed.
This breakthrough opens an exciting new frontier calculating more complicated
quantities, such as gluon structure and transverse-momentum dependence, which
will complement existing theoretical programs for the upcoming Electron-Ion
Collider (EIC) or Large Hadron-Electron Collider (LHeC). | hep-lat |
Axial Nucleon form factors from lattice QCD: We present results on the nucleon axial form factors within lattice QCD using
two flavors of degenerate twisted mass fermions. Volume effects are examined
using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm.
Cut-off effects are investigated using three different values of the lattice
spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial
charge is obtained in the continuum limit and chirally extrapolated to the
physical pion mass enabling comparison with experiment. | hep-lat |
Lattice calculation of matrix elements relevant for Delta I=1/2 rule and
epsilon-prime: We have gained enough statistical precision to distinguish signal from noise
in matrix elements of all operators relevant for the Delta I=1/2 rule in kaon
decays and for the direct CP violation parameter epsilon-prime. We confirm
significant enhancement of Delta I=1/2 transitions observed in experiments,
although a few large systematic uncertainties remain in our predictions:
higher-order chiral corrections and lattice spacing dependence. The estimate of
epsilon-prime parameter is further complicated by the problem of matching
lattice and continuum operators. | hep-lat |
Acceleration of the Arnoldi method and real eigenvalues of the
non-Hermitian Wilson-Dirac operator: In this paper, we present a method for the computation of the low-lying real
eigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These
eigenvalues contain information about several observables. We used them to
calculate the sign of the fermion determinant in one-flavor QCD and the sign of
the Pfaffian in N=1 super Yang-Mills theory. The method is based on polynomial
transformations of the Wilson-Dirac operator, leading to considerable
improvements of the computation of eigenvalues. We introduce an iterative
procedure for the construction of the polynomials and demonstrate the
improvement in the efficiency of the computation. In general, the method can be
applied to operators with a symmetric and bounded eigenspectrum. | hep-lat |
How the Quark Number fluctuates in QCD at small chemical potential: We discuss the distribution of the quark number over the gauge fields for QCD
at nonzero quark chemical potential. As the quark number operator is
non-hermitian, the distribution is over the complex plane. Moreover, because of
the fermion determinant, the distribution is not real and positive. The
computation is carried out within leading order chiral perturbation theory and
gives direct insight into the delicate cancellations that take place in
contributions to the total baryon number. | hep-lat |
A calculation of the $B_{B}$ parameter in the static limit: We calculate the $B_{B}$ parameter, relevant for $\overline{B}^0$ -- $B^0$
mixing, from a lattice gauge theory simulation at $\beta = 6.0$. The bottom
quarks are simulated in the static theory, the light quarks with Wilson
fermions. Improved smearing functions produced by a variational technique,
MOST, are used to reduce statistical errors and minimize excited-state
contamination of the ground-state signal. We obtain $B_B(4.33 GeV) =
0.98^{+4}_{-4}$ (statistical) $^{+3}_{-18}$ (systematic) which corresponds to
$\widehat{B}_B = 1.40^{+6}_{-6}$ (statistical) $^{+4}_{-26}$ (systematic) for
the one-loop renormalization-scheme-independent parameter. The systematic
errors include the uncertainty due to alternative (less favored) treatments of
the perturbatively-calculated mixing coefficients; this uncertainty is at least
as large as residual differences between Wilson-static and clover-static
results. Our result agrees with extrapolations of results from relativistic
(Wilson) heavy quark simulations. | hep-lat |
UV divergence of the quasi-PDF operator under the lattice regularization: Even since the "quasi" parton distribution function (PDF) was proposed under
the large-momentum effective theory (LaMET) framework, its renormalization
under the lattice regularization has been a central challenge to be solved due
to the linear divergence. Thus, we investigate several possible ways to
renormalize the quasi-PDF operators in high accuracy with non-perturbative
calculation using the quench configurations at several lattice spacings. We
find that the ratio of the UV divergences obtained from the Wilson loop and
off-shell quasi-PDF operator is not a constant of the Wilson link length $z$.
Although the linear divergence in them may be consistent to each other
numerically, there is some additional UV divergence in the quasi-PDF operator. | hep-lat |
Partially Quenched QCD with Non-Degenerate Dynamical Quarks: We discuss the importance of using partially quenched theories with three
degenerate quarks for extrapolating to QCD, and present some relevant results
from chiral perturbation theory. | hep-lat |
The Weak-Coupling Limit of Simplicial Quantum Gravity: In the weak-coupling limit, kappa_0 going to infinity, the partition function
of simplicial quantum gravity is dominated by an ensemble of triangulations
with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial
triangulation of the D--sphere this limit is 1/D. Defining an ensemble of
maximal triangulations, i.e. triangulations that have the maximal possible
number of vertices for a given volume, we investigate the properties of this
ensemble in three dimensions using both Monte Carlo simulations and a
strong-coupling expansion of the partition function, both for pure simplicial
gravity and a with a suitable modified measure. For the latter we observe a
continuous phase transition to a crinkled phase and we investigate the fractal
properties of this phase. | hep-lat |
Perturbative renormalization functions of local operators for staggered
fermions with stout improvement: In this paper we present the perturbative computation of the renormalization
functions for the quark field and for a complete set of ultra-local fermion
bilinears. The computation of the relevant Green's functions was carried out at
1-loop level for the staggered action using massive fermions. The gluon links
which appear both in the fermion action and in the definition of the bilinears
have been improved by applying a stout smearing procedure up to 2 times,
iteratively. In the gluon sector we employed the Symanzik improved gauge action
for different sets of values of the Symanzik coefficients. The renormalization
functions are presented in (two variants of) the RI' and in the MSbar
renormalization scheme; the dependence on all stout parameters, as well as on
the fermion mass, the gauge fixing parameter and the renormalization scale, is
shown explicitly. This work is related to our recent paper [Phys. Rev. D86
(2012) 094512, arXiv:1209.6015]. To make our results easily accessible to the
reader, we include them in the distribution package of this paper, as a
Mathematica input file, Staggered.m. | hep-lat |
Light-quark connected intermediate-window contributions to the muon
$g-2$ hadronic vacuum polarization from lattice QCD: We present a lattice-QCD calculation of the light-quark connected
contribution to window observables associated with the leading-order hadronic
vacuum polarization contribution to the anomalous magnetic moment of the muon,
$a_\mu^{\mathrm{HVP,LO}}$. We employ the MILC Collaboration's isospin-symmetric
QCD gauge-field ensembles, which contain four flavors of dynamical
highly-improved-staggered quarks with four lattice spacings between $a\approx
0.06$-$0.15$~fm and close-to-physical quark masses. We consider several
effective-field-theory-based schemes for finite-volume and other lattice
corrections and combine the results via Bayesian model averaging to obtain
robust estimates of the associated systematic uncertainties. After unblinding,
our final results for the intermediate and ``W2'' windows are $a^{ll,{\mathrm
W}}_{\mu}(\mathrm{conn.})=206.6(1.0) \times 10^{-10}$ and $a^{ll,\mathrm
{W2}}_{\mu}(\mathrm{conn.}) = 100.7(3.2)\times 10^{-10}$, respectively. | hep-lat |
Study of the finite temperature transition in 3-flavor QCD using the R
and RHMC algorithms: We study the finite temperature transition in QCD with three flavors of equal
masses using the R and RHMC algorithm on lattices with temporal extent
N_{\tau}=4 and 6. For the transition temperature in the continuum limit we find
r_0 T_c=0.429(8) for the light pseudo-scalar mass corresponding to the end
point of the 1st order transition region. When comparing the results obtained
with the R and RHMC algorithms for p4fat3 action we see no significant
step-size errors down to a lightest pseudo-scalar mass of m_{ps} r_0=0.4. | hep-lat |
Fast Partitioning of Pauli Strings into Commuting Families for
Expectation Value Measurements of Dense Operators: The cost of measuring quantum expectation values of an operator can be
reduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of
the operator into maximally commuting sets. We detail an algorithm, presented
in [1], to partition the full set of $m$-qubit Pauli strings into the minimal
number of commuting families, and benchmark the performance with dense
Hamiltonians on IBM hardware. Here we also compare how our method scales
compared to graph-theoretic techniques for the generally commuting case. | hep-lat |
Domain-wall and overlap fermions at nonzero quark chemical potential: We have recently given a construction of the overlap Dirac operator at
nonzero quark chemical potential. Here, we introduce a quark chemical potential
in the domain-wall fermion formalism and show that our earlier result is
reproduced if the extent of the fifth dimension is taken to infinity and its
lattice spacing is taken to zero. We also extend this result to include a bare
quark mass, consider its continuum limit, and prove a number of properties of
the overlap operator at nonzero quark chemical potential. In particular, we
show that the relation between the anomaly and the index of the overlap
operator remains valid. | hep-lat |
Vacuum structure of gauge theory on lattice with two parallel plaquette
action: We perform Monte Carlo simulations of a lattice gauge system with an action
which contains two parallel plaquettes. The action is defined as a product of
gauge group variables over two parallel plaquettes belonging to a given
three-dimensional cube. The peculiar property of this system is that it has
strong degeneracy of the vacuum state inherited from corresponding gonihedric
$Z_2$ gauge spin system. These vacuua are well separated and can not be
connected by a gauge transformation. We measure different observables in these
vacuua and compare their properties. | hep-lat |
$Λ(1405)$ from lattice QCD: Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in two-flavor lattice
QCD. In order to extract two low-lying states for each parity, we construct $2
\times 2$ cross correlators from flavor SU(3) ``octet'' and ``singlet'' baryon
operators, and diagonalize them. Two-flavor CP-PACS gauge configurations are
employed, which are generated with the renormalization-group improved gauge
action and the ${\mathcal O}(a)$-improved quark action. Simulation are
performed at three different $\beta$'s, $\beta = 1.80$, 1.95 and 2.10, whose
corresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each
cutoff, we adopt four different hopping parameters, ($\kappa_{\rm val},
\kappa_{\rm sea}$). The corresponding pion masses range from about 500 MeV to
1.1 GeV. The results are extrapolated to the physical quark-mass point. Our
results indicate that there are two negative-parity $\Lambda$ states nearly
degenerate at around 1.6 GeV, whereas no state as low as $\Lambda (1405)$ is
observed. By extracting the flavor components of each state, we find that the
lowest (1st-excited) negative-parity state is dominated by flavor-singlet
(flavor-octet) component. | hep-lat |
Applying Integrability to Gauge Theories: Lattice Yang-Mills theories in any dimension may be regarded as coupled
1+1-dimensional integrable field theories. These integrable systems decouple at
large center-of-mass energies, where the action becomes effectively
anisotropic. This effective action is the high-energy center-of-mass limit of
the gauge theory. In 2+1 dimensions, the quark-antiquark potential and the mass
spectrum can be calculated, using the exact 1+1-dimensional S-matrix and form
factors. The methods are quite similar to those applying integrability in
statistical and condensed-matter physics. The high-energy anisotropic action at
one loop in 3+1 dimensions has been found using a Wilsonian renormalization
method. We briefly discuss the isotropic theory in 2+1 dimensions and the
connection with soft scattering in 3+1 dimensions. | hep-lat |
Flavor Twisted Boundary Conditions in the Breit Frame: We use a generalization of chiral perturbation theory to account for the
effects of flavor twisted boundary conditions in the Breit frame. The relevant
framework for two light flavors is an SU(6|4) partially quenched theory, where
the extra valence quarks differ only by their boundary conditions. Focusing on
the pion electromagnetic form factor, finite volume corrections are calculated
at next-to-leading order in the chiral expansion and are estimated to be small
on current lattices. | hep-lat |
Formal Developments for Lattice QCD with Applications to Hadronic
Systems: Lattice quantum chromodynamics (QCD) will soon become the primary theoretical
tool in rigorous studies of single- and multi-hadron sectors of QCD. It is
truly ab initio meaning that its only parameters are those of standard model.
The result of a lattice QCD calculation corresponds to that of nature only in
the limit when the volume of spacetime is taken to infinity and the spacing
between discretized points on the lattice is taken to zero. A better
understanding of these discretization and volume effects not only provides the
connection to the infinite-volume continuum observables, but also leads to
optimized calculations that can be performed with available computational
resources. This thesis includes various formal developments in this direction,
along with proposals for improvements, to be applied to the upcoming lattice
QCD studies of nuclear and hadronic systems. Among these developments are i) an
analytical investigation of the recovery of rotational symmetry with the use of
suitably-formed smeared operators toward the continuum limit, ii) an extension
of the Luscher finite-volume method to two-nucleon systems with arbitrary
angular momentum, spin, parity and center of mass momentum, iii) the
application of such formalism in extracting the scattering parameters of the
3S1-3D1 coupled channels, iv) an investigation of twisted boundary conditions
in the single- and two-hadron sectors, with proposals for improving the
volume-dependence of the deuteron binding energy upon proper choices of
boundary conditions, and v) exploring the volume dependence of the masses of
hadrons and light-nuclei due to quantum electrodynamic interactions, including
the effects arising from particles' compositeness. The required background as
well as a brief status report of the field pertinent to the discussions in this
thesis are presented. | hep-lat |
A Study of PCAC for the Nonperturbative Improvement of the Wilson Action: We present an exploratory study for the nonperturbative determination of the
coefficient of the ${\cal O}(a)$ improvement term to the Wilson action,
$c_{SW}$. Following the work by L\"{u}scher et al., we impose the PCAC relation
as a nonperturbative improvement condition on $c_{SW}$, without, however, using
the Schr\"{o}dinger functional in our calculation. | hep-lat |
Spectrum of the Hermitian Wilson Dirac operator: Recent results on the spectral properties of the Hermitian Wilson-Dirac
operator are presented. | hep-lat |
QCD Thermodynamics with an almost realistic quark mass spectrum: We will report on the status of a new large scale calculation of
thermodynamic quantities in QCD with light up and down quarks corresponding to
an almost physical light quark mass value and a heavier strange quark mass.
These calculations are currently being performed on the QCDOC Teraflops
computers at BNL. We will present new lattice calculations of the transition
temperature and various susceptibilities reflecting properties of the chiral
transition. All these quantities are of immediate interest for heavy ion
phenomenology. | hep-lat |
Moments of Ioffe time parton distribution functions from non-local
matrix elements: We examine the relation of moments of parton distribution functions to matrix
elements of non-local operators computed in lattice quantum chromodynamics. We
argue that after the continuum limit is taken, these non-local matrix elements
give access to moments that are finite and can be matched to those defined in
the $\overline{MS}$ scheme. We demonstrate this fact with a numerical
computation of moments through non-local matrix elements in the quenched
approximation and we find that these moments are in excellent agreement with
the moments obtained from direct computations of local twist-2 matrix elements
in the quenched approximation. | hep-lat |
B-Bbar Mixing and Matching with Fermilab Heavy Quarks: We discuss the matching procedure for heavy-light 4-quark operators using the
Fermilab method for heavy quarks and staggered fermions for light quarks. These
ingredients enable us to construct the continuum-limit operator needed to
determine the oscillation frequency of neutral B mesons. The matching is then
carried out at the one-loop level. We also present an updated preliminary
result for the SU(3)-breaking ratio \xi, based on calculations using the MILC
Collaboration's ensembles of lattice gauge fields. | hep-lat |
A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional
Quantum Gravity: We perform Monte Carlo simulations using the Wolff cluster algorithm of the
q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of
spherical topology with up to 5000 nodes. We find that the measured critical
exponents are in reasonable agreement with those from the exact solution of the
Ising model and with those calculated from KPZ scaling for q=3,4 where no exact
solution is available. Using Binder's cumulant we find that the q=10 Potts
model displays a first order phase transition on a dynamical graph, as it does
on a fixed lattice. We also examine the internal geometry of the graphs
generated in the simulation, finding a linear relationship between ring length
probabilities and the central charge of the Potts model | hep-lat |
Relativistic Lattice Boltzmann Methods: Theory and Applications: We present a systematic account of recent developments of the relativistic
Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in
full detail a unified, compact and dimension-independent procedure to design
relativistic LB schemes capable of bridging the gap between the
ultra-relativistic regime, $k_{\rm B} T \gg mc^2$, and the non-relativistic
one, $k_{\rm B} T \ll mc^2$. We further develop a systematic derivation of the
transport coefficients as a function of the kinetic relaxation time in
$d=1,2,3$ spatial dimensions. The latter step allows to establish a
quantitative bridge between the parameters of the kinetic model and the
macroscopic transport coefficients. This leads to accurate calibrations of
simulation parameters and is also relevant at the theoretical level, as it
provides neat numerical evidence of the correctness of the Chapman-Enskog
procedure. We present an extended set of validation tests, in which simulation
results based on the RLBMs are compared with existing analytic or semi-analytic
results in the mildly-relativistic ($k_{\rm B} T \sim mc^2$) regime for the
case of shock propagations in quark-gluon plasmas and laminar electronic flows
in ultra-clean graphene samples. It is hoped and expected that the material
collected in this paper may allow the interested readers to reproduce the
present results and generate new applications of the RLBM scheme. | hep-lat |
Improved thermodynamics of SU(2) gauge theory: In this work we present the results of our investigation about the
thermodynamics of SU(2) gauge theory. We employ a Symanzik improved action to
reduce strongly the discretisations effects, and we use the scaling relations
to take into account the finite volume effects close to the critical
temperature. We determine the beta-function for this particular theory and we
use it in the determination of different thermodynamic observables. Finally we
compare our results with previous works where only the standard Wilson action
was considered. We confirm the relevance of using the improved action to access
easily the correct continuum thermodynamics of the theory. | hep-lat |
Three dimensional vacuum domains in four dimensional SU(2) gluodynamics: 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. | hep-lat |
$|V_{cb}|$ using lattice QCD: Lattice QCD calculations of hadronic matrix elements allow one to draw
inferences about quark flavor interactions from measurements of hadron decays.
Within the context of the Standard Model, the magnitude of the charm-bottom
quark coupling $V_{cb}$ can be determined from semileptonic decays such as
$B\to D^{(*)}\ell\nu$. This brief review summarizes the present status and
short-term outlook for determining $|V_{cb}|$ using lattice QCD. | hep-lat |
A no-go theorem for the Majorana fermion on a lattice: 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. | hep-lat |
N=1 super Yang-Mills on the lattice: We present results from a numerical study of N=1 supersymmetric Yang-Mills
theory using domain wall fermions. A set of dynamical simulations were
performed for the gauge group SU(2) using the Wilson gauge action on 8^3x8 and
16^3x32 lattices. We considered a range of gluino masses (i.e., fifth dimension
extents L_s=16-28 and input gluino mass values m_f=0.01-0.04) in order to
perform chiral limit extrapolations of physical quantities. In these
proceedings, we summarize our findings from a study of the Dirac spectrum and
present new results for the topological charge on beta=2.3, 2.353 and 2.4
ensembles. | hep-lat |
Spectral Functions of Hadrons in Lattice QCD: Using the maximum entropy method, spectral functions of the pseudo-scalar and
vector mesons are extracted from lattice Monte Carlo data of the imaginary time
Green's functions. The resonance and continuum structures as well as the ground
state peaks are successfully obtained. Error analysis of the resultant spectral
functions is also given on the basis of the Bayes probability theory. | hep-lat |
Determination of the renormalized heavy-quark mass in Lattice QCD: We study on the lattice the correlator of heavy-quark currents in the
vicinity of vanishing momentum. The renormalized charmed quark mass, the
renormalized strong coupling constant and gluon condensate can be defined in
terms of the derivatives of that correlator at zero momentum. We analyze
quenched Monte-Carlo data on a small lattice $8^3*16$ for $\beta=6$. We
generalize dispersion relations to the lattice theory in a simple way and use
them successfully to fit the correlator at both small and large distances. We
fit the short-distance part of the correlator with the relevant expressions of
perturbative QCD on the lattice and obtain the value of the renormalized quark
mass $m_c^{\bar{MS}}(m_c)\,=\,1.20(4)\,GeV$. | hep-lat |
Field Theory Simulations on a Fuzzy Sphere - an Alternative to the
Lattice: We explore a new way to simulate quantum field theory, without introducing a
spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4
model. The regularisation consists of a fuzzy sphere with radius R for the two
spatial directions, plus a discrete Euclidean time. The fuzzy sphere
approximates the algebra of functions of the sphere with a matrix algebra, and
the scalar field is represented by a Hermitian N x N matrix at each time site.
We evaluate the phase diagram, where we find a disordered phase and an ordered
regime, which splits into phases of uniform and non-uniform order. We discuss
the behaviour of the model in different limits of large N and R, which lead to
a commutative or to a non-commutative \lambda \phi^4 model in flat space. | hep-lat |
Lattice QCD calculation of hadronic light-by-light scattering: We perform a lattice QCD calculation of the hadronic light-by-light
scattering amplitude in a broad kinematical range. At forward kinematics, the
results are compared to a phenomenological analysis based on dispersive sum
rules for light-by-light scattering. The size of the pion pole contribution is
investigated for momenta of typical hadronic size. The presented numerical
methods can be used to compute the hadronic light-by-light contribution to the
anomalous magnetic moment of the muon. Our calculations are carried out in
two-flavor QCD with the pion mass in the range of 270 to 450MeV, and contain so
far only the diagrams with fully connected quark lines. | hep-lat |
Multigrid for Chiral Lattice Fermions: Domain Wall: Critical slowing down for the Krylov Dirac solver presents a major obstacle
to further advances in lattice field theory as it approaches the continuum
solution. We propose a new multi-grid approach for chiral fermions, applicable
to both the 5-d domain wall or 4-d Overlap operator. The central idea is to
directly coarsen the 4-d Wilson kernel, giving an effective domain wall or
overlap operator on each level. We provide here an explicit construction for
the Shamir domain wall formulation with numerical tests for the 2-d Schwinger
prototype, demonstrating near ideal multi-grid scaling. The framework is
designed for a natural extension to 4-d lattice QCD chiral fermions, such as
the M\"obius, Zolotarev or Borici domain wall discretizations or directly to a
rational expansion of the 4-d Overlap operator. For the Shamir operator, the
effective overlap operator is isolated by the use of a Pauli-Villars
preconditioner in the spirit of the K\"ahler-Dirac spectral map used in a
recent staggered MG algorithm [1]. | hep-lat |
Effective Monopole Potential for SU(2) Lattice Gluodynamics in Spatial
Maximal Abelian Gauge: We investigate the dual superconductor hypothesis in finite-temperature SU(2)
lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more
physical than the ordinary Maximal Abelian gauge due to absence of
non-localities in temporal direction. We show numerically that in the Spatial
Maximal Abelian gauge the probability distribution of the abelian monopole
field is consistent with the dual superconductor mechanism of confinement: the
abelian condensate vanishes in the deconfinement phase and is not zero in the
confinement phase. | hep-lat |
Finite-volume effects in long-distance processes with massless leptonic
propagators: In Ref. [1], a method was proposed to calculate QED corrections to hadronic
self energies from lattice QCD without power-law finite-volume errors. In this
paper, we extend the method to processes which occur at second-order in the
weak interaction and in which there is a massless (or almost massless) leptonic
propagator. We demonstrate that, in spite of the presence of the propagator of
an almost massless electron, such an infinite-volume reconstruction procedure
can be used to obtain the amplitude for the rare kaon decay
$K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with
only exponentially small finite-volume corrections. | hep-lat |
Dirac sheets and gauge fixing in $U(1)$ lattice gauge theory: Photon correlators in $~U(1)~$ pure gauge theory for different lattice
actions are considered under the Lorentz gauge condition. They are shown to
depend strongly on the gauge fixing ambiguity and on the corresponding
existence of Dirac sheets. For the Coulomb phase a gauge fixing algorithm is
proposed which avoids Dirac sheets and allows to find the global extremum of
the non-local gauge condition. Sorry, figures are not included and can be sent
by ordinary mail. | hep-lat |
Non-Perturbative Gauge-Higgs Unification in Five Dimensions: We study the phase diagram and mass spectrum of an $SU(2)$ Gauge-Higgs
Unification scenario on a five-dimensional orbifold.We observe spontaneous
symmetry breaking within the Higgs phase of the theory and, in the vicinity of
a newly discovered phase, we find that the ratio of Higgs to gauge boson masses
takes a Standard Model-like value. Precisely in this region of the phase
diagram, we observe dimensional reduction via localisation. | hep-lat |
Models of Walking Technicolor on the Lattice: We study QCD with 2 colour-sextet quarks as a walking-Technicolor candidate.
As such it provides a description of the Higgs sector of the standard model, in
which the Higgs field is replaced by the Goldstone `pions' of this QCD-like
theory, and the Higgs itself is the $\sigma$. Such a theory will need to be
extended if it is to also give masses to the quarks and leptons. What we are
attempting to determine is whether it is indeed QCD-like and hence walking, or
if it has an infrared fixed point making it a conformal field theory. We do
this by simulating its lattice version at finite temperature and observing the
running of the bare (lattice) coupling at the chiral transition, as the lattice
spacing is varied, and comparing this running with that predicted by 2-loop
perturbation theory. Our results on lattices with temporal extents ($N_t$) up
to 12 indicate that the coupling runs, but not as fast as asymptotic freedom
predicts. We discuss our program for studying the zero-temperature
phenomenology of this theory. | hep-lat |
Lattice study of the simplified model of M-theory for larger gauge
groups: Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is
dis cussed. First results of the quenched Monte Carlo simulations, for D=4 and
with higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier
(N=2) evidence tha t the system reveals different behaviours at low and high
temperatures separated by a narrow transiti on region. These two regimes may
correspond to a black hole and elementary excitations phases conjectured in the
M-theory. Dependence of the "transition temperature" on N is consistent with 't
Hooft scaling and shows a smooth saturation of lattice results towards the
large N limit. Is not yet resolved if the observed change between the two
regimes corresponds to a genuine phase transition or to a gentle crossover . A
new, noncompact formulation of the lattice model is also proposed and its
advantages are briefly discussed. | hep-lat |
SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons: We present results for the $SU(3)$ breaking ratios of decay constants
$f_{D_s}/f_D$ and $f_{B_s}/f_B$ and - for the first time with physical pion
masses - the ratio of bag parameters $B_{B_s}/B_{B_d}$, as well as the ratio
$\xi$, forming the ratio of the nonpeturbative contributions to neutral
$B_{(s)}$ meson mixing. Our results are based on Lattice QCD simulations with
chirally symmetric 2+1 dynamical flavors of domain wall fermions. Eight
ensembles at three different lattice spacing in the range $a = 0.11 -
0.07\,\mathrm{fm}$ enter the analysis two of which feature physical light quark
masses. Multiple heavy quark masses are simulated ranging from below the charm
quark mass to half the bottom quark mass. The $SU(3)$ breaking ratios display a
very benign heavy mass behaviour allowing for extrapolation to the physical
bottom quark mass. The results in the continuum limit including all sources of
systematic errors are $f_{D_s}/f_D =
1.1740(51)_\mathrm{stat}(^{+68}_{-68})_\mathrm{sys}$, $f_{B_s}/f_B =
1.1949(60)_\mathrm{stat}(^{+\hphantom{0}95}_{-175})_\mathrm{sys}$,
$B_{B_s}/B_{B_d} = 0.9984(45)_\mathrm{stat}(^{+80}_{-63})_\mathrm{sys}$ and
$\xi = 1.1939(67)_\mathrm{stat}(^{+\hphantom{0}95}_{-177})_\mathrm{sys}$.
Combining these with experimentally measured values we extract the ratios of
CKM matrix elements $|V_{cd}/V_{cs}| =
0.2164(57)_\mathrm{exp}(^{+12}_{-12})_\mathrm{lat}$ and $|V_{td}/V_{ts}| =
0.20329(41)_\mathrm{exp}(^{+162}_{-301})_\mathrm{lat}$. | hep-lat |
Euclidean lattice simulation for the dynamical supersymmetry breaking: The global supersymmetry is spontaneously broken if and only if the
ground-state energy is strictly positive. We propose to use this fact to
observe the spontaneous supersymmetry breaking in euclidean lattice
simulations. For lattice formulations that possess a manifest fermionic
symmetry, there exists a natural choice of a hamiltonian operator that is
consistent with a topological property of the Witten index. We confirm validity
of our idea in models of the supersymmetric quantum mechanics. We then examine
a possibility of a dynamical supersymmetry breaking in the two-dimensional
$\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\SU(2)$, for
which the Witten index is unknown. Differently from a recent conjectural claim,
our numerical result tempts us to conclude that supersymmetry is not
spontaneously broken in this system. | hep-lat |
Staggered domain wall fermions: Staggered Domain Wall Fermions (SDWF) combine the attractive chiral
properties of staggered fermions with those of domain wall fermions. SDWF
describe four flavors with exact U(1)xU(1) flavor chiral symmetry. An extra
lattice dimension is introduced and the full SU(4)xSU(4) flavor chiral symmetry
is recovered as its size is increased. Here, the free theory of SDWF is
described and a preliminary discussion of the interacting case is presented.
SDWF may be well suited for numerical simulation of lattice QCD thermodynamics. | hep-lat |
I=2 $π$-$π$ scattering length with dynamical overlap fermion: We report on a lattice QCD calculation of the I=2 $\pi\pi$ scattering length
using the overlap fermion formulation for both sea and valence quarks. We
investigate the consistency of the lattice data with the prediction of the
next-to-next-to-leading order chiral perturbation theory after correcting
finite volume effects. The calculation is performed on gauge ensembles of
two-flavor QCD generated by the JLQCD collaboration on a $16^3\times 32$
lattice at a lattice spacing $\sim$ 0.12 fm. | hep-lat |
Role of chiral symmetry in the nucleon excitation spectrum: The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has
been the subject of significant interest for many years, including several
investigations using lattice QCD. The majority of lattice studies have not
observed a low-lying excited state energy level in the region of the Roper
resonance. However, it has been claimed that chiral symmetry could play an
important role in our understanding of this resonance. The purpose of this
study is to systematically examine the role of chiral symmetry in the low-lying
nucleon spectrum by directly comparing the clover and overlap fermion actions.
To ensure any differences in results are attributable to the choice of fermion
action, simulations are performed on the same set of gauge field configurations
at matched pion masses. Correlation matrix techniques are employed to determine
the excitation energy of the first positive-parity excited state for each
action. The clover and overlap actions show a remarkable level of agreement. We
do not find any evidence that fermion action chiral symmetry plays a
significant role in understanding the Roper resonance on the lattice. | hep-lat |
Matching effective chiral Lagrangians with dimensional and lattice
regularization: We compute the free energy in the presence of a chemical potential coupled to
a conserved charge in effective O($n$) scalar field theory (without explicit
symmetry breaking terms) to NNL order for asymmetric volumes in general
$d$--dimensions, using dimensional (DR) and lattice regularizations. This
yields relations between the 4-derivative couplings appearing in the effective
actions for the two regularizations, which in turn allows us to translate
results, e.g. the mass gap in a finite periodic box in $d=3+1$ dimensions, from
one regularization to the other. Consistency is found with a new direct
computation of the mass gap using DR. For the case $n=4, d=4$ the model is the
low-energy effective theory of QCD with $N_{\rm f}=2$ massless quarks. The
results can thus be used to obtain estimates of low energy constants in the
effective chiral Lagrangian from measurements of the low energy observables,
including the low lying spectrum of $N_{\rm f}=2$ QCD in the $\delta$--regime
using lattice simulations, as proposed by Peter Hasenfratz, or from the
susceptibility corresponding to the chemical potential used. | hep-lat |
2+1 Flavor QCD simulated in the epsilon-regime in different topological
sectors: We generated configurations with the parametrized fixed-point Dirac operator
D_{FP} on a (1.6 fm)^4 box at a lattice spacing a=0.13 fm. We compare the
distributions of the three lowest k=1,2,3 eigenvalues in the nu= 0,1,2
topological sectors with that of the Random Matrix Theory predictions. The
ratios of expectation values of the lowest eigenvalues and the cumulative
eigenvalue distributions are studied for all combinations of k and nu. After
including the finite size correction from one-loop chiral perturbation theory
we obtained for the chiral condensate in the MSbar scheme
Sigma(2GeV)^{1/3}=0.239(11) GeV, where the error is statistical only. | hep-lat |
Calculation of $ρ$ meson decay width from the PACS-CS configurations: We present preliminary results on the $\rho$ meson decay width from $N_f=2+1$
full QCD configurations generated by PACS-CS Collaboration. The decay width is
estimated from the $P$-wave scattering phase shift for the isospin $I=1$
two-pion system. The finite size formula presented by L\"uscher in the center
of mass frame and its extension to non-zero total momentum frame by Rummukainen
and Gottlieb are employed for the calculations of the phase shift. Our
calculations are carried out at $m_\pi=410\ {\rm MeV}$ ($m_\pi/m_\rho=0.46$)
and $a=0.091\ {\rm fm}$ on a $32^3\times 64$ ($La=2.9 {\rm fm}$) lattice. | hep-lat |
Non-perturbative renormalisation of left-left four-fermion operators
with Neuberger fermions: We outline a general strategy for the non-perturbative renormalisation of
composite operators in discretisations based on Neuberger fermions, via a
matching to results obtained with Wilson-type fermions. As an application, we
consider the renormalisation of the four-quark operators entering the Delta S=1
and Delta S=2 effective Hamiltonians. Our results are an essential ingredient
for the determination of the low-energy constants governing non-leptonic kaon
decays. | hep-lat |
Transversity PDFs of the proton from lattice QCD with physical quark
masses: We present a lattice QCD calculation of the transversity isovector- and
isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a
perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we
determine the isovector and isoscalar tensor charges for the proton. In both
calculations, the disconnected contributions to the isoscalar matrix elements
have been ignored. The calculations are performed using a single ensemble of
$N_f = 2 +1$ highly-improved staggered quarks simulated with physical-mass
quarks and a lattice spacing of $a = 0.076$ fm. The Wilson-clover action, with
physical quark masses and smeared gauge links obtained from one iteration of
hypercubic (HYP) smearing, is used in the valence sector. Using the NLO
operator product expansion, we extract the lowest four to six Mellin moments
and the PDFs from the matrix elements via a neural network. In addition, we
calculate the $x$-dependence of the PDFs with hybrid-scheme renormalization and
the recently developed leading-renormalon resummation technique, at NLO with
the resummation of leading small-$x$ logarithms. | hep-lat |
Influence of Fermions on Vortices in SU(2)-QCD: Gauge fields control the dynamics of fermions, also a back reaction of
fermions on the gauge field is expected. This back reaction is investigated
within the vortex picture of the QCD vacuum. We show that the center vortex
model reproduces the string tension of the full theory also with the presence
of fermionic fields. | hep-lat |
Provenance for Lattice QCD workflows: We present a provenance model for the generic workflow of numerical Lattice
Quantum Chromodynamics (QCD) calculations, which constitute an important
component of particle physics research. These calculations are carried out on
the largest supercomputers worldwide with data in the multi-PetaByte range
being generated and analyzed. In the Lattice QCD community, a custom metadata
standard (QCDml) that includes certain provenance information already exists
for one part of the workflow, the so-called generation of configurations.
In this paper, we follow the W3C PROV standard and formulate a provenance
model that includes both the generation part and the so-called measurement part
of the Lattice QCD workflow. We demonstrate the applicability of this model and
show how the model can be used to answer some provenance-related research
questions. However, many important provenance questions in the Lattice QCD
community require extensions of this provenance model. To this end, we propose
a multi-layered provenance approach that combines prospective and retrospective
elements. | hep-lat |
Complete Monopole Dominance of the Yang-Mills Confining Potential: We continue our investigation of quark confinement using a particular variant
of the Cho-Duan-Ge gauge independent Abelian decomposition. The decomposition
splits the gauge field into a restricted Abelian part and a coloured part in a
way that preserves gauge covariance. The restricted part of the gauge field can
be divided into a Maxwell term and a topological term. Previously, we showed
that by a particular choice of this decomposition we could fully describe the
confining potential using only the restricted gauge field. We proposed that
various topological objects (a form of magnetic monopole) could arise in the
restricted field which would drive confinement. Our mechanism does not
explicitly refer to a dual Meissner effect, nor does it use centre vortices. We
did not need to gauge fix or introduce any new dynamical fields.
We show that if we do gauge fix as well as performing the Abelian
decomposition then it is possible to ensure that the topological part of the
restricted field fully accounts for the confining potential. Our relationship
is exact: there is no approximation or model involved. This isolates the
objects responsible for confinement from non-confining contributions to the
gauge field, allowing a direct search for our proposed topological objects.
Using numerical studies in SU(2), we confirm that our proposed monopoles are
present in the field, and the winding number associated with these monopoles is
a key factor driving quark confinement.
In SU(2), our monopoles are described by two parameters. We show that it is
possible to re-parametrise the Yang Mills action and the functional integration
measure in terms of these variables (plus the necessary additional parameters).
We can thus treat the monopoles as dynamical variables in the functional
integral. This might be the first step in a future analytical computation to
complement our numerical results. | hep-lat |
Quarkonium mass splittings in three-flavor lattice QCD: We report on calculations of the charmonium and bottomonium spectrum in
lattice QCD. We use ensembles of gauge fields with three flavors of sea quarks,
simulated with the asqtad improved action for staggered fermions. For the heavy
quarks we employ the Fermilab interpretation of the clover action for Wilson
fermions. These calculations provide a test of lattice QCD, including the
theory of discretization errors for heavy quarks. We provide, therefore, a
careful discussion of the results in light of the heavy-quark effective
Lagrangian. By and large, we find that the computed results are in agreement
with experiment, once parametric and discretization errors are taken into
account. | hep-lat |
Linear Covariant Gauges on the Lattice: Linear covariant gauges, such as Feynman gauge, are very useful in
perturbative calculations. Their nonperturbative formulation is, however,
highly non-trivial. In particular, it is a challenge to define linear covariant
gauges on a lattice. We consider a class of gauges in lattice gauge theory that
coincides with the perturbative definition of linear covariant gauges in the
formal continuum limit. The corresponding gauge-fixing procedure is described
and analyzed in detail, with an application to the pure SU(2) case. In
addition, results for the gluon propagator in the two-dimensional case are
given. | hep-lat |
Hyperon sigma terms for 2+1 quark flavours: QCD lattice simulations determine hadron masses as functions of the quark
masses. From the gradients of these masses and using the Feynman-Hellmann
theorem the hadron sigma terms can then be determined. We use here a novel
approach of keeping the singlet quark mass constant in our simulations which
upon using an SU(3) flavour symmetry breaking expansion gives highly
constrained (i.e. few parameter) fits for hadron masses in a multiplet. This is
a highly advantageous procedure for determining the hadron mass gradient as it
avoids the use of delicate chiral perturbation theory. We illustrate the
procedure here by estimating the light and strange sigma terms for the baryon
octet. | hep-lat |
Towards an algebraic approach to the discretisation of fermions: A discretisation scheme for differential geometry is applied to the problem
of constructing lattice actions, the naive and staggered action are thus
derived. It is found that after specifying an ansatz for the space of fields,
the corresponding lattice action is obtained. The gauging procedure, and the
applicability of the method to twisted super-symmetry on a lattice is outlined.
Some comments on the QED axial anomaly are made, for the theory in which the
lattice projection operator is not inserted. | hep-lat |
Improved Perturbation Theory for Improved Lattice Actions: We study a systematic improvement of perturbation theory for gauge fields on
the lattice; the improvement entails resumming, to all orders in the coupling
constant, a dominant subclass of tadpole diagrams.
This method, originally proposed for the Wilson gluon action, is extended
here to encompass all possible gluon actions made of closed Wilson loops; any
fermion action can be employed as well. The effect of resummation is to replace
various parameters in the action (coupling constant, Symanzik coefficients,
clover coefficient) by ``dressed'' values; the latter are solutions to certain
coupled integral equations, which are easy to solve numerically.
Some positive features of this method are: a) It is gauge invariant, b) it
can be systematically applied to improve (to all orders) results obtained at
any given order in perturbation theory, c) it does indeed absorb in the dressed
parameters the bulk of tadpole contributions.
Two different applications are presented: The additive renormalization of
fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector
(axial) current. In many cases where non-perturbative estimates of
renormalization functions are also available for comparison, the agreement with
improved perturbative results is significantly better as compared to results
from bare perturbation theory. | hep-lat |
High-accuracy two-loop computation of the critical mass for Wilson
fermions: We test an algebraic algorithm based on the coordinate-space method,
evaluating with high accuracy the critical mass for Wilson fermions in lattice
QCD at two loops. We test the results by using different types of infrared
regularization. | hep-lat |
Duality and scaling in 3-dimensional scalar electrodynamics: Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry,
is believed to be dual to a scalar theory with a global U(1) symmetry, near the
phase transition point. The conjectured duality leads to definite predictions
for the scaling exponents of the gauge theory transition in the type II region,
and allows thus to be scrutinized empirically. We review these predictions, and
carry out numerical lattice Monte Carlo measurements to test them: a number of
exponents, characterising the two phases as well as the transition point, are
found to agree with expectations, supporting the conjecture. We explain why
some others, like the exponent characterising the photon correlation length,
appear to disagree with expectations, unless very large system sizes and the
extreme vicinity of the transition point are considered. Finally, we remark
that in the type I region the duality implies an interesting quantitative
relationship between a magnetic flux tube and a 2-dimensional non-topological
soliton. | hep-lat |
Neutron Electric Dipole Moment on the Lattice: a Theoretical Reappraisal: We present a strategy for a lattice evaluation of the neutron electric dipole
moment induced by the strong CP violating term of the QCD Lagrangian. Our
strategy is based on the standard definition of the electric dipole moment,
involving the charge density operator J0, in case of three flavors with
non-degenerate masses. We present a complete diagrammatic analysis showing how
the axial chiral Ward identities can be used to replace the opological charge
operator with the flavor-singlet pseudoscalar density PS. Our final result is
characterized only by disconnected diagrams, where the disconnected part can be
either the single insertion of PS or the separate insertions of both PS and J0.
The applicability of our strategy to the case of lattice formulations that
explicitly break chiral symmetry, like the Wilson and Clover actions, is
discussed. | hep-lat |
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