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Wave functions of $SU(3)$ pure gauge glueballs on the lattice: The Bethe-Salpeter wave functions of $SU(3)$ pure gauge glueballs are
revisited in this study. The ground and the first excited states of scalar and
tensor glueballs are identified unambiguously by using the variational method
on the basis of large operator sets. We calculate their wave functions in the
Coulomb gauge and use two lattices with different lattice spacings to check the
discretization artifacts. For ground states, the radial wave functions are
approximately Gaussian and the size of the tensor is twice as large as that of
the scalar. For the first excited states, the radial nodes are clearly observed
for both the scalar and the tensor glueballs, such that they can be interpreted
as the first radial excitations. These observations may shed light on the
theoretical understanding of the inner structure of glueballs. | hep-lat |
Is there any gender/race bias in hep-lat primary publication?
Machine-Learning Evaluation of Author Ethnicity and Gender: In this work, we analyze papers that are classified as primary hep-lat to
study whether there is any race or gender bias in the journal-publication
process. We implement machine learning to predict the race and gender of
authors based on their names and look for measurable differences between
publication outcomes based on author classification. We would like to invite
discussion on how journals can make improvements in their editorial process and
how institutions or grant offices should account for these publication
differences in gender and race. | hep-lat |
Euclidean partons?: In this talk we reexamine the possibility of evaluating parton distribution
functions from lattice simulations. We show that, while in principle individual
moments can be extracted from lattice data, in all cases the process of
renormalization, hindered by lattice momenta limitation, represents an
obstruction to a direct calculation of the full parton distribution function
from QCD simulations. We discuss the case of the Ji quasi-parton distribution
functions, the possibility of using the reduced Ioffe-time distributions and
the more recent proposal of directly subtracting power divergent mixings in
perturbation theory. | hep-lat |
$|V_{ub}|$ determination in lattice QCD: The 2012 PDG reports a tension at the level of $3 \sigma$ between two
exclusive determinations of $|V_{ub}|$. They are obtained by combining the
experimental branching ratios of $B \to \tau \nu$ and $B \to \pi l \nu$
(respectively) with a theoretical computation of the hadronic matrix elements
$\fB$ and the $B \to \pi$ form factor $f_+(q^2)$. To understand the tension,
improved precision and a careful analysis of the systematics involved are
necessary. We report the results of the ALPHA collaboration for $\fB$ from the
lattice with 2 flavors of $O(a)$ improved Wilson fermions. We employ HQET,
including $1/m_b$ corrections, with pion masses ranging down to $\approx$ 190
MeV. Renormalization and matching were performed non-perturbatively, and three
lattice spacings reaching $a^{-1}\approx 4.1$ GeV are used in the continuum
extrapolation. We also present progress towards a computation of $f_+(q^2)$, to
directly compare two independent exclusive determinations of $|V_{ub}|$ with
each other and with inclusive determinations. Additionally, we report on
preliminary results for $\fBq{s}$, needed for the analysis of $B_s \to
\mu^+\mu^-$.} | hep-lat |
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the
Lattice: L\"uscher's recent formulation of Abelian chiral gauge theories on the
lattice, in the vacuum (or perturbative) sector in infinite volume, is
reinterpreted in terms of the lattice covariant regularization. The gauge
invariance of the effective action and the integrability of the gauge current
in anomaly-free cases become transparent. The real part of the effective action
is simply one-half that of the Dirac fermion and, when the Dirac operator
behaves properly in the continuum limit, the imaginary part in this limit
reproduces the $\eta$-invariant. | hep-lat |
Comment on Implications of new physics in the decays $B_c \to
(J/ψ,η_c)τν$: As part of a study BSM corrections to leptonic decays of the $B_c$ meson,
Tran et al. (arXiv:1801.06927) use the covariant confining quark model (CCQM)
to estimate the matrix element of the pseudo-scalar curent between the vacuum
and the $B_c$ meson. We note that this matrix element can be determined using
existing lattice QCD results. | hep-lat |
Gauge-invariant nonlocal quark condensates in QCD: We study, by numerical simulations on a lattice, the behaviour of the
gauge-invariant nonlocal quark condensates in the QCD vacuum both in the
quenched approximation and with four flavours of dynamical staggered fermions.
The correlation length of the condensate is determined to be roughly twice as
big as in the case of the gluon field strength correlators. | hep-lat |
Electromagnetic structure of charmed baryons in Lattice QCD: As a continuation of our recent work on the electromagnetic properties of the
doubly charmed $\Xi_{cc}$ baryon, we compute the charge radii and the magnetic
moments of the singly charmed $\Sigma_c$, $\Omega_c$ and the doubly charmed
$\Omega_{cc}$ baryons in 2+1 flavor Lattice QCD. In general, the charmed
baryons are found to be compact as compared to the proton. The charm quark acts
to decrease the size of the baryons to smaller values. We discuss the mechanism
behind the dependence of the charge radii on the light valence- and sea-quark
masses. The magnetic moments are found to be almost stable with respect to
changing quark mass. We investigate the individual quark sector contributions
to the charge radii and the magnetic moments. The magnetic moments of the
singly charmed baryons are found to be dominantly determined by the light quark
and the role of the charm quark is significantly enhanced for the doubly
charmed baryons. | hep-lat |
Nonperturbative Collins-Soper Kernel from Chiral Quarks with Physical
Masses: We present a lattice QCD calculation of the rapidity anomalous dimension of
quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS)
kernel, up to transverse separations of about 1 fm. This unitary lattice
calculation is conducted, for the first time, employing the
chiral-symmetry-preserving domain wall fermion discretization and physical
values of light and strange quark masses. The CS kernel is extracted from the
ratios of pion quasi-transverse-momentum-dependent wave functions
(quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. Also for
the first time, we utilize the recently proposed Coulomb-gauge-fixed
quasi-TMDWF correlator without a Wilson line. We observe significantly slower
signal decay with increasing quark separations compared to the established
gauge-invariant method with a staple-shaped Wilson line. This enables us to
determine the CS kernel at large nonperturbative transverse separations and
find its near-linear dependence on the latter. Our result is consistent with
the recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees
with various recent phenomenological parametrizations of experimental data. | hep-lat |
Hadron Structure and Form Factors: We review recent results on hadron form factors and nucleon generalized
parton distibutions obtained with dynamical lattice QCD simulations. We discuss
lattice artifacts and open questions, and present the connection of lattice
results to hadron structure and to the corresponding quantities measured in
experiment. | 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 |
Is SU(3) gauge theory with 13 massless flavors conformal?: We use lattice simulations to study SU(3) gauge theory with 13 massless
fermions in the fundamental representation. We present evidence that the theory
is conformal with a non-zero infrared fixed point in the gauge coupling. We use
a newly-developed technique to calculate the mass anomalous dimension at the
fixed point via step-scaling of the mode number, allowing us to take the
continuum limit and compare to perturbative predictions. We comment on the
relevance of these findings to the extended search for the conformal window in
the fundamental representation and in particular 12 massless flavors. | hep-lat |
Automatic differentiation for error analysis: We present ADerrors.jl, a software for linear error propagation and analysis
of Monte Carlo data. Although the focus is in data analysis in Lattice QCD,
where estimates of the observables have to be computed from Monte Carlo
samples, the software also deals with variables with uncertainties, either
correlated or uncorrelated. Thanks to automatic differentiation techniques
linear error propagation is performed exactly, even in iterative algorithms
(i.e. errors in parameters of non-linear fits). In this contribution we present
an overview of the capabilities of the software, including access to
uncertainties in fit parameters and dealing with correlated data. The software,
written in julia, is available for download and use in
https://gitlab.ift.uam-csic.es/alberto/aderrors.jl | hep-lat |
Lattice QCD Determination of $g_A$: The nucleon axial coupling, $g_A$, is a fundamental property of protons and
neutrons, dictating the strength with which the weak axial current of the
Standard Model couples to nucleons, and hence, the lifetime of a free neutron.
The prominence of $g_A$ in nuclear physics has made it a benchmark quantity
with which to calibrate lattice QCD calculations of nucleon structure and more
complex calculations of electroweak matrix elements in one and few nucleon
systems. There were a number of significant challenges in determining $g_A$,
notably the notorious exponentially-bad signal-to-noise problem and the
requirement for hundreds of thousands of stochastic samples, that rendered this
goal more difficult to obtain than originally thought.
I will describe the use of an unconventional computation method, coupled with
"ludicrously'" fast GPU code, access to publicly available lattice QCD
configurations from MILC and access to leadership computing that have allowed
these challenges to be overcome resulting in a determination of $g_A$ with 1%
precision and all sources of systematic uncertainty controlled. I will discuss
the implications of these results for the convergence of $SU(2)$ Chiral
Perturbation theory for nucleons, as well as prospects for further improvements
to $g_A$ (sub-percent precision, for which we have preliminary results) which
is part of a more comprehensive application of lattice QCD to nuclear physics.
This is particularly exciting in light of the new CORAL supercomputers coming
online, Sierra and Summit, for which our lattice QCD codes achieve a
machine-to-machine speed up over Titan of an order of magnitude. | hep-lat |
SPHERICALLY SYMMETRIC RANDOM WALKS I. REPRESENTATION IN TERMS OF
ORTHOGONAL POLYNOMIALS: Spherically symmetric random walks in arbitrary dimension $D$ can be
described in terms of Gegenbauer (ultraspherical) polynomials. For example,
Legendre polynomials can be used to represent the special case of
two-dimensional spherically symmetric random walks. In general, there is a
connection between orthogonal polynomials and semibounded one-dimensional
random walks; such a random walk can be viewed as taking place on the set of
integers $n$, $n=0,~1,~2,~\ldots$, that index the polynomials. This connection
allows one to express random-walk probabilities as weighted inner products of
the polynomials. The correspondence between polynomials and random walks is
exploited here to construct and analyze spherically symmetric random walks in
$D$-dimensional space, where $D$ is {\sl not} restricted to be an integer. The
weighted inner-product representation is used to calculate exact closed-form
spatial and temporal moments of the probability distribution associated with
the random walk. The polynomial representation of spherically symmetric random
walks is also used to calculate the two-point Green's function for a
rotationally symmetric free scalar quantum field theory. | hep-lat |
Determinant of a new fermionic action on a lattice - (II): We investigate the fermion determinant of a new action on a
$(1+D)$-dimensional lattice for SU(2) gauge groups. This action possesses the
discrete chiral symmetry and provides $2^D$-component fermions. We also comment
on the numerical results on fermion determinants in the $(1+D)$-dimensional
SU(3) gauge fields. | hep-lat |
Failure of Mean Field Theory at Large N: We study strongly coupled lattice QCD with $N$ colors of staggered fermions
in 3+1 dimensions. While mean field theory describes the low temperature
behavior of this theory at large $N$, it fails in the scaling region close to
the finite temperature second order chiral phase transition. The universal
critical region close to the phase transition belongs to the 3d XY universality
class even when $N$ becomes large. This is in contrast to Gross-Neveu models
where the critical region shrinks as $N$ (the number of flavors) increases and
mean field theory is expected to describe the phase transition exactly in the
limit of infinite $N$. Our work demonstrates that close to second order phase
transitions infrared fluctuations can sometimes be important even when $N$ is
strictly infinite. | hep-lat |
Hamiltonian effective field theory study of the $\mathbf{N^*(1535)}$
resonance in lattice QCD: Drawing on experimental data for baryon resonances, Hamiltonian effective
field theory (HEFT) is used to predict the positions of the finite-volume
energy levels to be observed in lattice QCD simulations of the lowest-lying
$J^P=1/2^-$ nucleon excitation. In the initial analysis, the phenomenological
parameters of the Hamiltonian model are constrained by experiment and the
finite-volume eigenstate energies are a prediction of the model. The agreement
between HEFT predictions and lattice QCD results obtained on volumes with
spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a
more conventional analysis where the low-energy coefficients are constrained by
lattice QCD results, enabling a determination of resonance properties from
lattice QCD itself. Finally, the role and importance of various components of
the Hamiltonian model are examined. | hep-lat |
Free energy of an SU(2) monopole-antimonopole pair: We induce an external ${Z}_2$ monopole-antimonopole pair in an SU(2) lattice
gauge system and measure its free energy as a way to probe the vacuum
structure. We discuss the motivation and computational methodology of the
investigation and illustrate our preliminary results. | hep-lat |
Phase diagram of the three dimensional Thirring model - A Monte Carlo
study: Certain approximate solutions of the continuum Schwinger-Dyson Equations
(SDEs) predict chiral symmetry breaking in the 3d Thirring model when the
number of fermion flavors N_f<4.32 whereas others predict symmetry breaking for
all N_f. Our results from Monte Carlo simulations with N_f=6, predict a second
order chiral phase transition. The critical coupling in this case corresponds
to an ultra-violet fixed point of the renormalization group defining a
non-trivial continuum limit. Further, our numerical simulations provide an
estimate for the critical number of fermion flavors, N_fc \approx 6.5. | hep-lat |
A physicist-friendly reformulation of the Atiyah-Patodi-Singer index (on
a lattice): The Atiyah-Singer index theorem on a closed manifold is well understood and
appreciated in physics. On the other hand, the Atiyah-Patodi-Singer index,
which is an extension to a manifold with boundary, is physicist-unfriendly, in
that it is formulated with a nonlocal boundary condition. Recently we proved
that the same index as APS is obtained from the domain-wall fermion Dirac
operator. Our theorem indicates that the index can be expressed without any
nonlocal conditions, in such a physicist-friendly way that application to the
lattice gauge theory is straightforward. The domain-wall fermion provides a
natural mathematical foundation for understanding the bulk-edge correspondence
of the anomaly inflow. | hep-lat |
Measures of critical exponents in the four dimensional site percolation: Using finite-size scaling methods we measure the thermal and magnetic
exponents of the site percolation in four dimensions, obtaining a value for the
anomalous dimension very different from the results found in the literature. We
also obtain the leading corrections-to-scaling exponent and, with great
accuracy, the critical density. | hep-lat |
A Dual Algorithm for Non-abelian Yang-Mills coupled to Dynamical
Fermions: We extend the dual algorithm recently described for pure, non-abelian
Yang-Mills on the lattice to the case of lattice fermions coupled to
Yang-Mills, by constructing an ergodic Metropolis algorithm for dynamic
fermions that is local, exact, and built from gauge-invariant boson-fermion
coupled configurations. For concreteness, we present in detail the case of
three dimensions, for the group SU(2) and staggered fermions, however the
algorithm readily generalizes with regard to group and dimension. The treatment
of the fermion determinant makes use of a polymer expansion; as with previous
proposals making use of the polymer expansion in higher than two dimensions,
the critical question for practical applications is whether the presence of
negative amplitudes can be managed in the continuum limit. | hep-lat |
Chiral perturbation theory in a theta vacuum: We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due
to the CP violating term, the vacuum of chiral fields is shifted to a
non-trivial element on the SU(N_f) group manifold. The CP violation also
provides mixing of different CP eigenstates, between scalar and pseudoscalar,
or vector and axialvector operators. We investigate upto O(theta^2) effects on
the mesonic two point correlators of ChPT to the one-loop order. We also
address the effects of fixing topology, by using saddle point integration in
the Fourier transform with respect to theta. | hep-lat |
Preliminary Study of B_K on 2+1 flavor DWF lattices from QCDOC: I present some preliminary calculations of B_K on 2+1 flavor domain-wall
fermion lattices from the QCDOC, including a set of 16^3x32x8 lattices with
a^{-1} near 1.6 GeV. Although a final result awaits the production of a much
longer run, I will compare this preliminary value to previous results. | hep-lat |
Lattice Study of Radiative $J/ψ$ Decay to a Tensor Glueball: The radiative decay of $J/\psi$ into a pure gauge tensor glueball is studied
in the quenched lattice QCD formalism. With two anisotropic lattices, the
mutlipole amplitudes E_1(0), M_2(0) and E_3(0) are obtained to be
0.114(12)(6)GeV, -0.011(5)(1)GeV, and 0.023(8)(1)GeV, respectively. The first
error comes from the statistics, the Q^2 interpolation, and the continuum
extrapolation, while the second is due to the uncertainty of the scale
parameter r_0^{-1}=410(20) MeV. Thus the partial decay width
$\Gamma(J/\psi\rightarrow \gamma G_{2^{++}})$ is estimated to be 1.01(22)(10)
keV which corresponds to a large branch ratio 1.1(2)(1)x10^{-2}. The
phenomenological implication of this result is also discussed. | hep-lat |
Existence and Non-Existence of Doubly Heavy Tetraquark Bound States: In this work we investigate the existence of bound states for doubly heavy
tetraquark systems $ \bar{Q}\bar{Q}'qq' $ in a full lattice-QCD computation,
where heavy bottom quarks are treated in the framework of non-relativistic QCD.
We focus on three systems with quark content $ \bar{b}\bar{b}ud $, $
\bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $. We show evidence for the existence
of $ \bar{b}\bar{b}ud $ and $ \bar{b}\bar{b}us $ bound states, while no binding
appears to be present for $ \bar{b}\bar{c}ud $. For the bound four-quark states
we also discuss the importance of various creation operators and give an
estimate of the meson-meson and diquark-antidiquark percentages. | hep-lat |
First dynamical simulations with minimally doubled fermions: For thermodynamics studies it is desirable to simulate two degenerate flavors
and retain at least a remnant of the chiral symmetry. Staggered fermions can
achieve this at the cost of rooting the determinant. Rooting can be avoided
using minimally doubled fermions. This discretization describes two degenerate
quark flavors while explicitly breaking hyper-cubic symmetry, thus, requiring
additional counter-terms. We use one particular formulation of minimally
doubled fermions called the Kirsten-Wilczek action and mitigate lattice
artifacts by improving the spatial derivatives in the Dirac operator. In this
pilot study we determine the counter-terms non-perturbatively to facilitate
proper dynamical simulations. | hep-lat |
A novel Bayesian approach to spectral function reconstruction: We present a novel approach to the inference of spectral functions from
Euclidean time correlator data that makes close contact with modern Bayesian
concepts. Our method differs significantly from the maximum entropy method
(MEM). A new set of axioms is postulated for the prior probability, leading to
an improved expression, which is devoid of the asymptotically flat directions
present in the Shanon-Jaynes entropy. Hyperparameters are integrated out
explicitly, liberating us from the Gaussian approximations underlying the
evidence approach of the MEM. We present a realistic test of our method in the
context of the non-perturbative extraction of the heavy quark potential. Based
on hard-thermal-loop correlator mock data, we establish firm requirements in
the number of data points and their accuracy for a successful extraction of the
potential from lattice QCD. An improved potential estimation from previously
investigated quenched lattice QCD correlators is provided. | hep-lat |
Phase transition in fluctuating branched geometry: We study grand--canonical and canonical properties of the model of branched
polymers proposed in \cite{adfo}. We show that the model has a fourth order
phase transition and calculate critical exponents. At the transition the
exponent $\gamma$ of the grand-canonical ensemble, analogous to the string
susceptibility exponent of surface models, $\gamma \sim 0.3237525...$ is the
first known example of positive $\gamma$ which is not of the form $1/n,\,
n=2,3,\ldots$. We show that a slight modification of the model produces a
continuos spectrum of $\gamma$'s in the range $(0,1/2]$ and changes the order
of the transition. | hep-lat |
Bound states for Overlap and Fixed Point Actions close to the chiral
limit: We study the overlap and the fixed point Dirac operators for massive fermions
in the two-flavor lattice Schwinger model. The masses of the triplet (pion) and
singlet (eta) bound states are determined down to small fermion masses and the
mass dependence is compared with various continuum model approximations. Near
the chiral limit, at very small fermion masses the fixed point operator has
stability problems, which in this study are dominated by finite size effects, | hep-lat |
Anomalous finite-size scaling at thermal first-order transitions in
systems with disordered boundary conditions: We investigate the equilibrium and off-equilibrium behaviors of systems at
thermal first-order transitions (FOTs) when the boundary conditions favor one
of the two phases. As a theoretical laboratory we consider the two-dimensional
Potts model. We show that an anomalous finite-size scaling emerges in systems
with open boundary conditions favoring the disordered phase, associated with a
mixed regime where the two phases are spatially separated. Correspondingly, if
the system is slowly heated across the transition, the characteristic times of
the off-equilibrium dynamics scale with a power of the size. We argue that
these features generally apply to systems at FOTs, when boundary conditions
favor one of the two phases. In particular, they should be relevant for the
experimental search of FOTs of the quark-gluon plasma in heavy-ion collisions. | hep-lat |
Accurate Scale Determinations for the Wilson Gauge Action: Accurate determinations of the physical scale of a lattice action are
required to check scaling and take the continuum limit. We present a high
statistics study of the static potential for the SU(3) Wilson gauge action on
coarse lattices ($5.54 \leq \beta \leq 6.0$). Using an improved analysis
procedure we determine the string tension and the Sommer scale $r_0$ (and
related quantities) to 1% accuracy, including all systematic errors. Combining
our results with earlier ones on finer lattices, we present parameterizations
of these quantities that should be accurate to about 1% for $5.6 \leq \beta
\leq 6.5$. We estimate the $\La$-parameter of quenched QCD to be $\La_\MSb =
247(16)$ MeV. | hep-lat |
Quarkonium correlators at finite temperature and potential models: We discuss the calculations of quarkonium spectral functions in potential
models and their implications for the interpretation of the lattice data on
quarkonium correlators. In particular, we find that melting of different
quarkonium states does not lead to significant change in the Euclidean time
correlators. The large change of the quarkonium correlators above deconfinement
observed in the scalar and axial-vector channels appears to be due to the zero
mode contribution. | hep-lat |
The Infrared Landau Gauge Gluon Propagator from Lattice QCD: The quenched Landau gauge gluon propagator is investigated in lattice QCD
with large assimetric lattices, accessing momenta as low as $q \sim 100$ MeV or
smaller. Our investigation focus on the IR limit of the gluon dressing
function, testing the compatibility with recent solutions of the
Dyson-Schwinger equations. In particular, the low energy parameters $\kappa$
and $\alpha (0)$ are measured. | hep-lat |
Correlations equalities and some upper bounds for the coupling constant
implying area decay of Wilson loop for $Z_3$ lattice gauge theories: Correlation identities are obtained for $Z_3$ lattice gauge theory where the
bonds of the plaquettes are decorated by generalized three-state Ising
variables. Making use of correlation inequalities we obtain the area decay of
the Wilson loop observable in a range of the coupling parameter larger than
those obtained from mean field theory considerations. | hep-lat |
Prepotential formulation of SU(3) lattice gauge theory: The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential
harmonic oscillators. This reformulation has enlarged $SU(3)\otimes U(1)
\otimes U(1)$ gauge invariance under which the prepotential operators transform
like matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to
be equivalent to the Hilbert space of the prepotential formulation satisfying
certain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential
operators which solve these Sp(2,R) constraints are used to construct SU(3)
gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge
invariant vertex operators. The electric fields and the link operators are
reconstructed in terms of these SU(3) irreducible prepotential operators. We
show that all the SU(3) Mandelstam constraints become local and take very
simple form within this approach. We also discuss the construction of all
possible linearly independent SU(3) loop states which solve the Mandelstam
constraints. The techniques can be easily generalized to SU(N). | hep-lat |
Specific heat and energy for the three-dimensional O(2) model: We investigate the three-dimensional O(2) model on lattices of size 8^3 to
160^3 close to the critical point at zero magnetic field. We confirm explicitly
the value of the critical coupling J_c found by Ballesteros et al. and estimate
there the universal values of g_r and xi/L. At the critical point we study the
finite size dependencies of the energy density epsilon and the specific heat C.
We find that the nonsingular part of the specific heat C_{ns} is linearly
dependent on 1/alpha. From the critical behaviour of the specific heat for T
not T_c on the largest lattices we determine the universal amplitude ratio
A+/A-. The alpha- dependence of this ratio is close to the phenomenological
relation A+/A- = 1-4alpha. | hep-lat |
Nucleon form factors on a large volume lattice near the physical point
in 2+1 flavor QCD: We present results for the isovector nucleon form factors measured on a
$96^4$ lattice at almost the physical pion mass with a lattice spacing of 0.085
fm in 2+1 flavor QCD. The configurations are generated with the stout-smeared
$O(a)$-improved Wilson quark action and the Iwasaki gauge action at
$\beta$=1.82. The pion mass at the simulation point is about 146 MeV. A large
spatial volume of $(8.1~{\rm fm})^3$ allows us to investigate the form factors
in the small momentum transfer region. We determine the isovector electric
radius and magnetic moment from nucleon electric ($G_E$) and magnetic ($G_M$)
form factors as well as the axial-vector coupling $g_A$. We also report on the
results of the axial-vector ($F_A$), induced pseudoscalar ($F_P$) and
pseudoscalar ($G_P$) form factors in order to verify the axial Ward-Takahashi
identity in terms of the nucleon matrix elements, which may be called the
generalized Goldberger-Treiman relation. | hep-lat |
On observable particles in theories with a Brout-Englert-Higgs effect: Even at weak coupling the physical, observable spectrum of gauge theories
with a Brout-Englert-Higgs effect can deviate from the elementary one of
perturbation theory. This can be analytically described and treated using the
Fr\"ohlich-Morchio-Strocchi mechanism. We confirm this by lattice simulation
for an SU(3) gauge theory with a fundamental scalar, a toy model for grand
unification. We also show that this has experimentally observable consequence,
e.g., in scattering cross-sections of lepton collisions in this toy model. | hep-lat |
Moments of meson distribution functions with dynamical twisted mass
fermions: We present our preliminary results on the lowest moment <x> of quark
distribution functions of the pion using two flavor dynamical simulations with
Wilson twisted mass fermions at maximal twist. The calculation is done in a
range of pion masses from 300 to 500 MeV. A stochastic source method is used to
reduce inversions in calculating propagators. Finite volume effects at the
lowest quark mass are examined by using two different lattice volumes. Our
results show that we achieve statistical errors of only a few percent. We plan
to compute renormalization constants non-perturbatively and extend the
calculation to two more lattice spacings and to the nucleons. | hep-lat |
Strategies for the Determination of the Running Coupling of
$(2+1)$-dimensional QED with Quantum Computing: We propose to utilize NISQ-era quantum devices to compute short distance
quantities in $(2+1)$-dimensional QED and to combine them with large volume
Monte Carlo simulations and perturbation theory. On the quantum computing side,
we perform a calculation of the mass gap in the small and intermediate regime,
demonstrating, in the latter case, that it can be resolved reliably. The so
obtained mass gap can be used to match corresponding results from Monte Carlo
simulations, which can be used eventually to set the physical scale. In this
paper we provide the setup for the quantum computation and show results for the
mass gap and the plaquette expectation value. In addition, we discuss some
ideas that can be applied to the computation of the running coupling. Since the
theory is asymptotically free, it would serve as a training ground for future
studies of QCD in $(3+1)$-dimensions on quantum computers. | hep-lat |
The twelve-flavor $\boldsymbolβ$-function and dilaton tests of the
sextet scalar: We discuss near-conformal gauge theories beyond the standard model (BSM)
where interesting results on the twelve-flavor $\beta$-function of massless
fermions in the fundamental representation of the SU(3) color gauge group and
dilaton tests of the light scalar with two massless fermions in the two-index
symmetric tensor (sextet) representation can be viewed as parts of the same BSM
paradigm under investigation. We report results from high precision analysis of
the twelve-flavor $\beta$-function \cite{Fodor:2016zil} refuting its published
IRFP \cite{Cheng:2014jba,Hasenfratz:2016dou}. We present our objections to
recent claims \cite{Hasenfratz:2017mdh,Hasenfratz:2017qyr} for non-universal
behavior of staggered fermions used in our analysis. We also report our first
analysis of dilaton tests of the light $0^{++}$ scalar in the sextet model and
comment on related post-conference developments. The dilaton test is the main
thrust of this conference contribution including presentation #405 on the
$n_f=12$ $\beta$-function and presentation #260 on dilaton tests of the sextet
model. They are both selected from the near-conformal BSM paradigm. | hep-lat |
Fermions as global correction in lattice QCD: The fermion determinant is a highly non-local object and its logarithm is an
extensive quantity. For these reasons it is widely believed that the
determinant cannot be treated in acceptance steps of gauge link configurations
that differ in a large fraction of the links. However, for exact factorisations
of the determinant that separate the ultraviolet from the infra-red modes of
the Dirac operator it is known that the latter show less variation under
changes of the gauge field compared to the former. Using a factorisation based
on recursive domain decomposition allows for a hierarchical algorithm that
starts with pure gauge updates of the links within the domains and ends after a
number of filters with a global acceptance step. We find that the global
acceptance rate is high on moderate lattice sizes. Whether this type of
algorithm can help in curing the problem of critical slowing down is presently
under study. | hep-lat |
Self-Avoiding Gonihedric Srting and Spin Systems: We classify different theories of self-intersecting random surfaces assigning
special weights to intersections. When self-intersection coupling constant
$\kappa$ tends to zero, then the surface can freely inetrsect and it is
completely self-avoiding when $\kappa$ tends to infinity. Equivalent spin
systems for this general case were constructed. In two-dimension the system
with $\kappa = 0$ is in complete disorder as it is in the case of 2D gauge
Ising system. | hep-lat |
Induced representations of Poincare group on the lattice: spin 1/2 and 1
case: Following standard methods we explore the construction of the discrete
Poincare group, the semidirect product of discrete translations and integral
Lorentz transformations, using the Wigner-Mackey construction restricted to the
momentum and position space on the lattice. The orbit condition, irreducibility
and assimptotic limit are discussed. | hep-lat |
On ambiguities of sign determination of the S-matrix from energy levels
in a finite box: In a recent paper the authors make a study on the determination of the
S-matrix elements for scattering of particles in the infinite volume from the
energy levels in the finite box for the case of multiple channels. The study is
done with a toy model in 1+1 dimension and the authors find that there is some
ambiguity in the sign of nondiagonal matrix elements, casting doubts on whether
the needed observables in the infinite volume can be obtained from the energy
levels of the box. In this paper I present an easy derivation, confirming the
ambiguity of the sign and argue that this, however, does not put restrictions
in the determination of observables. | hep-lat |
Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation: It is shown that the Ginsparg-Wilson relation implies an exact symmetry of
the fermion action, which may be regarded as a lattice form of an infinitesimal
chiral rotation. Using this result it is straightforward to construct lattice
Yukawa models with unbroken flavour and chiral symmetries and no doubling of
the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is
avoided, because the chiral symmetry is realized in a different way than has
been assumed when proving the theorem. | hep-lat |
A precise determination of T_c in QCD from scaling: Existing lattice data on the QCD phase transition are analyzed in
renormalized perturbation theory. In quenched QCD it is found that T_c scales
for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05.
A preliminary estimate in QCD with two flavours of dynamical quarks shows that
this ratio depends on the quark mass. For realistic quark masses we estimate
T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in
quenched QCD at 1-loop order in renormalised perturbation theory. | hep-lat |
Accelerating Staggered Fermion Dynamics with the Rational Hybrid Monte
Carlo (RHMC) Algorithm: Improved staggered fermion formulations are a popular choice for lattice QCD
calculations. Historically, the algorithm used for such calculations has been
the inexact R algorithm, which has systematic errors that only vanish as the
square of the integration step-size. We describe how the exact Rational Hybrid
Monte Carlo (RHMC) algorithm may be used in this context, and show that for
parameters corresponding to current state-of-the-art computations it leads to a
factor of approximately seven decrease in cost as well as having no step-size
errors. | hep-lat |
Preliminary results of $ΔI=1/2$ and $3/2$, $K$ to $ππ$ Decay
Amplitudes from Lattice QCD: We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix
elements for both $\Delta I=1/2$ and $3/2$ channels on 2+1 flavor, domain wall
fermion, $16^3\times32$ lattices with zero $\pi\pi$ relative momentum and
$m_\pi=420$ MeV. All $K^0$ to $\pi\pi$ contractions are carefully listed and
calculated. The decay into the isospin zero $\pi\pi$ final state, which
receives contributions from the disconnected graphs, is very difficult to
calculate, but a clear signal in the similar disconnected $\pi\pi$ correlator
can be seen. Preliminary results, some with large errors, will be presented for
the various contributions to the renormalized weak matrix elements $A_0$ and
$A_2$. We obtain Re$(A_0)$ with $25%$ error in the case of zero momentum on
shell decay, and find a factor of 6 enhancement for the $\Delta I=1/2$ rule in
the $420$ MeV pion system. | hep-lat |
Large-N reduction with two adjoint Dirac fermions: We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson
fermions for values of N up to 53. We determine the phase diagram of the theory
as a function of the hopping parameter kappa and the inverse 't Hooft coupling
b, searching for the region in which the Z_N^4 center symmetry is unbroken. In
this region the theory is equivalent to the infinite volume theory when N goes
to infinity. We find a region of values of kappa on both sides of kappa_c for
which the symmetry is unbroken, including both light physical quarks and masses
~O(1/a). This is surrounded by a region with a complicated sequence of
partially broken phases. We calculate Wilson loop expectation values and find
that using N <= 53 it is possible to extract the heavy-quark potential at small
distances (1-3 links) but not at longer distances. For this, larger values of
N, or lattices with more sites, are needed. | hep-lat |
Physical properties of Polyakov loop geometrical clusters in SU(2)
gluodynamics: We apply the liquid droplet model to describe the clustering phenomenon in
SU(2) gluodynamics, especially, in the vicinity of the deconfinement phase
transition. In particular, we analyze the size distributions of clusters formed
by the Polyakov loops of the same sign. Within such an approach this phase
transition can be considered as the transition between two types of liquids
where one of the liquids (the largest droplet of a certain Polyakov loop sign)
experiences a condensation, while the other one (the next to largest droplet of
opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two
accompanying gases, and their size distributions are described by the liquid
droplet parameterization. By fitting the lattice data we have extracted the
value of Fisher exponent $\tau =$ 1.806 $\pm$ 0.008. Also we found that the
temperature dependences of the surface tension of both gaseous clusters are
entirely different below and above the phase transition and, hence, they can
serve as an order parameter. The critical exponents of the surface tension
coefficient in the vicinity of the phase transition are found. Our analysis
shows that the temperature dependence of the surface tension coefficient above
the critical temperature has a $T^2$ behavior in one gas of clusters and $T^4$
in the other one. | hep-lat |
Lattice study of the chiral magnetic effect in a chirally imbalanced
matter: We investigate the chiral magnetic effect by lattice QCD with a chiral
chemical potential. In a chirally imbalanced matter, we obtain a finite induced
current along an external magnetic field. We analyze the dependence on the
lattice spacing, the temperature, the spatial volume, and the fermion mass. The
present result indicates that the continuum limit is important for the
quantitative argument of the strength of the induced current. | hep-lat |
On Dirac Zero Modes in Hyperdiamond Model: Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of
4D graphene given in "Four Dimensional Graphene" (L.B Drissi, E.H Saidi, M.
Bousmina, CPM-11-01, Phys. Rev. D (2011)), we engineer a class of 4D lattice
QCD fermions whose Dirac operators have two zero modes. We show that generally
the zero modes of the Dirac operator in hyperdiamond fermions are captured by a
tensor {\Omega}_{{\mu}}^{l} with 4\times5 complex components linking the
Euclidean SO(4) vector {\mu}; and the 5-dimensional representation of SU(5).
The Bori\c{c}i-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their
Dirac zero modes are rederived as particular realizations of
{\Omega}_{{\mu}}^{l}. Other features are also given. Keywords: Lattice QCD,
Bori\c{c}i-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene,
SU(5) Symmetry. | hep-lat |
From deep inelastic scattering to heavy-flavor semi-leptonic decays:
Total rates into multi-hadron final states from lattice QCD: We present a new technique for extracting decay and transition rates into
final states with any number of hadrons. The approach is only sensitive to
total rates, in which all out-states with a given set of QCD quantum numbers
are included. For processes involving photons or leptons, differential rates
with respect to the non-hadronic kinematics may also be extracted. Our method
involves constructing a finite-volume Euclidean four-point function, whose
corresponding spectral function measures the decay and transition rates in the
infinite-volume limit. This requires solving the inverse problem of extracting
the spectral function from the correlator and also necessitates a smoothing
procedure so that a well-defined infinite-volume limit exists. Both of these
steps are accomplished by the Backus-Gilbert method and, as we show with a
numerical example, reasonable precision can be expected in cases with multiple
open decay channels. Potential applications include nucleon structure functions
and the onset of the deep inelastic scattering regime, as well as semi-leptonic
$D$ and $B$ decay rates. | hep-lat |
Pion electric polarizability from lattice QCD: Electromagnetic polarizabilities are important parameters for understanding
the interaction between photons and hadrons. For pions these quantities are
poorly constrained experimentally since they can only be measured indirectly.
New experiments at CERN and Jefferson Lab are planned that will measure the
polarizabilities more precisely. Lattice QCD can be used to compute these
quantities directly in terms of quark and gluons degrees of freedom, using the
background field method. We present results for the electric polarizability for
two different quark masses, light enough to connect to chiral perturbation
theory. These are currently the lightest quark masses used in polarizability
studies. | hep-lat |
K->pi form factors with reduced model dependence: Using partially twisted boundary conditions we compute the K->pi
semi-leptonic form factors in the range of momentum transfers 0 <~ q^2 <=
q^2_{max}=(mK-mpi)^2 in lattice QCD with N_f=2+1 dynamical flavours. In this
way we are able to determine f+(0) without any interpolation in the momentum
transfer, thus eliminating one source of systematic error. This study confirms
our earlier phenomenological ansatz for the strange quark mass dependence of
the scalar form factor. We identify and estimate potentially significant NNLO
effects in the chiral expansion that guides the extrapolation of the data to
the physical point. Our main result is f+(0) = 0.9599(34)(^{+31}_{-43})(14)$,
where the first error is statistical, the second error is due to the
uncertainties in the chiral extrapolation of the lattice data and the last
error is an estimate of potential discretisation effects. | hep-lat |
Distributions of the Phase Angle of the Fermion Determinant in QCD: The distribution of the phase angle and the magnitude of the fermion
determinant as well as its correlations with the baryon number and the chiral
condensate are studied for QCD at non zero quark chemical potential. Results
are derived to one-loop order in chiral perturbation theory. We find that the
distribution of the phase angle is Gaussian for small chemical potential and a
periodic Lorentzian when the quark mass is inside the support of the Dirac
spectrum. The baryon number and chiral condensate are computed as a function of
the phase of the fermion determinant and we discuss the severe cancellations
which occur upon integration over the angle. We compute the distribution of the
magnitude of the fermion determinant as well as the baryon number and chiral
condensate at fixed magnitude.
Finally, we consider QCD in one Euclidean dimension where it is shown
analytically, starting from the fundamental QCD partition function, that the
distribution of the phase of the fermion determinant is a periodic Lorentzian
when the quark mass is inside the spectral density of the Dirac operator. | hep-lat |
Numerical tests of the electroweak phase transition and thermodynamics
of the electroweak plasma: The finite temperature phase transition in the SU(2) Higgs model at a Higgs
boson mass $M_H \simeq 34$ GeV is studied in numerical simulations on
four-dimensional lattices with time-like extensions up to $L_t=5$. The effects
of the finite volume and finite lattice spacing on masses and couplings are
studied in detail. The errors due to uncertainties in the critical hopping
parameter are estimated. The thermodynamics of the electroweak plasma near the
phase transition is investigated by determining the relation between energy
density and pressure. | hep-lat |
Semileptonic $B$-meson decays to light pseudoscalar mesons on the HISQ
ensembles: We report the status of an ongoing lattice-QCD calculation of form factors
for exclusive semileptonic decays of $B$ mesons with both charged currents
($B\to\pi\ell\nu$, $B_s\to K\ell\nu$) and neutral currents
($B\to\pi\ell^+\ell^-$, $B\to K\ell^+\ell^-$). The results are important for
constraining or revealing physics beyond the Standard Model. This work uses
MILC's (2+1+1)-flavor ensembles with the HISQ action for the sea and light
valence quarks and the clover action in the Fermilab interpretation for the $b$
quark. Simulations are carried out at three lattice spacings down to $0.088$
fm, with both physical and unphysical sea-quark masses. We present preliminary
results for correlation-function fits. | hep-lat |
Study of spatial meson correlators at finite temperature in quenched
anisotropic lattice QCD: We analyze the meson correlator in the spatial direction at finite
temperature. To achieve fine resolution in the spatial direction, we use an
anisotropic lattice with the standard Wilson plaquette gauge action and the
$O(a)$ improved Wilson quark action. Below and above $T_c$, properties of
correlators are investigated by two methods: fits with ansatz for the spectral
function, and direct reconstruction of the spectral function using the maximum
entropy method. | hep-lat |
Chiral behavior of $K \to πl ν$ decay form factors in lattice QCD
with exact chiral symmetry: We calculate the form factors of the $K \to \pi l \nu$ semileptonic decays in
three-flavor lattice QCD, and study their chiral behavior as a function of the
momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is
exactly preserved by using the overlap quark action, which enables us to
directly compare the lattice data with chiral perturbation theory (ChPT). We
generate gauge ensembles at a lattice spacing of 0.11fm with four pion masses
covering 290-540 MeV and a strange quark mass m_s close to its physical value.
By using the all-to-all quark propagator, we calculate the vector and scalar
form factors with high precision. Their dependence on m_s and the momentum
transfer is studied by using the reweighting technique and the twisted boundary
conditions for the quark fields. We compare the results for the semileptonic
form factors with ChPT at next-to-next-to leading order in detail. While many
low-energy constants appear at this order, we make use of our data of the light
meson electromagnetic form factors in order to control the chiral
extrapolation. We determine the normalization of the form factors as f_+(0) =
0.9636(36)(+57/-35), and observe reasonable agreement of their shape with
experiment. | hep-lat |
K-meson vector and tensor decay constants and BK-parameter from Nf=2
tmQCD: We present work in progress on the computation of the K-meson vector and
tensor decay constants, as well as the B-parameter in Kaon oscillations. Our
simulations are performed in a partially quenched setup, with two dynamical
(sea) Wilson quark flavours, having a maximally twisted mass term. Valence
quarks are either of the standard or the Osterwalder-Seiler maximally twisted
variety. These two regularizations can be suitably combined in order to obtain
a BK parameter which is both multiplicatively renormalizable and O(a) improved. | hep-lat |
Better Domain-Wall Fermions: We discuss two modifications of domain-wall fermions, aimed to reduce the
chiral-symmetry violations presently encountered in numerical simulations. | hep-lat |
Effective Polyakov line actions, and their solutions at finite chemical
potential: I outline recent progress in the relative weights approach to deriving
effective Polyakov line actions from an underlying lattice gauge theory, and
compare mean field and complex Langevin methods for solving such theories at
finite chemical potential. | hep-lat |
Locality and exponential error reduction in numerical lattice gauge
theory: In non-abelian gauge theories without matter fields, expectation values of
large Wilson loops and loop correlation functions are difficult to compute
through numerical simulation, because the signal-to-noise ratio is very rapidly
decaying for increasing loop sizes. Using a multilevel scheme that exploits the
locality of the theory, we show that the statistical errors in such
calculations can be exponentially reduced. We explicitly demonstrate this in
the SU(3) theory, for the case of the Polyakov loop correlation function, where
the efficiency of the simulation is improved by many orders of magnitude when
the area bounded by the loops exceeds 1 fm^2. | hep-lat |
A new phase in the Lorentzian type IIB matrix model and the emergence of
continuous space-time: The Lorentzian type IIB matrix model is a promising candidate for a
non-perturbative formulation of superstring theory. In previous studies, Monte
Carlo calculations provided interesting results indicating the spontaneous
breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time.
However, an approximation was used to avoid the sign problem, which seemed to
make the space-time structure singular. In this talk, we report our results
obtained by using the complex Langevin method to overcome the sign problem
instead of using this approximation. In particular, we discuss the emergence of
continuous space-time in a new phase, which we discovered recently. | hep-lat |
Lattice 2001: Reflections: A few subjects which strongly intertwine our field are discussed: K --> Pi Pi
decay, chiral symmetry on the lattice and a few other selected topics. Open
questions are touched also on perturbation theory, locality, Gribov copies, CP
symmetry in chiral gauge theories and cut-off effects. | hep-lat |
Properties of light pseudoscalars from lattice QCD with HISQ ensembles: We fit lattice-QCD data for light-pseudoscalar masses and decay constants,
from HISQ configurations generated by MILC, to SU(3) staggered chiral
perturbation theory. At present such fits have rather high values of
chi^2/d.o.f., possibly due to the lack of ensembles with lighter-than-physical
sea strange-quark masses. We propose solutions to this problem for future work.
We also perform simple linear interpolations near the physical point on two
ensembles with different lattice spacings, and obtain the preliminary result
(f_K / f_pi)^phys = 1.1872(41) in the continuum limit. | hep-lat |
Solutions of the Ginsparg-Wilson relation and improved domain wall
fermions: We discuss a number of lattice fermion actions solving the Ginsparg-Wilson
relation. We also consider short ranged approximate solutions. In particular,
we are interested in reducing the lattice artifacts, while avoiding (or
suppressing) additive mass renormalization. In this context, we also arrive at
a formulation of improved domain wall fermions. | hep-lat |
Decomposition of the static potential in the Maximal Abelian gauge: Decomposition of SU(2) gauge field into the monopole and monopoleless
components is studied in the Maximal Abelian gauge using Monte-Carlo
simulations in lattice SU(2) gluodynamics as well as in two-color QCD with both
zero and nonzero quark chemical potential. The interaction potential between
static charges is calculated for each component and their sum is compared with
the non-Abelian static potential. A good agreement is found in the confinement
phase. Implications of this result are discussed. | hep-lat |
Large $N$ scaling and factorization in $\mathrm{SU}(N)$ Yang-Mills
theory: We present results for Wilson loops smoothed with the Yang-Mills gradient
flow and matched through the scale $t_0$. They provide renormalized and precise
operators allowing to test the $1/N^2$ scaling both at finite lattice spacing
and in the continuum limit. Our results show an excellent scaling up to $1/N =
1/3$. Additionally, we obtain a very precise non-perturbative confirmation of
factorization in the large $N$ limit. | hep-lat |
The Charge and Matter radial distributions of Heavy-Light mesons
calculated on a lattice: For a heavy-light meson with a static heavy quark, we can explore the light
quark distribution. The charge and matter radial distributions of these
heavy-light mesons are measured on a 16^3 * 24 lattice at beta=5.7 and a
hopping parameter corresponding to a light quark mass about that of the strange
quark. Both distributions can be well fitted up to 4 lattice spacings (r approx
0.7 fm) with the exponential form w_i^2(r), where w_i(r)=A exp(-r/r_i). For the
charge(c) and matter(m) distributions r_c approx 0.32(2) fm and r_m approx
0.24(2) fm. We also discuss the normalisation of the total charge and matter
integrated over all space, finding 1.30(5) and 0.4(1) respectively. | hep-lat |
Probes of nearly conformal behavior in lattice simulations of minimal
walking technicolor: We present results from high precision, large volume simulations of the
lattice gauge theory corresponding to minimal walking technicolor. We find
evidence that the pion decay constant vanishes in the infinite volume limit and
that the dependence of the chiral condensate on quark mass m_q is inconsistent
with spontaneous symmetry breaking. These findings are consistent with the
all-orders beta function prediction as well as the Schroedinger functional
studies that indicate the existence of a nontrivial infrared fixed point. | hep-lat |
The compact Q=2 Abelian Higgs model in the London limit: vortex-monopole
chains and the photon propagator: The confining and topological properties of the compact Abelian Higgs model
with doubly-charged Higgs field in three space-time dimensions are studied. We
consider the London limit of the model. We show that the monopoles are forming
chain-like structures (kept together by ANO vortices) the presence of which is
essential for getting simultaneously permanent confinement of singly-charged
particles and breaking of the string spanned between doubly-charged particles.
In the confinement phase the chains are forming percolating clusters while in
the deconfinement (Higgs) phase the chains are of finite size. The described
picture is in close analogy with the synthesis of the Abelian monopole and the
center vortex pictures in confining non--Abelian gauge models. The screening
properties of the vacuum are studied by means of the photon propagator in the
Landau gauge. | hep-lat |
Dual formulations of Polyakov loop lattice models: Dual representations are constructed for non-abelian lattice spin models with
U(N) and SU(N) symmetry groups, for all N and in any dimension. These models
are usually related to the effective models describing the interaction between
Polyakov loops in the strong coupled QCD. The original spin degrees of freedom
are explicitly integrated out and a dual theory appears to be a local theory
for the dual integer-valued variables. The construction is performed for the
partition function and for the most general correlation function. The latter
include the two-point function corresponding to quark-anti-quark free energy
and the N-point function related to the free energy of a baryon. We consider
both pure gauge models and models with static fermion determinant for both the
staggered and Wilson fermions with an arbitrary number of flavours. While the
Boltzmann weights of such models are complex in the presence of non-zero
chemical potential the dual Boltzmann weights appear to be strictly positive on
admissible configurations. An essential part of this work with respect to
previous studies is an extension of the dual representation to the case of 1)
an arbitrary value of the temporal coupling constant in the Wilson action and
2) an arbitrary number of flavours of static quark determinants. The
applications and extensions of the results are discussed in detail. In
particular, we outline a possible approach to Monte-Carlo simulations of the
dual theory, to the large N expansion and to the development of a tensor
renormalization group. | hep-lat |
Universality and Scaling at the chiral transition in two-flavor QCD at
finite temperature: The order of the phase transition in finite-temperature QCD with two
degenerate light quarks is still an open problem and corresponds to the last
question mark in the zero-density phase diagram of QCD. We argue that
establishing the nature of the transition in this case is also a crucial test
for numerical simulations of lattice QCD, allowing precise estimates of
possible systematic errors related e.g. to the choice of fermion-simulation
algorithm or of discretized formulation for fermions. | hep-lat |
Lattice QCD study on $K^\ast(892)$ meson decay width: We deliver an exploratory lattice QCD examination of the $K^\ast(892)$ meson
decay width with the help of the p-wave scattering phase $\delta_1$ of
pion-kaon ($\pi K$) system in the isospin $I=1/2$ channel, which are extracted
by the modified Rummukainen-Gottlieb formula for two-particle system with
arbitrary mass, and it clearly reveals the entity of a resonance at a mass
around $K^\ast(892)$ meson mass. The effective range formula is applied to
describe the energy dependence of the scattering phase and we obtain the
effective $K^\ast \to \pi K$ coupling constant as $g_{K^\ast \pi K} =
6.38(78)$, and subsequently achieve the decay width to be $64.9 \pm 8.0$ MeV,
which is in reasonable accordance with the current experiment. Our lattice
investigations are conducted on a $20^3\times48$ MILC full QCD gauge
configuration at $(m_\pi + m_K) / m_{K^\ast} \approx 0.739$ and the lattice
spacing $a \approx 0.15$ fm. | hep-lat |
Matching coefficients for improved staggered bilinears: We calculate one-loop matching factors for bilinear operators composed of
improved staggered fermions. We compare the results for different improvement
schemes used in the recent literature, including the HYP action and an action
close to the Asqtad action. We find that all improvement schemes substantially
reduce the size of the one-loop contributions to matching factors. The
resulting corrections are comparable to, or smaller than, those found with
Wilson and domain-wall fermions. | hep-lat |
Covariant gauge on the lattice: a new implementation: We derive a new implementation of linear covariant gauges on the lattice,
based on a minimizing functional that can be interpreted as the Hamiltonian of
a spin-glass model in a random external magnetic field. We show that our method
solves most problems encountered in earlier implementations, mostly related to
the no-go condition formulated by L. Giusti, Nucl. Phys. B 498, 331 (1997). We
carry out tests in the SU(2) case in four space-time dimensions. We also
present preliminary results for the transverse gluon propagator at different
values of the gauge parameter xi. | hep-lat |
New insight in the 2-flavor Schwinger model based on lattice simulations: We consider the Schwinger model with two degenerate, light fermion flavors by
means of lattice simulations. At finite temperature, we probe the viability of
a bosonization method by Hosotani et al. Next we explore an analogue to the
pion decay constant, which agrees for independent formulations based on the
Gell-Mann--Oakes--Renner relation, the 2-dimensional Witten--Veneziano formula
and the $\delta$-regime. Finally we confront several conjectures about the
chiral condensate with lattice results. | hep-lat |
Perfect Lattice Topology: The Quantum Rotor as a Test Case: Lattice actions and topological charges that are classically and quantum
mechanically perfect (i.e. free of lattice artifacts) are constructed
analytically for the quantum rotor. It is demonstrated that the Manton action
is classically perfect while the Villain action is quantum perfect. The
geometric construction for the topological charge is only perfect at the
classical level. The quantum perfect lattice topology associates a topological
charge distribution, not just a single charge, with each lattice field
configuration. For the quantum rotor with the classically perfect action and
topological charge, the remaining cut-off effects are exponentially suppressed. | hep-lat |
Two-color QCD with staggered fermions at finite temperature under the
influence of a magnetic field: In this paper we investigate the influence of a constant external magnetic
field on the finite-temperature phase structure and the chiral properties of a
simplified lattice model for QCD. We assume an SU(2) gauge symmetry and employ
dynamical staggered fermions of identical mass without rooting, corresponding
to Nf=4 flavors of identical electric charge. For fixed mass (given in lattice
units) the critical temperature is seen to rise with the magnetic field
strength. For three fixed beta-values, selected such that we stay (i) within
the chirally broken phase, (ii) within the transition region or (iii) within
the chirally restored phase, we study the approach to the chiral limit for
various values of the magnetic field. Within the chirally broken (confinement)
phase the chiral condensate is found to increase monotonically with a growing
magnetic field strength. In the chiral limit the increase starts linear in
agreement with a chiral model studied by Shushpanov and Smilga. Within the
chirally restored (deconfinement) phase the chiral condensate tends to zero in
the chiral limit, irrespective of the strength of the magnetic field. | hep-lat |
Observing instantons directly on the lattice without cooling: Based on the study of the simple Abelian Higgs model in $1+1$ dimensions we
will present a new method to identify and localize extended instantons. The
idea is to measure the topological charge on regions somewhat larger than the
extended instantons so as to average out the ultraviolet fluctuations but
without losing the detailed topological information when going to the full
space. The instanton size and probability density can be directly extracted
from this analysis. Local dislocations, which can be avoided for fine enough
lattices, can be reinterpreted as modified boundary conditions producing
sectors with net topological charge. | hep-lat |
Staggered Baryon Operators with Flavor SU(3) Quantum Numbers: The construction of the first baryon operators for staggered lattice QCD
exploited the taste symmetry to emulate physical quark flavor; contemporary 2+1
flavor simulations explicitly include three physical quark flavors and
necessitate interpreting a valence sector with twelve quarks. After discussing
expected features of the resulting baryon spectrum, I consider the spectra of
operators transforming irreducibly under SU(3)xGTS, the direct product of
flavor SU(3) and the geometrical time-slice group of the 1-flavor staggered
theory. I then describe the construction of a set of maximally local baryon
operators transforming irreducibly under SU(3)xGTS and enumerate this set. In
principle, the operators listed here could be used to extract the masses of all
the lightest spin-1/2 and spin-3/2 baryon resonances of staggered QCD. Using
appropriate operators from this set in partially quenched simulations should
allow for particularly clean 2+1 flavor calculations of the masses of the
nucleon and the lightest decuplet. | hep-lat |
Renormalization of the effective theory for heavy quarks at small
velocity: The slope of the Isgur-Wise function at the normalization point,
$\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$
matrix element $V_{cb}$ from exclusive semileptonic decay data. A method for
measuring this parameter on the lattice is the effective theory for heavy
quarks at small velocity $v$. This theory is a variant of the heavy quark
effective theory in which the motion of the quark is treated as a perturbation.
In this work we study the lattice renormalization of the slow heavy quark
effective theory. We show that the renormalization of $\xi^{(1)}(1)$ is not
affected by ultraviolet power divergences, implying no need of difficult
non-perturbative subtractions. A lattice computation of $\xi^{(1)}(1)$ with
this method is therefore feasible in principle. The one-loop renormalization
constants of the effective theory for slow heavy quarks are computed to order
$v^2$ together with the lattice-continuum renormalization constant of
$\xi^{(1)}(1)$ . We demonstrate that the expansion in the heavy-quark velocity
reproduces correctly the infrared structure of the original (non-expanded)
theory to every order. We compute also the one-loop renormalization constants
of the slow heavy quark effective theory to higher orders in $v^2$ and the
lattice-continuum renormalization constants of the higher derivatives of the
$\xi$ function. Unfortunately, the renormalization constants of the higher
derivatives are affected by ultraviolet power divergences, implying the
necessity of numerical non-perturbative subtractions. The lattice computation
of higher derivatives of the Isgur-Wise function seems therefore problematic. | hep-lat |
Power-counting theorem for staggered fermions: Lattice power-counting is extended to QCD with staggered fermions. As
preparation, the difficulties encountered by Reisz's original formulation of
the lattice power-counting theorem are illustrated. One of the assumptions that
is used in his proof does not hold for staggered fermions, as was pointed out
long ago by Luscher. Finally, I generalize the power-counting theorem, and the
methods of Reisz's proof, such that the difficulties posed by staggered
fermions are overcome. | hep-lat |
Universal critical behavior and the transition temperature in
(2+1)-flavor QCD: We discuss the universal critical behavior in (2+1)-flavor QCD by analyzing
lattice data from improved staggered fermions generated by the HotQCD
Collaboration. We present recent results from two different lattice
discretizations and various lattice spacings ($N_\tau=6,8,12$) at fixed
physical strange quark mass ($m_s$) but varying light quark mass ($m_l$). We
find that the chiral order-parameter, i.e. the chiral condensate, shows the
expected universal scaling that is associated with the critical point in the
chiral limit already for light quark masses $m_l/m_s \lsim 0.05$. From an
analysis of the disconnected chiral susceptibility we estimate a preliminary
value of the QCD transition temperature. | hep-lat |
Computing the static potential using non-string-like trial states: We present a method for computing the static quark-antiquark potential, which
is not based on Wilson loops, but where the trial states are formed by
eigenvector components of the covariant lattice Laplace operator. We have
tested this method in SU(2) Yang-Mills theory and have obtained results with
statistical errors of similar magnitude compared to a standard Wilson loop
computation. The runtime of the method is, however, significantly smaller, when
computing the static potential not only for on-axis, but also for many off-axis
quark-antiquark separations, i.e. when a fine spatial resolution is required. | hep-lat |
B- and D-meson decay constants from three-flavor lattice QCD: We calculate the leptonic decay constants of B_{(s)} and D_{(s)} mesons in
lattice QCD using staggered light quarks and Fermilab bottom and charm quarks.
We compute the heavy-light meson correlation functions on the MILC
asqtad-improved staggered gauge configurations which include the effects of
three light dynamical sea quarks. We simulate with several values of the light
valence- and sea-quark masses (down to ~m_s/10) and at three lattice spacings
(a ~ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark
masses and the continuum using expressions derived in heavy-light meson
staggered chiral perturbation theory. We renormalize the heavy-light axial
current using a mostly nonperturbative method such that only a small correction
to unity must be computed in lattice perturbation theory and higher-order terms
are expected to be small. We obtain f_{B^+} = 196.9(8.9) MeV, f_{B_s} =
242.0(9.5) MeV, f_{D^+} = 218.9(11.3) MeV, f_{D_s} = 260.1(10.8) MeV, and the
SU(3) flavor-breaking ratios f_{B_s}/f_{B} = 1.229(26) and f_{D_s}/f_{D} =
1.188(25), where the numbers in parentheses are the total statistical and
systematic uncertainties added in quadrature. | hep-lat |
Light hadron spectrum and quark masses: Recent developments in lattice QCD calculations of the light hadron spectrum
and quark masses are reviewed. | hep-lat |
Calculating the Two-photon Contribution to $π^0 \rightarrow e^+ e^-$
Decay Amplitude: We develop a new method that allows us to deal with two-photon intermediate
states in a lattice QCD calculation. We apply this method to perform a
first-principles calculation of the $\pi^0 \rightarrow e^+ e^-$ decay
amplitude. Both the real and imaginary parts of amplitude are calculated. The
imaginary part is compared with the prediction of optical theorem to
demonstrate the effectiveness of this method. Our result for the real part of
decay amplitude is $19.68(52)(1.10) \ \text{eV}$, where the first error is
statistical and the second is systematic. | hep-lat |
Operator product expansion and the short distance behavior of 3-flavor
baryon potentials: The short distance behavior of baryon-baryon potentials defined through
Nambu-Bethe-Salpeter wave functions is investigated using the operator product
expansion. In a previous analysis of the nucleon-nucleon case, corresponding to
the SU(3) channels $27_s$ and $\overline{10}_a$, we argued that the potentials
have a repulsive core. A new feature occurs for the case of baryons made up of
three flavors: manifestly asymptotically attractive potentials appear in the
singlet and octet channels. Attraction in the singlet channel was first
indicated by quark model considerations, and recently been found in numerical
lattice simulations. The latter have however not yet revealed asymptotic
attraction in the octet channels; we give a speculative explanation for this
apparent discrepancy. | hep-lat |
Current Status of Indirect CP Violation in Neutral Kaon System: In the standard model (SM), the CP violation is introduced through a single
phase in the CKM matrix. The neutral kaon system is one of the most precise
channels to test how the SM theory describes the experiment data such as
$\epsilon_K$ accurately. The indirect CP violation is parametrized into
$\epsilon_{K}$, which can be calculated directly using lattice QCD. In this
calculation, the largest uncertainty comes from two sources: one is $\hat{B}_K$
and the other is $V_{cb}$. We use the lattice results of $\hat{B}_K$ and
exclusive $V_{cb}$ to calculate the theoretical estimate of $\epsilon_K$, which
turns out to be $3.1\sigma$ away from its experimental value. Here, the error
is evaluated using the standard error propagation method. | hep-lat |
On the entropy bound of three dimensional simplicial gravity: It is proven that the partition function of 3-dimensional simplicial gravity
has an exponential upper bound with the following assumption: any three
dimensional sphere $S^3$ is constructed by repeated identification of
neighboring links and neighboring triangles in the boundary of a simplicial
3-ball. This assumption is weaker than the one proposed by other authors. | hep-lat |
Density of states for gravitational waves: We present ongoing investigations of the first-order confinement transition
of a composite dark matter model, to predict the resulting spectrum of
gravitational waves. To avoid long autocorrelations at the first-order
transition, we employ the Logarithmic Linear Relaxation (LLR) density of states
algorithm. After testing our calculations by reproducing existing results for
compact U(1) lattice gauge theory, we focus on the pure-gauge SU(4) theory
related to the Stealth Dark Matter model. | hep-lat |
Mitigating topological freezing using out-of-equilibrium simulations: Motivated by the recently-established connection between Jarzynski's equality
and the theoretical framework of Stochastic Normalizing Flows, we investigate a
protocol relying on out-of-equilibrium lattice Monte Carlo simulations to
mitigate the infamous computational problem of topological freezing. We test
our proposal on $2d$ $\mathrm{CP}^{N-1}$ models and compare our results with
those obtained adopting the Parallel Tempering on Boundary Conditions proposed
by M. Hasenbusch, obtaining comparable performances. Our work thus sets the
stage for future applications combining our Monte Carlo setup with machine
learning techniques. | hep-lat |
Higgs boson mass bounds in the presence of a very heavy fourth quark
generation: We study the effect of a potential fourth quark generation on the upper and
lower Higgs boson mass bounds. This investigation is based on the numerical
evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the
same Higgs-fermion coupling structure as in the Higgs sector of the electroweak
Standard Model. In particular, the considered model obeys a Ginsparg-Wilson
version of the underlying ${SU}(2)_L\times {U}(1)_Y$ symmetry, being a global
symmetry here due to the neglection of gauge fields in this model. We present
our results on the modification of the upper and lower Higgs boson mass bounds
induced by the presence of a hypothetical very heavy fourth quark doublet.
Finally, we compare these findings to the standard scenario of three fermion
generations. | hep-lat |
Using Gradient Flow to Renormalise Matrix Elements for Meson Mixing and
Lifetimes: Neutral meson mixing and meson lifetimes are theory-side parametrised in
terms four-quark operators which can be determined by calculating weak decay
matrix elements using lattice Quantum Chromodynamics. While calculations of
meson mixing matrix elements are standard, determinations of lifetimes
typically suffer from complications in renormalisation procedures because
dimension-6 four-quark operators can mix with operators of lower mass dimension
and, moreover, quark-line disconnected diagrams contribute.
We present work detailing the idea to use fermionic gradient flow to
non-perturbatively renormalise matrix elements describing meson mixing or
lifetimes, and combining it with a perturbative calculation to match to the
$\overline{\rm MS}$ scheme using the shoft-flow-time expansion. | hep-lat |
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