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Review on Algorithms for dynamical fermions: This review gives an overview on the research of algorithms for dynamical
fermions used in large scale lattice QCD simulations.
First a short overview on the state-of-the-art of ensemble generation at the
physical point is given.
Followed by an overview on necessary steps towards simulation of large
lattices with the Hybrid Monte Carlo algorithm. Here, the status of iterative
solvers and tuning procedures for numerical integrators within the molecular
dynamics are discussed.
This is followed by a review on the on-going developments for algorithms,
with a focus on methods which are potentially useful to simulate gauge theories
at very fine lattice spacings, i.e. well suited to overcome freezing of the
topological charge. This includes modification of the HMC algorithm as well as
a discussion of algorithms which includes the fermion weight via global
correction steps. Parts of the discussions are on the application of generative
models via gauge equivariant flows as well as multi-level algorithms. | hep-lat |
Non-perturbative calculation of Z_m using Asqtad fermions: We report progress on a non-perturbative calculation of the light quark mass
renormalization factor Z_m, using dynamical Asqtad fermions. This quantity is
used to determine the light quark masses in the conventional MS-bar scheme.
Such a non-perturbative determination of Z_m removes uncertainties due to
truncation of its perturbative expansion, currently known to two loops. These
calculations have been carried out using publicly available MILC lattices with
spacings of approximately 0.125 and 0.09 fm. | hep-lat |
Supercurrent conservation in the lattice Wess-Zumino model with
Ginsparg-Wilson fermions: We study supercurrent conservation for the four-dimensional Wess-Zumino model
formulated on the lattice. The formulation is one that has been discussed
several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger)
variety, together with an auxiliary fermion (plus superpartners), such that a
lattice version of U(1)_R symmetry is exactly preserved in the limit of
vanishing bare mass. We show that the almost naive supercurrent is conserved at
one loop. By contrast we find that this is not true for Wilson fermions and a
canonical scalar action. We provide nonperturbative evidence for the
nonconservation of the supercurrent in Monte Carlo simulations. | hep-lat |
Numerical sign problem and the tempered Lefschetz thimble method: The numerical sign problem is a major obstacle to the quantitative
understanding of many important physical systems with first-principles
calculations. Typical examples for such systems include finite-density QCD,
strongly-correlated electron systems and frustrated spin systems, as well as
the real-time dynamics of quantum systems. In this talk, we argue that the
"tempered Lefschetz thimble method" (TLTM) [M. Fukuma and N. Umeda,
arXiv:1703.00861] and its extension, the "worldvolume tempered Lefschetz
thimble method" (WV-TLTM) [M. Fukuma and N. Matsumoto, arXiv:2012.08468], may
be a reliable and versatile solution to the sign problem. We demonstrate the
effectiveness of the algorithm by exemplifying a successful application of
WV-TLTM to the Stephanov model, which is an important toy model of
finite-density QCD. We also discuss the computational scaling of WV-TLTM. | hep-lat |
Condensation of vortices in the X-Y model in 3d: a disorder parameter: A disorder parameter is constructed which signals the condensation of
vortices. The construction is tested by numerical simulations on lattice. | hep-lat |
From confinement to new states of dense QCD matter: Transitions between centre sectors are related to confinement in pure
Yang-Mills theories. We study the impact of these transitions in QCD-like
theories for which centre symmetry is explicitly broken by the presence of
matter. For low temperatures, we provide numerical evidence that centre
transitions do occur with matter merely providing a bias towards the trivial
centre sector until centre symmetry is spontaneously broken at high
temperatures. The phenomenological consequences of these transitions for dense
hadron matter are illustrated in an SU(3) effective quark theory: centre
dressed quarks undergo condensation due to Bose-type statistics forming a
hitherto unknown state of dense but cold quark matter. | hep-lat |
A density of states approach to the hexagonal Hubbard model at finite
density: We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes
the Wang-Landau algorithm to quantum systems with continuous degrees of
freedom, to the fermionic Hubbard model with repulsive interactions on the
honeycomb lattice. We compute the generalized density of states of the average
Hubbard field and divise two reconstruction schemes to extract physical
observables from this result. By computing the particle density as a function
of chemical potential we assess the utility of LLR in dealing with the sign
problem of this model, which arises away from half filling. We show that the
relative advantage over brute-force reweighting grows as the interaction
strength is increased and discuss possible future improvements. | hep-lat |
Status of the QCDOC project: A status report is given of the QCDOC project, a massively parallel computer
optimized for lattice QCD using system-on-a-chip technology. We describe
several of the hardware and software features unique to the QCDOC architecture
and present performance figures obtained from simulating the current VHDL
design of the QCDOC chip with single-cycle accuracy. | hep-lat |
Ordering monomial factors of polynomials in the product representation: The numerical construction of polynomials in the product representation (as
used for instance in variants of the multiboson technique) can become
problematic if rounding errors induce an imprecise or even unstable evaluation
of the polynomial. We give criteria to quantify the effects of these rounding
errors on the computation of polynomials approximating the function $1/s$. We
consider polynomials both in a real variable $s$ and in a Hermitian matrix. By
investigating several ordering schemes for the monomials of these polynomials,
we finally demonstrate that there exist orderings of the monomials that keep
rounding errors at a tolerable level. | hep-lat |
The Renormalized Trajectory of the O(N) Non-linear Sigma Model: The renormalized trajectory (RT) is determined from two different Monte Carlo
renormalization group techniques with $\delta$-function block spin
transformation in the multi-dimensional coupling parameter space of the
two-dimensional non-linear sigma model with O(3) symmetry. At a correlation
length $\xi \approx 3$-$5$, the RT is shown to break away from the straight
line of the fixed point trajectory (FPT) which is orthogonal to the critical
surface and originates from the ultraviolet fixed point (UVFP). The large $N$
calculation of the RT is also presented in the coupling parameter space of the
most general bilinear Hamiltonian. The RT in the large $N$ approximation
exhibits a similar shape with the sharp break occurring at a somewhat smaller
correlation length. | hep-lat |
Polynomial Hybrid Monte Carlo algorithm for lattice QCD with an odd
number of flavors: We present a polynomial hybrid Monte Carlo (PHMC) algorithm for lattice QCD
with odd numbers of flavors of O(a)-improved Wilson quark action. The algorithm
makes use of the non-Hermitian Chebyshev polynomial to approximate the inverse
square root of the fermion matrix required for an odd number of flavors. The
systematic error from the polynomial approximation is removed by a noisy
Metropolis test for which a new method is developed. Investigating the property
of our PHMC algorithm in the N_f=2 QCD case, we find that it is as efficient as
the conventional HMC algorithm for a moderately large lattice size (16^3 times
48) with intermediate quark masses (m_{PS}/m_V ~ 0.7-0.8). We test our
odd-flavor algorithm through extensive simulations of two-flavor QCD treated as
an N_f = 1+1 system, and comparing the results with those of the established
algorithms for N_f=2 QCD. These tests establish that our PHMC algorithm works
on a moderately large lattice size with intermediate quark masses (16^3 times
48, m_{PS}/m_V ~ 0.7-0.8). Finally we experiment with the (2+1)-flavor QCD
simulation on small lattices (4^3 times 8 and 8^3 times 16), and confirm the
agreement of our results with those obtained with the R algorithm and
extrapolated to a zero molecular dynamics step size. | hep-lat |
Cascade Baryon Spectrum from Lattice QCD: A comprehensive study of the cascade baryon spectrum using lattice QCD
affords the prospect of predicting the masses of states not yet discovered
experimentally, and determining the spin and parity of those states for which
the quantum numbers are not yet known. The study of the cascades, containing
two strange quarks, is particularly attractive for lattice QCD in that the
chiral effects are reduced compared to states composed only of u/d quarks, and
the states are typically narrow. We report preliminary results for the cascade
spectrum obtained by using anisotropic N_f = 2 Wilson lattices with temporal
lattice spacing inverse 5.56 GeV. | hep-lat |
Domain-wall fermions with U(1) dynamical gauge fields in
(4+1)-dimensions: We carry out a numerical simulation of a domain-wall model in (4+1)
dimensions, in the presence of a quenched U(1) dynamical gauge field only in an
extra dimension, corresponding to the weak coupling limit of a (4-dimensional)
physical gauge coupling. Our numerical data suggest that the zero mode seems
absent in the symmetric phase, so that it is difficult to construct a lattice
chiral gauge theory in the continuum limit. | hep-lat |
Towards reduction of autocorrelation in HMC by machine learning: In this paper we propose new algorithm to reduce autocorrelation in Markov
chain Monte-Carlo algorithms for euclidean field theories on the lattice. Our
proposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restricted
Boltzmann machine. We examine the validity of the algorithm by employing the
phi-fourth theory in three dimension. We observe reduction of the
autocorrelation both in symmetric and broken phase as well. Our proposing
algorithm provides consistent central values of expectation values of the
action density and one-point Green's function with ones from the original HMC
in both the symmetric phase and broken phase within the statistical error. On
the other hand, two-point Green's functions have slight difference between one
calculated by the HMC and one by our proposing algorithm in the symmetric
phase. Furthermore, near the criticality, the distribution of the one-point
Green's function differs from the one from HMC. We discuss the origin of
discrepancies and its improvement. | hep-lat |
On Scale Determination in Lattice QCD with Dynamical Quarks: Dependence of a/r_c (inverse Sommer parameter in units of lattice spacing a)
on am_q (quark mass in lattice unit) has been observed in all lattice QCD
simulations with sea quarks including the ones with improved actions. How much
of this dependence is a scaling violation has remained an intriguing question.
Our approach has been to investigate the issue with an action with known
lattice artifacts, i.e., the standard Wilson quark and gauge action with
beta=5.6 and 2 degenerate flavors of sea quarks on 16^3 times 32 lattices. In
order to study in detail the sea quark mass dependence, measurements are
carried out at eight values of the PCAC quark mass values am_q from about 0.07
to below 0.015. Though scaling violations may indeed be present for relatively
large am_q, a consistent scenario at sufficiently small am_q seems to emerge in
the mass-independent scheme where for a fixed beta, 1/r_0 and sqrt{sigma} have
linear dependence on m_q as physical effects similar to the quark mass
dependence of the rho mass. We present evidence for this scenario and
accordingly extract the lattice scale (a = 0.0805(7) fm, a^{-1} = 2.45(2) GeV)
by chiral extrapolation to the physical point. | hep-lat |
Split of the pseudo-critical temperatures of chiral and
confine/deconfine transitions by temperature gradient: Searching of the critical endpoint of the phase transition of Quantum
Chromodynamics~(QCD) matter in experiments is of great interest. The
temperature in the fireball of a collider is location dependent, however, most
theoretical studies address the scenario of uniform temperature. In this work,
the effect of temperature gradients is investigated using lattice QCD approach.
We find that the temperature gradient catalyzes chiral symmetry breaking,
meanwhile the temperature gradient increases the Polyakov loop in the confined
phase but suppresses the Polyakov loop in the deconfined phase. Furthermore,
the temperature gradient decreases the pseudo-critical temperature of chiral
transition but increases the pseudo-critical temperature of the
confine/deconfine transition. | hep-lat |
B- and D-meson leptonic decay constants and quark masses from
four-flavor lattice QCD: We describe a recent lattice-QCD calculation of the leptonic decay constants
of heavy-light pseudoscalar mesons containing charm and bottom quarks and of
the masses of the up, down, strange, charm, and bottom quarks. Results for
these quantities are of the highest precision to date. Calculations use 24
isospin-symmetric ensembles of gauge-field configurations with six different
lattice spacings as small as approximately 0.03 fm and several values of the
light quark masses down to physical values of the average up- and
down-sea-quark masses. We use the highly-improved staggered quark (HISQ)
formulation for valence and sea quarks, including the bottom quark. The
analysis employs heavy-quark effective theory (HQET). A novel HQET method is
used in the determination of the quark masses. | hep-lat |
Taste breaking effects in scalar meson correlators: As a consistency check of the staggered-fermion fourth-root approximation, we
analyze the a_0 and f_0 correlators, including the effects of two-meson
taste-multiplet intermediate states. Rooted staggered chiral perturbation
theory describes the contributions from the pseudoscalar taste multiplets in
terms of only a few low energy constants, which have all been previously
determined by the MILC collaboration. In previous work one of us (Prelovsek)
showed that the two-meson ``bubble'' contributions could explain the observed
anomalies in the lattice data for the isovector a_0 channel. In the present
work we extend this analysis to the f_0 channel. On a MILC collaboration
lattice ensemble at 0.12 fm with 2+1 flavors of Asqtad-improved staggered
fermions, we have made new measurements of correlators in both channels for a
variety of momenta. A fit to these correlators gives low energy constants that
are reasonably consistent with previous determinations by the MILC
collaboration.} | hep-lat |
Pion condensation at lower than physical quark masses: In QCD at large enough isospin chemical potential Bose-Einstein Condensation
(BEC) takes place, separated from the normal phase by a phase transition. From
previous studies the location of the BEC line at the physical point is known.
In the chiral limit the condensation happens already at infinitesimally small
isospin chemical potential for zero temperature according to chiral
perturbation theory. The thermal chiral transition at zero density might then
be affected, depending on the shape of the BEC boundary, by its proximity. As a
first step towards the chiral limit, we perform simulations of 2+1 flavors QCD
at half the physical quark masses. The position of the BEC transition is then
extracted and compared with the results at physical masses. | hep-lat |
Recent progress in finite temperature lattice QCD: I review recent progress in the determination of the QCD phase diagram at
finite temperature, in investigations of the nature of the transition or
crossover from the hadronic phase to the quark-gluon plasma phase and in the
determination of the equation of state. This talk will focus on results at zero
chemical potential. | hep-lat |
Lattice Calculations of B to K/K*l+l- form factors: This paper gives a brief review on the recent lattice QCD calculations of the
B to K/K*l+l- semi-leptonic decay form factors. | hep-lat |
Meson spectral functions at nonzero momentum in hot QCD: We present preliminary results for meson spectral functions at nonzero
momentum, obtained from quenched lattice QCD simulations at finite temperature
using the Maximal Entropy Method. Twisted boundary conditions are used to have
access to many momenta p~T. For light quarks, we observe a drastic modification
when heating the system from below to above Tc. In particular, for the vector
spectral density we find a nonzero spectral weight at all energies. | hep-lat |
No coincidence of center percolation and deconfinement in SU(4) lattice
gauge theory: We study the behavior of center sectors in pure SU(4) lattice gauge theory at
finite temperature. The center sectors are defined as spatial clusters of
neighboring sites with values of their local Polyakov loops near the same
center elements. We study the connectedness and percolation properties of the
center clusters across the deconfinement transition. We show that for SU(4)
gauge theory deconfinement cannot be described as a percolation transition of
center clusters, a finding which is different from pure SU(2) or pure SU(3)
Yang Mills theory, where the percolation description even allows for a
continuum limit. | hep-lat |
Asymptotically free models and discrete non-Abelian groups: We study the two-dimensional renormalization-group flow induced by
perturbations that reduce the global symmetry of the O(3) sigma-model to the
discrete symmetries of Platonic solids. We estimate the value of the
correlation length at which differences in the behaviour of the various models
should be expected. For the icosahedron model, we find xi > 200. We provide an
explanation for the recent numerical results of Patrascioiu and Seiler and of
Hasenfratz and Niedermayer. | hep-lat |
Precise Determination of the Charm Quark Mass: The determination of the charm quark mass is now possible to 1% from QCD,
with lattice QCD pushing the error down below 1%. I will describe the
ingredients of this approach and how it can achieve this accuracy. Results for
quark mass ratios, m_c/m_s and m_b/m_c, can also be determined to 1% from
lattice QCD, allowing accuracy for the heavy quark masses to be leveraged into
the light quark sector. I will discuss the prospects for, and importance of,
improving results in future calculations. | hep-lat |
Improved Error Estimate for the Valence Approximation: We construct a systematic mean-field-improved coupling constant and quark
loop expansion for corrections to the valence (quenched) approximation to
vacuum expectation values in the lattice formulation of QCD. Terms in the
expansion are evaluated by a combination of weak coupling perturbation theory
and a Monte Carlo algorithm. | hep-lat |
Restoring rotational invariance for lattice QCD propagators: This note presents a method to reduce the discretization errors appearing
when solving a Quantum Field Theory in a hypercubic lattice in both position
and momentum-space. The method exploits the artifacts that break rotational
symmetry to recover rotationally invariant results for two-point Green
functions. We show that a combination of the results obtained in position and
momentum space can be useful to signal the presence of rotationally invariant
artifacts making use of their approximate Fourier transforms in the continuum.
The method will be introduced using a Klein-Gordon propagator, and a direct
application to gluon propagator in quenched lattice QCD will be given. | hep-lat |
Progress Towards finding Quark Masses and the QCD scale Lambda from the
Lattice: We discuss recent work trying to extract the renormalised quark masses and
Lambda, the QCD scale, from dynamical simulations in lattice gauge theory. | hep-lat |
Topological Features in a Two-Dimensional Higgs Model: Topological properties of the gauge field in a two-dimensional Higgs model
are investigated. Results of exploratory numerical simulations are presented. | hep-lat |
Confinement Physics in Quantum Chromodynamics: We study the confinement physics in QCD in the maximally abelian (MA) gauge
using the SU(2) lattice QCD, based on the dual-superconductor picture. In the
MA gauge, off-diagonal gluon components are forced to be small, and the
off-diagonal angle variable $\chi_\mu(s)$ tends to be random. Within the
random-variable approximation for $\chi_\mu(s)$, we analytically prove the
perimeter law of the off-diagonal gluon contribution to the Wilson loop in the
MA gauge, which leads to abelian dominance on the string tension. To clarify
the origin of abelian dominance for the long-range physics, we study the
charged-gluon propagator in the MA gauge using the lattice QCD, and find that
the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon is
induced by the MA gauge fixing. In the MA gauge, there appears the macroscopic
network of the monopole world-line covering the whole system, which would be
identified as monopole condensation at a large scale. To prove monopole
condensation in the field-theoretical manner, we derive the inter-monopole
potential from the dual Wilson loop in the monopole part of QCD, which carries
the nonperturbative QCD aspects, in the MA gauge. The dual gluon mass is
evaluated as $m_B \simeq $0.5GeV in the monopole part in the infrared region,
which is the evidence of the dual Higgs mechanism by monopole condensation. | hep-lat |
The lattice Schwinger model as a discrete sum of filled Wilson loops: Using techniques from hopping expansion we identically map the lattice
Schwinger model with Wilson fermions to a model of oriented loops on the
lattice. This is done by first computing the explicit form of the fermion
determinant in the external field. Subsequent integration of the gauge fields
renders a sum over all loop configurations with simple Gaussian weights
depending on the number of plaquettes enclosed by the loops. In our new
representation vacuum expectation values of local fermionic operators (scalars,
vectors) can be computed by simply counting the loop flow through the sites
(links) supporting the scalars (vectors). The strong coupling limit, possible
applications of our methods to 4-D models and the introduction of a chemical
potential are discussed. | hep-lat |
Toward the excited isoscalar meson spectrum from lattice QCD: We report on the extraction of an excited spectrum of isoscalar mesons using
lattice QCD. Calculations on several lattice volumes are performed with a range
of light quark masses corresponding to pion masses down to about 400 MeV. The
distillation method enables us to evaluate the required disconnected
contributions with high statistical precision for a large number of meson
interpolating fields. We find relatively little mixing between light and
strange in most JPC channels; one notable exception is the pseudoscalar sector
where the approximate SU(3)F octet, singlet structure of the {\eta}, {\eta}' is
reproduced. We extract exotic JPC states, identified as hybrid mesons in which
an excited gluonic field is coupled to a color-octet qqbar pair, along with
non-exotic hybrid mesons embedded in a qqbar-like spectrum. | hep-lat |
The finite temperature QCD using 2+1 flavors of domain wall fermions at
N_t = 8: We study the region of the QCD phase transition using 2+1 flavors of domain
wall fermions (DWF) and a $16^3 \times 8$ lattice volume with a fifth dimension
of $L_s = 32$. The disconnected light quark chiral susceptibility, quark number
susceptibility and the Polyakov loop suggest a chiral and deconfining crossover
transition lying between 155 and 185 MeV for our choice of quark mass and
lattice spacing. In this region the lattice scale deduced from the Sommer
parameter $r_0$ is $a^{-1} \approx 1.3$ GeV, the pion mass is $\approx 300$ MeV
and the kaon mass is approximately physical. The peak in the chiral
susceptibility implies a pseudo critical temperature $T_c = 171(10)(17)$ MeV
where the first error is associated with determining the peak location and the
second with our unphysical light quark mass and non-zero lattice spacing. The
effects of residual chiral symmetry breaking on the chiral condensate and
disconnected chiral susceptibility are studied using several values of the
valence $L_s$. | hep-lat |
Charm quark mass and D-meson decay constants from two-flavour lattice
QCD: We present a computation of the charm quark's mass and the leptonic D-meson
decay constants f_D and f_{D_s} in two-flavour lattice QCD with
non-perturbatively O(a) improved Wilson quarks. Our analysis is based on the
CLS configurations at two lattice spacings (a=0.065 and 0.048 fm, where the
lattice scale is set by f_K) and pion masses ranging down to ~ 190 MeV at
L*m_pi > 4, in order to perform controlled continuum and chiral extrapolations
with small systematic uncertainties. | hep-lat |
Thermodynamic Study for Conformal Phase in Large Nf Gauge Theory: We investigate the chiral phase transition at finite temperature (T) in
colour SU(3) Quantum Chromodynamics (QCD) with six species of fermions (Nf = 6)
in the fundamental representation. The simulations have been performed by using
lattice QCD with improved staggered fermions. The critical couplings (bc) for
the chiral phase transition are observed for several temporal extensions Nt,
and the two-loop asymptotic scaling of the dimensionless ratio Tc/Lambda_L
(Lambda_L = Lattice Lambda-parameter) is found to be achieved for Nt >= 6.
Further, we collect bc at Nf = 0 (quenched), and Nf = 4 at a fixed Nt = 6 as
well as Nf = 8 at Nt = 6 and 12, the latter relying on our earlier study. The
results are consistent with enhanced fermionic screening at larger Nf. The
ratio Tc/Lambda_L depends very mildly on Nf in the Nf = 0-4 region, begins
increasing at Nf = 6, and significantly grows up at Nf = 8, as Nf reaches to
the edge of the conformal window. We discuss the interrelation of the results
with preconformal dynamics in the light of a functional renormalization group
analysis. | hep-lat |
Wilson Fermions, Random Matrix Theory and the Aoki Phase: The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero
lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a
systematic expansion in the quark mass, the momentum and $a^2$. Starting from
this chiral Lagrangian we obtain an analytical expression for the spectral
density of $\gamma_5 (D_W+m)$ in the microscopic domain. It is shown that the
$\gamma_5$-Hermiticity of the Dirac operator necessarily leads to a coefficient
of the $a^2$ term that is consistent with the existence of an Aoki phase. The
transition to the Aoki phase is explained, and the interplay of the index of
$D_W$ and nonzero $a$ is discussed. We formulate a random matrix theory for the
Wilson Dirac operator with index $\nu$ (which, in the continuum limit, becomes
equal to the topological charge of gauge field configurations). It is shown by
an explicit calculation that this random matrix theory reproduces the
$a^2$-dependence of the chiral Lagrangian in the microscopic domain, and that
the sign of the $a^2$-term is directly related to the $\gamma_5$-Hermiticity of
$D_W$. | hep-lat |
Proton and neutron electromagnetic radii and magnetic moments from
lattice QCD: We present results for the electromagnetic form factors of the proton and
neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS)
ensembles including both quark-connected and -disconnected contributions. The
$Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form
factor data is fitted simultaneously to the expressions resulting from
covariant chiral perturbation theory including vector mesons amended by models
for lattice artefacts. From these fits, we determine the electric and magnetic
radii and the magnetic moments of the proton and neutron, as well as the Zemach
radius of the proton. To assess the influence of systematic effects, we average
over various cuts in the pion mass and the momentum transfer, as well as over
different models for the lattice-spacing and finite-volume dependence, using
weights derived from the Akaike Information Criterion (AIC). | hep-lat |
Glueball spectroscopy in lattice QCD using gradient flow: Removing ultraviolet noise from the gauge fields is necessary for glueball
spectroscopy in lattice QCD. It is known that the Yang-Mills gradient flow
method is an alternative approach instead of link smearing or link fuzzing in
various aspects. In this work we study the application of the gradient flow
technique to the construction of the extended glueball operators. We examine a
simple application of the gradient flow method, which has some problems in
glueball mass calculations at large flow time because of its nature of
diffusion in space-time. To avoid this problem, the spatial links are evolved
by the ``spatial gradient flow'', that is defined to restrict the diffusion to
spatial directions only. We test the spatial gradient flow in calculations of
glueball two-point functions and Wilson loops as a new smearing method, and
then discuss its efficiency in comparison with the original gradient flow
method and the conventional method. Furthermore, to demonstrate the feasibility
of our proposed method, we determine the masses of the three lowest-lying
glueball states, corresponding to the $0^{++}$, $2^{++}$ and $0^{-+}$
glueballs, in the continuum limit in the pure Yang-Mills theory. | hep-lat |
Current status of $\varepsilon_K$ in lattice QCD: We present the current status of $\varepsilon_K$ evaluated directly from the
standard model using lattice QCD inputs. The lattice QCD inputs include
$\hat{B}_K$, $\xi_0$, $\xi_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$.
Recently, FLAG has updated $\hat{B}_K$, exclusive $|V_{cb}|$ has been updated
with new lattice data in the $\bar{B}\to D\ell\bar{\nu}$ decay mode, and
RBC-UKQCD has updated $\xi_0$ and $\xi_2$. We find that the standard model
evaluation of $\varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) is
$3.2\sigma$ lower than the experimental value, while that with inclusive
$|V_{cb}|$ (heavy quark expansion) shows no tension. | hep-lat |
Sensitivity of the Polyakov loop to chiral symmetry restoration: In the heavy, static quark mass regime of QCD, the Polyakov loop is well
known to be an order parameter of the deconfinement phase transition; however,
the sensitivity of the Polyakov loop to the deconfinement of light, dynamical
quarks is less clear. On the other hand, from the perspective of an effective
Lagrangian written in the vicinity of the chiral transition, the Polyakov loop
is an energy-like operator and should hence scale as any energy-like operator
would. We show here that the Polyakov loop and heavy-quark free energy are
sensitive to the chiral transition, i.e. their scaling is consistent with
energy-like observables in 3-$d$ $O(N)$ universality classes. | hep-lat |
Numerical Evaluation of a Soliton Pair with Long Range Interaction: Within the model of topological particles (MTP) we determine the interaction
energy of monopole pairs, sources and sinks of a Coulombic field. The monopoles
are represented by topological solitons of finite size and mass, described by a
field without any divergences. We fix the soliton centres in numerical
calculations at varying distance. Due to the finite size of the solitons we get
deviations from the Coulomb potential at distances of a few soliton radii. We
compare the numerical results for these deviations with the running of the
coupling in perturbative QED. | hep-lat |
Recent Developments in Dual Lattice Algorithms: We review recent progress in numerical simulations with dually transformed
SU(2) LGT, starting with a discussion of explicit dual amplitudes and
algorithms for SU(2) pure Yang Mills in D=3 and D=4. In the D=3 case, we
discuss results that validate the dual algorithm against conventional
simulations. We also review how a local, exact dynamical fermion algorithm can
naturally be incorporated into the dual framework. We conclude with an outlook
for this technique and a look at some of the current challenges we've
encountered with this method, specifically critical slowing down and the sign
problem. | hep-lat |
Renormalization Group Therapy: We point out a general problem with the procedures commonly used to obtain
improved actions from MCRG decimated configurations. Straightforward
measurement of the couplings from the decimated configurations, by one of the
known methods, can result into actions that do not correctly reproduce the
physics on the undecimated lattice. This is because the decimated
configurations are generally not representative of the equilibrium
configurations of the assumed form of the effective action at the measured
couplings. Curing this involves fine-tuning of the chosen MCRG decimation
procedure, which is also dependent on the form assumed for the effective
action. We illustrate this in decimation studies of the SU(2) LGT using
Swendsen and Double Smeared Blocking decimation procedures. A single-plaquette
improved action involving five group representations and free of this pathology
is given. | hep-lat |
Lattice QCD Impact on Determination of the CKM Matrix: We review many lattice QCD calculations that impact the precise determination
of the CKM matrix. We focus on decay constants and semileptonic form factors of
both light ($\pi$ and K) and heavy-light ($D_{(s)}$ and $B_{(s)}$) mesons.
Implication of $\Lambda_b$ form factors will be shown. When combined with
experimental results for branching fractions and differential decay rates, the
above calculations strongly constrain the first two rows of the CKM matrix. We
discuss a long standing difference between $|V_{ub}|$ and $|V_{cb}|$ as
determined from exclusive or inclusive decays. | hep-lat |
Confining Classical Configurations: We construct a family of smooth, almost self-dual, non-thermalized SU(2)
gauge field configurations, and measure the average of the fundamental, adjoint
and spin $\frac{3}{2}$ representation Wilson loops on them. We get area law in
all three cases. We also study thermalised configurations at $\beta= 2.325$
after cooling. The ratio of string tension in the spin j representation over
that in the fundamental, stays constant with cooling. | hep-lat |
A classification of 2-dim Lattice Theory: A unified classification and analysis is presented of two dimensional Dirac
operators of QCD-like theories in the continuum as well as in a naive lattice
discretization. Thereby we consider the quenched theory in the strong coupling
limit. We do not only consider the case of a lattice which has an even number
of lattice sites in both directions and is thus equivalent to the case of
staggered fermions. We also study lattices with one or both directions with an
odd parity to understand the general mechanism of changing the universality
class via a discretization. Furthermore we identify the corresponding random
matrix ensembles sharing the global symmetries of these QCD-like theories.
Despite the Mermin-Wagner-Coleman theorem we find good agreement of lattice
data with our random matrix predictions. | hep-lat |
QCD with domain wall quarks: We present lattice calculations in QCD using a variant of Kaplan fermions
which retain the continuum SU(N)xSU(N) chiral symmetry on the lattice in the
limit of an infinite extra dimension. In particular, we show that the pion mass
and the four quark matrix element related to K_0-K_0-bar mixing have the
expected behavior in the chiral limit, even on lattices with modest extent in
the extra dimension, e.g. N_s=10. | hep-lat |
Improved gradient flow for step scaling function and scale setting: The gradient flow renormalized coupling offers a simple and relatively
inexpensive way to calculate the step scaling function and the lattice scale,
but both applications can be hindered by large lattice artifacts. Recently we
introduced an empirical non-perturbative improvement that can reduce, even
remove $\mathcal{O}(a^2)$ lattice artifacts. The method is easy to implement
and can be applied to any lattice gauge theory of interest both in step scaling
studies and for scale setting. In this talk I will briefly review this
improvement method and discuss its application for determining the discrete
$\beta$ function of the 8 and 12 flavor SU(3) systems and for improved scale
setting in 2+1+1 flavor QCD | hep-lat |
Radiative transitions in charmonium from $N_f=2$ twisted mass lattice
QCD: We present a study for charmonium radiative transitions:
$J/\psi\rightarrow\eta_c\gamma$, $\chi_{c0}\rightarrow J/\Psi\gamma$ and
$h_c\rightarrow\eta_c\gamma$ using $N_f=2$ twisted mass lattice QCD gauge
configurations. The single-quark vector form factors for $\eta_c$ and
$\chi_{c0}$ are also determined. The simulation is performed at a lattice
spacing of $a= 0.06666$ fm and the lattice size is $32^3\times 64$. After
extrapolation of lattice data at nonzero $Q^2$ to 0, we compare our results
with previous quenched lattice results and the available experimental values. | hep-lat |
Warped Domain Wall Fermions: We consider Kaplan's domain wall fermions in the presence of an Anti-de
Sitter (AdS) background in the extra dimension. Just as in the flat space case,
in a completely vector-like gauge theory defined after discretizing this extra
dimension, the spectrum contains a very light charged fermion whose chiral
components are localized at the ends of the extra dimensional interval. The
component on the IR boundary of the AdS space can be given a large mass by
coupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge
invariance can be restored either by taking the limit of infinite proper length
of the extra dimension or by reducing the AdS curvature radius towards zero. In
the latter case, the Kaluza-Klein modes stay heavy and the resulting classical
theory approaches a chiral gauge theory, as we verify numerically. Potential
difficulties for this approach could arise from the coupling of the
longitudinal mode of the light gauge boson, which has to be treated
non-perturbatively. | hep-lat |
Rigidity and percolation of center vortices: Effective action of center vortices in SU(2) lattice gauge theory is
investigated by studying the correlation between the action density on their
worldsheets and their geometric properties. It turns out that center vortices
are rigid, however, their dynamics is more complicated than that of rigid
random surfaces, since some coupling constants have nonstandard scaling
dimensions. As a result, the properties of center vortices are almost
completely determined by curvature-dependent effects. This, in turn, provides a
qualitative explanation of vortex percolation. | hep-lat |
Study of intermediate states in the inclusive semileptonic $B
\rightarrow X_c l ν$ decay structure function: We analyze the inclusive semileptonic $B \to X_c \ell\nu$ structure functions
in 2+1-flavor lattice QCD. The M\"obius domain-wall fermion action is used for
light, strange, charm and bottom quarks. The structure function receives
contributions from various exclusive modes, including the dominant S-wave
states $D^{(*)}_s$ as well as the P-wave states $D_s^{**}$. We can identify
them in the lattice data, from which we put some constraints on the $B_s \to
D_s^{**}\ell\nu$ form factors. | hep-lat |
Excited States of U(1)$_{2+1}$ Lattice Gauge Theory from Monte Carlo
Hamiltonian: We address an old problem in lattice gauge theory - the computation of the
spectrum and wave functions of excited states. Our method is based on the
Hamiltonian formulation of lattice gauge theory. As strategy, we propose to
construct a stochastic basis of Bargmann link states, drawn from a physical
probability density distribution. Then we compute transition amplitudes between
stochastic basis states. From a matrix of transition elements we extract energy
spectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge
theory. We test the method by computing the energy spectrum, wave functions and
thermodynamical functions of the electric Hamiltonian of this theory and
compare them with analytical results. We observe a reasonable scaling of
energies and wave functions in the variable of time. We also present first
results on a small lattice for the full Hamiltonian including the magnetic
term. | hep-lat |
Hadron Spectrum and Matrix Elements in QCD with Dynamical Wilson
Fermions at 6/g^2=5.3: We present results of a lattice simulation of quantum chromodynamics with two
degenerate flavors of dynamic Wilson fermions at $6/g^2=5.3$ at each of two
dynamical fermion hopping parameters, $\kappa=0.1670$ and 0.1675, corresponding
to pion masses in lattice units of about 0.45 and 0.31. The simulations include
three other values of valence quark mass, in addition to the dynamical quarks.
We present calculations of masses and of the decay constants of vector mesons
and of pseudoscalars, including the D-meson decay constant. The effects of sea
quarks on matrix elements and spectroscopy are small. | hep-lat |
Topological Fluctuations in Dense Matter with Two Colors: We study the topological charge fluctuations of an SU(2) lattice gauge theory
containing both N_f=2 and 4 flavors of Wilson fermion, at low temperature with
non-zero chemical potential $\mu$. The topological susceptibility, chi_T, is
used to characterize differing physical regimes as mu is varied between the
onset of matter at mu_o and and color deconfinement at mu_d. Suppression of
instantons by matter via Debye screening is also investigated, revealing
effects not captured by perturbative predictions. In particular, the breaking
of scale invariance leads to the mean instanton size rho becoming mu-dependent
in the regime between onset and deconfinement, with a scaling rho~1/mu^2 over
the range mu_o<mu<mu_d, resulting in an enhancement of chi_T immediately above
onset. | hep-lat |
Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model
Embedding: We investigate SU(2) gauge fields topology using new approach, which exploits
the well known connection between SU(2) gauge theory and quaternionic
projective sigma-models and allows to formulate the topological charge density
entirely in terms of sigma-model fields. The method is studied in details and
for thermalized vacuum configurations is shown to be compatible with
overlap-based definition. We confirm that the topological charge is distributed
in localized four dimensional regions which, however, are not compatible with
instantons. Topological density bulk distribution is investigated at different
lattice spacings and is shown to possess some universal properties. | hep-lat |
Gradient flow, confinement, and magnetic monopole in U(1) lattice gauge
theory: In the gradient flow method of lattice gauge theory, coarse graining is
performed so as to reduce the action, and as the coarse graining progresses,
the field strength becomes very small. However, the confinement property that
particles interact strongly is not lost by the gradient flow. It is seemingly
mysterious, and something stable against coarse graining is expected to be
behind the nature of confinement. By performing Monte Carlo simulations of U(1)
lattice gauge theory, we discuss the relationship between the gradient flow and
magnetic monopoles created by the compactness of the U(1) gauge group. Many
magnetic monopoles are generated in the confinement phase but not so many in
the deconfinement phase. Since the monopole is a kind of topological quantity,
the number of monopoles does not change much by the coarse graining. To
investigate why the confinement properties are not lost by the gradient flow,
we computed Wilson loops and Polyakov loops separating them into the field
strength and the monopole contributions. We found that the field strength,
which decreases with the gradient flow, does not affect confinement properties,
and the monopole and the confinement properties are strongly related.
Furthermore, we discuss the relationship between the magnetic monopole and the
center symmetry, which is the symmetry broken by the confinement phase
transition. | hep-lat |
Fermi point in graphene as a monopole in momentum space: We consider the effective field theory of graphene monolayer with the Coulomb
interaction between fermions taken into account. The gauge field in momentum
space is introduced. The position of the Fermi point coincides with the
position of the corresponding monopole. The procedure of extracting such
monopoles during lattice simulations is suggested. | hep-lat |
Staggered fermions and their $O(a)$ improvements: Expanding upon the arguments of Sharpe, we explicitly implement the Symanzik
improvement program demonstrating the absence of order $a$ terms in the
staggered fermion action. We propose a general program to improve fermion
operators to remove $O(a)$ corrections from their matrix elements, and
demonstrate this program for the examples of matrix elements of fermion
bilinears and $B_K$. We also determine the additional operators which must be
added to improve the staggered fermion currents. | hep-lat |
Identifying spin and parity of charmonia in flight with lattice QCD: The spectrum of charmonium resonances contains a number of unanticipated
states along with several conventional quark-model excitations. The hadrons of
different quantum numbers $J^P$ appear in a fairly narrow energy band, where
$J^P$ refers to the spin-parity of a hadron at rest. This poses a challenge for
Lattice QCD studies of (coupled-channel) meson-meson scattering aimed at the
determination of scattering amplitudes and resonance pole positions. A wealth
of information for this purpose can be obtained from the lattice spectra in
frames with nonzero total momentum. These are particularly dense since hadrons
with different $J^P$ contribute to any given lattice irreducible
representation. This is because $J^P$ is not a good quantum number in flight,
and also because the continuum symmetry is reduced on the lattice. In this
paper we address the assignment of the underlying continuum $J^P$ quantum
numbers to charmonia in flight using a $N_f = 2 + 1$ CLS ensemble. As a first
step, we apply the single-hadron approach, where only interpolating fields of
quark-antiquark type are used. The approach follows techniques previously
applied to the light meson spectrum by the Hadron Spectrum Collaboration. The
resulting spectra of charmonia with assigned $J^P$ will provide valuable
information for the parameterization of (resonant) amplitudes in future
determinations of resonance properties with lattice QCD. | hep-lat |
Spontaneous symmetry breaking via inhomogeneities and the differential
surface tension: We discuss spontaneously broken quantum field theories with a continuous
symmetry group via the constraint effective potential. Employing lattice
simulations with constrained values of the order parameter, we demonstrate
explicitly that the path integral is dominated by inhomogeneous field
configurations and that these are unambiguously related to the flatness of the
effective potential in the broken phase. We determine characteristic features
of these inhomogeneities, including their topology and the scaling of the
associated excess energy with their size. Concerning the latter we introduce
the differential surface tension -- the generalization of the concept of a
surface tension pertaining to discrete symmetries. Within our approach,
spontaneous symmetry breaking is captured merely via the existence of
inhomogeneities, i.e. without the inclusion of an explicit breaking parameter
and a careful double limiting procedure to define the order parameter. While
here we consider the three-dimensional $O(2)$ model, we also elaborate on
possible implications of our findings for the chiral limit of QCD. | hep-lat |
GomalizingFlow.jl: A Julia package for Flow-based sampling algorithm for
lattice field theory: GomalizingFlow.jl: is a package to generate configurations for quantum field
theory on the lattice using the flow based sampling algorithm in Julia
programming language. This software serves two main purposes: to accelerate
research of lattice QCD with machine learning with easy prototyping, and to
provide an independent implementation to an existing public Jupyter notebook in
Python/PyTorch. GomalizingFlow.jl implements, the flow based sampling
algorithm, namely, RealNVP and Metropolis-Hastings test for two dimension and
three dimensional scalar field, which can be switched by a parameter file. HMC
for that theory also implemented for comparison. This package has Docker image,
which reduces effort for environment construction. This code works both on CPU
and NVIDIA GPU. | hep-lat |
Weak Decays of Heavy-Light Mesons on the Lattice: Semi-Leptonic
Formfactors: We report results (on an intermediate statistics sample) of a study of weak
semi-leptonic formfactors of $B$ and $D$ decays, addressing the uncertainties
from mass extrapolations to chiral and to heavy quarks. Moreover, we present a
nonperturbative test to the LMK current renormalization scheme for vector
current {\it transition} matrix elements and find remarkable agreement. | hep-lat |
Vortices, monopoles and confinement: We construct the creation operator of a vortex using the methods developed
for monopoles. The vacuum expectation value of this operator is interpreted as
a disorder parameter describing vortex condensation and is studied numerically
on a lattice in SU(2) gauge theory. The result is that vortices behave in the
vacuum in a similar way to monopoles. The disorder parameter is different from
zero in the confined phase, and vanishes at the deconfining phase transition.
We discuss this behaviour in terms of symmetry. Correlation functions of the
vortex creation operator at zero temperature are also investigated. A
comparison is made with related results by other groups. | hep-lat |
Dynamically-coupled partial-waves in $ρπ$ isospin-2 scattering from
lattice QCD: We present the first determination of $\rho \pi$ scattering, incorporating
dynamically-coupled partial-waves, using lattice QCD, a first-principles
numerical approach to QCD. Considering the case of isospin-2 $\rho \pi$, we
calculate partial-wave amplitudes with $J \le 3$ and determine the degree of
dynamical mixing between the coupled $S$ and $D$-wave channels with $J^P=1^+$.
The analysis makes use of the relationship between scattering amplitudes and
the discrete spectrum of states in the finite volume lattice. Constraints on
the scattering amplitudes are provided by over one hundred energy levels
computed on two lattice volumes at various overall momenta and in several
irreducible representations of the relevant symmetry groups. The spectra follow
from variational analyses of matrices of correlations functions computed with
large bases of meson-meson operators. Calculations are performed with
degenerate light and strange quarks tuned to the physical strange quark mass so
that $m_\pi \sim 700$ MeV, ensuring that the $\rho$ is stable against strong
decay. This work demonstrates the successful application of techniques, opening
the door to calculations of scattering processes that incorporate the effects
of dynamically-coupled partial-waves, including those involving resonances or
bound states. | hep-lat |
Contour deformations for non-holomorphic actions: We show how contour deformations may be used to control the sign problem of
lattice Monte Carlo calculations with non-holomorphic actions. Such actions
arise naturally in quantum mechanical scattering problems. The approach is
demonstrated in conjunction with the holomorphic gradient flow. As our central
example we compute the real-time evolution of a particle in a one-dimensional
analog of the Yukawa potential. | hep-lat |
Comparing meson-meson and diquark-antidiquark creation operators for a
$\bar b \bar b u d$ tetraquark: We compare two frequently discussed competing structures for a stable $\bar b
\bar b u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ by considering a
meson-meson as well as a diquark-antidiquark creation operator. We treat the
heavy antiquarks as static with fixed positions and find diquark-antidiquark
dominance for $\bar b \bar b$ separations $r < 0.2 \, \text{fm}$, while for $r
> 0.5 \, \text{fm}$ the system essentially corresponds to a pair of $B$ mesons.
For the meson-meson to diquark-antidiquark ratio of the tetraquark we obtain
around $58\%/42\%$. | hep-lat |
Numerical Study of Dense Adjoint Matter in Two Color QCD: We identify the global symmetries of SU(2) lattice gauge theory with N
flavors of staggered fermion in the presence of a quark chemical potential mu,
for fermions in both fundamental and adjoint representations, and anticipate
likely patterns of symmetry breaking at both low and high densities. Results
from numerical simulations of the model with N=1 adjoint flavor on a 4^3x8
lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson
algorithms. It is shown that the sign of the fermion determinant starts to
fluctuate once the model enters a phase with non-zero baryon charge density.
HMC simulations are not ergodic in this regime, but TSMB simulations retain
ergodicity even in the dense phase, and in addition appear to show superior
decorrelation. The HMC results for the equation of state and the pion mass show
good quantitative agreement with the predictions of chiral perturbation theory,
which should hold only for N>=2. The TSMB results incorporating the sign of the
determinant support a delayed onset transition, consistent with the pattern of
symmetry breaking expected for N=1. | hep-lat |
Meson screening masses at finite temperature with Highly Improved
Staggered Quarks: We report on the first study of the screening properties of the mesonic
excitations with strange ($s$) and charm ($c$) quarks, specifically the ground
states of the pseudo-scalar and vector meson excitations for the $\bar{s}s$,
$\bar{s}c$ and $\bar{c}c$ flavor combinations, using the Highly Improved
Staggered Quark action with dynamical physical strange quark and
nearly-physical up and down quarks. By comparing with their respective vacuum
meson masses and by investigating the influence of the changing temporal
boundary conditions of the valence quarks we study the thermal modifications of
these mesonic excitations. While the $\bar{s}s$ states show significant
modifications even below the chiral crossover temperature $T_c$, the
modifications of the open-charm and charmonium like states become visible only
for temperatures $T\gtrsim T_c$ and $T\gtrsim1.2T_c$, respectively. | hep-lat |
The pion quasiparticle in the low-temperature phase of QCD: We investigate the properties of the pion quasiparticle in the
low-temperature phase of two-flavor QCD on the lattice with support from chiral
effective theory. We find that the pion quasiparticle mass is significantly
reduced compared to its value in the vacuum, in contrast to the static
screening mass, which increases with temperature. By a simple argument, the two
masses are expected to determine the quasiparticle dispersion relation near the
chiral limit. Analyzing two-point functions of the axial charge density at
non-vanishing spatial momentum, we find that the predicted dispersion relation
and the residue of the pion pole are simultaneously consistent with the lattice
data at low momentum. The test, based on fits to the correlation functions, is
confirmed by a second analysis using the Backus-Gilbert method. | hep-lat |
Matrix product states for gauge field theories: The matrix product state formalism is used to simulate Hamiltonian lattice
gauge theories. To this end, we define matrix product state manifolds which are
manifestly gauge invariant. As an application, we study 1+1 dimensional one
flavour quantum electrodynamics, also known as the massive Schwinger model, and
are able to determine very accurately the ground state properties and
elementary one-particle excitations in the continuum limit. In particular, a
novel particle excitation in the form of a heavy vector boson is uncovered,
compatible with the strong coupling expansion in the continuum. We also study
non-equilibrium dynamics by simulating the real-time evolution of the system
induced by a quench in the form of a uniform background electric field. | hep-lat |
Comparison of Improved and Unimproved Quenched Hadron Spectroscopy: We make a comparison between our quenched-hadron-spectroscopy results for the
non-perturbatively-improved Wilson action and the corresponding unimproved
case, at beta=6.2 on the same set of gauge configurations. Within our
statistics, we find a sizeable improvement for the baryon spectrum and for the
determination of the strange-quark mass. | hep-lat |
Direct detection of metal-insulator phase transitions using the modified
Backus-Gilbert method: The detection of the (semi)metal-insulator phase transition can be extremely
difficult if the local order parameter which characterizes the ordered phase is
unknown.In some cases, it is even impossible to define a local order parameter:
the most prominent example of such system is the spin liquid state. This state
was proposed to exist in theHubbard model on the hexagonal lattice in a region
between the semimetal phase and the antiferromagnetic insulator phase. The
existence of this phase has been the subject of a long debate. In order to
detect these exotic phases we must use alternative methods to those used for
more familiar examples of spontaneous symmetry breaking. We have modified the
Backus-Gilbert method of analytic continuation which was previously used in the
calculation of the pion quasiparticle mass in lattice QCD. The modification of
the method consists of the introduction of the Tikhonov regularization scheme
which was used to treat the ill-conditioned kernel. This modified
Backus-Gilbert method is applied to the Euclidean propagators in momentum space
calculated using the hybridMonte Carlo algorithm. In this way, it is possible
to reconstruct the full dispersion relation and to estimate the mass gap, which
is a direct signal of the transition to the insulating state. We demonstrate
the utility of this method in our calculations for the Hubbard model on the
hexagonal lattice. We also apply the method to the metal-insulator phase
transition in the Hubbard-Coulomb model on the square lattice. | hep-lat |
Cluster Percolation and Critical Behaviour in Spin Models and SU(N)
Gauge Theories: The critical behaviour of several spin models can be simply described as
percolation of some suitably defined clusters, or droplets: the onset of the
geometrical transition coincides with the critical point and the percolation
exponents are equal to the thermal exponents. It is still unknown whether,
given a model, one can define at all the droplets. In the cases where this is
possible, the droplet definition depends in general on the specific model at
study and can be quite involved. We propose here a simple general definition
for the droplets: they are clusters obtained by joining nearest-neighbour spins
of the same sign with some bond probability p_B, which is the minimal
probability that still allows the existence of a percolating cluster at the
critical temperature T_c. By means of lattice Monte Carlo simulations we find
that this definition indeed satisfies the conditions required for the droplets,
for many classical spin models, discrete and continuous, both in two and in
three dimensions. In particular, our prescription allows to describe exactly
the confinement-deconfinement transition of SU(N) gauge theories as Polyakov
loop percolation. | hep-lat |
Nucleon Properties at Finite Volume: the Epsilon Prime Regime: We study the properties of the nucleon in highly asymmetric volumes where the
spatial dimensions are small but the time dimension is large in comparison to
the inverse pion mass. To facilitate power-counting at the level of Feynman
diagrams, we introduce $\epsilon^\prime$-power-counting which is a special case
of Leutwyler's $\delta$-power-counting. Pion zero-modes enter the
$\epsilon^\prime$-counting perturbatively, in contrast to both the $\epsilon$-
and $\delta$-power-countings, since $m_q < q\bar{q}> V$ remains large. However,
these modes are enhanced over those with non-zero momenta and enter at lower
orders in the $\epsilon^\prime$-expansion than they would in large volume
chiral perturbation theory. We discuss an application of
$\epsilon^\prime$-counting by determining the nucleon mass, magnetic moment and
axial matrix element at the first nontrivial order in the
$\epsilon^\prime$-expansion. | hep-lat |
Hadron form factors using density-density correlators: Gauge invariant density-density correlators yield detailed information on
hadron structure. Hadron deformation and form factors can be extracted for
momentum transfers up to about 6 GeV$^2$. We use stochastic techniques and
dilution to compute the all to all propagator required for the exact evaluation
of density-density correlators. We present first results for the pion form
factor. | hep-lat |
Proton momentum and angular momentum decompositions with overlap
fermions: We present a calculation of the proton momentum and angular momentum
decompositions using overlap fermions on a $2+1$-flavor RBC/UKQCD domain-wall
lattice at 0.143 fm with a pion mass of 171 MeV which is close to the physical
one. A complete determination of the momentum and angular momentum fractions
carried by up, down, strange and glue inside the proton has been done with
valence pion masses varying from 171 to 391 MeV. We have utilized fast Fourier
transform on the stochastic-sandwich method for connected-insertion parts and
the cluster-decomposition error reduction technique for disconnected-insertion
parts has been used to reduce statistical errors. The full nonperturbative
renormalization and mixing between the quark and glue operators are carried
out. The final results are normalized with the momentum and angular momentum
sum rules and reported at the physical valence pion mass at ${\overline{\rm
{MS}}}\, (\mu = 2\ {\rm{GeV}})$. The renormalized momentum fractions for the
quarks and glue are $\langle x \rangle^q = 0.491(20)(23)$ and $\langle x
\rangle^g = 0.509(20)(23)$, respectively, and the renormalized total angular
momentum fractions for quarks and glue are $2 J^q = 0.539(22)(44)$ and $2 J^g =
0.461(22)(44)$, respectively. The quark spin fraction is $\Sigma =
0.405(25)(37)$ from our previous work and the quark orbital angular momentum
fraction is deduced from $2 L^q = 2 J^q - \Sigma$ to be $0.134(22)(44)$. | hep-lat |
Improved determination of $B_K$ with staggered quarks: We present results for the kaon mixing parameter $B_K$ obtained using
improved staggered fermions on a much enlarged set of MILC asqtad lattices.
Compared to our previous publication, which was based largely on a single
ensemble at each of the three lattice spacings $a\approx 0.09\;$fm, $0.06\;$fm
and $0.045\;$fm, we have added seven new fine and four new superfine ensembles,
with a range of values of the light and strange sea-quark masses. We have also
increased the number of measurements on one of the original ensembles. This
allows us to do controlled extrapolations in the light and strange sea-quark
masses, which we do simultaneously with the continuum extrapolation. This
reduces the extrapolation error and improves the reliability of our error
estimates. Our final result is $\hat{B}_K = 0.7379 \pm 0.0047 (\text{stat}) \pm
0.0365 (\text{sys})$. | hep-lat |
The spectrum of lattice QCD with staggered fermions at strong coupling: Using 4 flavors of staggered fermions at infinite gauge coupling, we compare
various analytic results for the hadron spectrum with exact Monte Carlo
simulations. Agreement with Ref. \cite{Martin_etal} is very good, at the level
of a few percent.
Our results give credence to a discrepancy between the baryon mass and the
critical chemical potential, for which baryons fill the lattice at zero
temperature and infinite gauge coupling. Independent determinations of the
latter set it at about 30% less than the baryon mass. One possible explanation
is that the nuclear attraction becomes strong at infinite gauge coupling. | hep-lat |
Twist free energy and critical behavior of 3D U(1) LGT at finite
temperature: The twist free energy is computed in the Villain formulation of the 3D U(1)
lattice gauge theory at finite temperature. This enables us to obtain
renormalization group equations describing a critical behavior of the model in
the vicinity of the deconfinement phase transition. These equations are used to
check the validity of the Svetitsky-Yaffe conjecture regarding the critical
behavior of the lattice U(1) model. In particular, we calculate the two-point
correlation function of the Polyakov loops and determine some critical indices. | 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 |
The phase diagram of the three-dimensional Z2 gauge Higgs system at zero
and finite temperature: We study the effect of adding a matter field to the Z2 gauge model in three
dimensions at zero and finite temperature. Up to a given value of the parameter
regulating the coupling, the matter field produces a slight shift of the
transition line without changing the universality class of the pure gauge
theory, as seen by finite size scaling analysis or by comparison, in the finite
temperature case, to exact formulas of conformal field theory. At zero
temperature the critical line turns into a first-order transition. The fate of
this kind of transition in the finite temperature case is discussed. | hep-lat |
Static quark-antiquark potential in the quark-gluon plasma from lattice
QCD: We present a state-of-the-art determination of the complex valued static
quark-antiquark potential at phenomenologically relevant temperatures around
the deconfinement phase transition. Its values are obtained from
non-perturbative lattice QCD simulations using spectral functions extracted via
a novel Bayesian inference prescription. We find that the real part, both in a
gluonic medium as well as in realistic QCD with light $u$, $d$ and $s$ quarks,
lies close to the color singlet free energies in Coulomb gauge and shows Debye
screening above the (pseudo) critical temperature $T_c$. The imaginary part is
estimated in the gluonic medium, where we find that it is of the same order of
magnitude as in hard-thermal loop resummed perturbation theory in the
deconfined phase. | hep-lat |
Numerical study of chiral magnetic effect in quenched SU(2) lattice
gauge theory: A possible experimental observation of the chiral magnetic effect in heavy
ion collisions at RHIC was recently reported by the STAR Collaboration. We
study signatures of this effect in SU(2) lattice gluodynamics with the chirally
invariant Dirac operator. We find that at zero temperature the local
fluctuations of an electric current of quarks and chirality fluctuations
increase with external Abelian magnetic field. The external magnetic field
leads to spatial separation of the quark's electric charges. The separation
increases with the strength of the magnetic field. As temperature gets higher
the dependence of these quantities on the strength of the magnetic field
becomes weaker. In the deconfinement phase the local fluctuations of the chiral
density and of the spatial components of the quarks electric current are large
and are almost independent on the external magnetic field. The local
fluctuations of the electric charge density decrease with the strength of the
magnetic field in this phase. | hep-lat |
On isospin breaking in $τ$ decays for $(g-2)_μ$ from Lattice QCD: Hadronic spectral functions of $\tau$ decays have been used in the past to
provide an alternative determination of the LO Hadronic Vacuum Polarization
relevant for the (g-2) of the muon. Following recent developments and results
in Lattice QCD+QED calculations, we explore the possibility of studying the
isospin breaking corrections of $\tau$ spectral functions for this prediction.
We present preliminary results at physical pion mass based on Domain Wall
Fermion ensembles generated by the RBC/UKQCD collaboration. | hep-lat |
N=2 Wess-Zumino model on the d=2 Euclidean lattice: We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean lattice
in connection with a restoration of the Leibniz rule in the limit $a\to0$ in
perturbatively finite theory. We are interested in the difference between the
Wilson and Ginsparg-Wilson fermions and in the effects of extra interactions
introduced by an analysis of Nicolai mapping. As for the Wilson fermion, it
induces a linear divergence to individual tadpole diagrams in the limit
$a\to0$, which is absent in the Ginsparg-Wilson fermion. This divergence
suggests that a careful choice of lattice regularization is required in a
reliable numerical simulation. As for the effects of the extra couplings
introduced by an analysis of Nicolai mapping, the extra couplings do not
completely remedy the supersymmetry breaking in correlation functions induced
by the failure of the Leibniz rule in perturbation theory, though those
couplings ensure the vanishing of vacuum energy arising from disconnected
diagrams. Supersymmetry in correlation functions is recovered in the limit
$a\to 0$ {\em with or without} those extra couplings. In the context of lattice
theory, it may be properly said that supersymmetry does not improve ultraviolet
properties but rather it is well accommodated in theories with good ultraviolet
properties. | hep-lat |
Scaling Properties of the Probability Distribution of Lattice Gribov
Copies: We study the problem of the Landau gauge fixing in the case of the SU(2)
lattice gauge theory. We show that the probability to find a lattice Gribov
copy increases considerably when the physical size of the lattice exceeds some
critical value $\approx2.75/\sqrt{\sigma}$, almost independent of the lattice
spacing. The impact of the choice of the copy on Green functions is presented.
We confirm that the ghost propagator depends on the choice of the copy, this
dependence decreasing for increasing volumes above the critical one. The gluon
propagator as well as the gluonic three-point functions are insensitive to
choice of the copy (within present statistical errors). Finally we show that
gauge copies which have the same value of the minimisation functional ($\int
d^4x (A^a_\mu)^2$) are equivalent, up to a global gauge transformation, and
yield the same Green functions. | hep-lat |
Lattice-QCD Determination of the Hyperon Axial Couplings in the
Continuum Limit: We present the first continuum extrapolation of the hyperon octet axial
couplings ($g_{\Sigma \Sigma}$ and $g_{\Xi \Xi}$) from $N_f=2+1+1$ lattice QCD.
These couplings are important parameters in the low-energy effective field
theory description of the octet baryons and fundamental to the nonleptonic
decays of hyperons and to hyperon-hyperon and hyperon-nucleon scattering with
application to neutron stars. We use clover lattice fermion action for the
valence quarks with sea quarks coming from configurations of $N_f=2+1+1$ highly
improved staggered quarks (HISQ) generated by MILC Collaboration. Our work
includes the first calculation of $g_{\Sigma \Sigma}$ and $g_{\Xi \Xi}$
directly at the physical pion mass on the lattice, and a full account of
systematic uncertainty, including excited-state contamination, finite-volume
effects and continuum extrapolation, all addressed for the first time. We find
the continuum-limit hyperon coupling constants to be $g_{\Sigma
\Sigma}=0.4455(55)_\text{stat}(65)_\text{sys}$ and $g_{\Xi \Xi}
=-0.2703(47)_\text{stat}(13)_\text{sys}$, which correspond to low-energy
constants of $D = 0.708(10)_\text{stat}(6)_\text{sys}$ and $F =
0.438(7)_\text{stat}(6)_\text{sys}$. The corresponding SU(3) symmetry breaking
is 9\% which is about a factor of 2 smaller than the earlier lattice estimate. | hep-lat |
Wilson fermions with imaginary chemical potential: We study the phase structure of imaginary chemical potential.
We calculate the Polyakov loop using clover-improved Wilson action and
renormalization improved gauge action. We obtain a two-state signals indicating
the first order phase transition for $\beta = 1.9, \mu_I = 0.2618,
\kappa=0.1388$ on $8^3\times 4$ lattice volume We also present a result of the
matrix reduction formula for the Wilson fermion. | hep-lat |
Light Meson Distribution Amplitudes: We calculated the first two moments of the light-cone distribution amplitudes
for the pseudoscalar mesons ($\pi$ and $K$) and the longitudinally polarised
vector mesons ($\rho$, $K^*$ and $\phi$) as part of the UKQCD and RBC
collaborations' $N_f=2+1$ domain-wall fermion phenomenology programme. These
quantities were obtained with a good precision and, in particular, the expected
effects of $SU(3)$-flavour symmetry breaking were observed. Operators were
renormalised non-perturbatively and extrapolations to the physical point were
made, guided by leading order chiral perturbation theory. The main results
presented are for two volumes, $16^3\times 32$ and $24^3\times 64$, with a
common lattice spacing. Preliminary results for a lattice with a finer lattice
spacing, $32^3\times64$, are discussed and a first look is taken at the use of
twisted boundary conditions to extract distribution amplitudes. | hep-lat |
Wilson fermions with chirally twisted mass: Lattice formulations of QCD with Wilson fermions and a chirally twisted quark
mass matrix provide an attractive framework for non-perturbative numerical
studies. Owing to reparameterization invariance, the limiting continuum theory
is just QCD. No spurious quark zero modes, which are responsible for the
problem with exceptional configurations, can occur at finite values of the
quark mass. Moreover, the details of the lattice formulation can be adjusted so
as to simplify the renormalization and the O($a$) improvement of several
quantities of phenomenological relevance. The first exploratory studies in the
quenched approximation yield very encouraging results. | hep-lat |
Scattering of two and three physical pions at maximal isospin from
lattice QCD: We present the first direct $N_f=2$ lattice QCD computation of two- and
three-$\pi^+$ scattering quantities that includes an ensemble at the physical
point. We study the quark mass dependence of the two-pion phase shift, and the
three-particle interaction parameters. We also compare to phenomenology and
chiral perturbation theory (ChPT). In the two-particle sector, we observe good
agreement to the phenomenological fits in $s$- and $d$-wave, and obtain $M_\pi
a_0 = -0.0481(86)$ at the physical point from a direct computation. In the
three-particle sector, we observe reasonable agreement at threshold to the
leading order chiral expansion, i.e.\@ a mildly attractive three-particle
contact term. In contrast, we observe that the energy-dependent part of the
three-particle quasilocal scattering quantity is not well described by leading
order ChPT. | hep-lat |
Non-perturbative renormalization of tensor currents: strategy and
results for $N_f = 0$ and $N_f = 2$ QCD: Tensor currents are the only quark bilinear operators lacking a
non-perturbative determination of their renormalisation group (RG) running
between hadronic and electroweak scales. We develop the setup to carry out the
computation in lattice QCD via standard recursive finite-size scaling
techniques, and provide results for the RG running of tensor currents in $N_f =
0$ and $N_f = 2$ QCD in the continuum for various Schr\"odinger Functional
schemes. The matching factors between bare and renormalisation group invariant
currents are also determined for a range of values of the lattice spacing
relevant for large-volume simulations, thus enabling a fully non-perturbative
renormalization of physical amplitudes mediated by tensor currents. | hep-lat |
Gap in the Dirac spectrum and quark propagator symmetries in lattice QCD: Recent studies on lattice QCD have shown the emergence of large symmetries at
high temperature. This includes not only the restoration $SU(n_F)_L \times
SU(n_F)_R$, but also the effective emergence of an unexpected symmetry group,
namely $SU(2)_{CS}$, which contains $U(1)_A$ as subgroup. At the same time, at
high $T$, a gap in Dirac spectrum appears. As it is argued in several works of
\textit{L. Glozman et al.}, there should be a connection between a gap in the
Dirac spectrum and the presence of $SU(2)_{CS}$.In this paper, we analyze
whether the quark propagator can be invariant under $SU(n_F)_L \times
SU(n_F)_R$ and $SU(2)_{CS}$ transformations, in case of a gap in the Dirac
spectrum, and consequently the invariance of hadron correlators, giving the
condition for a quark propagator to be invariant under $SU(2)_{CS}$. | hep-lat |
ΔS=2 and ΔC=2 bag parameters in the SM and beyond from
Nf=2+1+1 twisted-mass LQCD: We present unquenched lattice QCD results for the matrix elements of
four-fermion operators relevant to the description of the neutral K and D
mixing in the Standard Model and its extensions. We have employed simulations
with Nf = 2 + 1 + 1 dynamical sea quarks at three values of the lattice
spacings in the interval 0.06 - 0.09 fm and pseudoscalar meson masses in the
range 210 - 450 MeV. Our results are extrapolated to the continuum limit and to
the physical pion mass. Renormalization constants have been determined
non-perturbatively in the RI-MOM scheme. In particular, for the Kaon
bag-parameter, which is relevant for the \overline{K}^0-K^0 mixing in the
Standard Model, we obtain B_K^{RGI} = 0.717(24). | hep-lat |
Algorithms for Lattice QCD with Dynamical Fermions: We consider recent progress in algorithms for generating gauge field
configurations that include the dynamical effects of light fermions. We survey
what has been achieved in recent state-of-the-art computations, and examine the
trade-offs between performance and control of systematic errors. We briefly
review the use of polynomial and rational approximations in Hybrid Monte Carlo
algorithms, and some of the theory of on-shell chiral fermions on the lattice.
This provides a theoretical framework within which we compare algorithmic
alternatives for their implementation; and again we examine the trade-offs
between speed and error control. | hep-lat |
A Lattice Study of Spectator Effects in Inclusive Decays of B-Mesons: We compute the matrix elements of the operators which contribute to spectator
effects in inclusive decays of $B$-mesons. The results agree well with
estimates based on the vacuum saturation (factorization) hypothesis. For the
ratio of lifetimes of charged and neutral mesons we find
$\tau(B^-)/\tau(B_d)=1.03\pm 0.02\pm 0.03$, where the first error represents
the uncertainty in our evaluation of the matrix elements, and the second is an
estimate of the uncertainty due to the fact that the Wilson coefficient
functions have only been evaluated at tree-level in perturbation theory. This
result is in agreement with the experimental measurement. We also discuss the
implications of our results for the semileptonic branching ratio and the charm
yield. | hep-lat |
Gauge theory of things alive and universal dynamics: Positing complex adaptive systems made of agents with relations between them
that can be composed, it follows that they can be described by gauge theories
similar to elementary particle theory and general relativity. By definition, a
universal dynamics is able to determine the time development of any such system
without need for further specification. The possibilities are limited, but one
of them - reproduction fork dynamics - describes DNA replication and is the
basis of biological life on earth. It is a universal copy machine and a
renormalization group fixed point. A universal equation of motion in continuous
time is also presented. | hep-lat |
Nucleon axial form factors using lattice QCD simulations with a physical
value of the pion mass: We present results on the nucleon axial and induced pseudo-scalar form
factors using an ensemble of two degenerate twisted mass clover-improved
fermions generated at the physical value of the pion mass. We evaluate the
isovector and the isoscalar, as well as, the strange and the charm axial form
factors. The disconnected contributions are evaluated using recently developed
methods that include deflation of the lower eigenstates, allowing us to extract
the isoscalar, strange and charm axial form factors. We find that the
disconnected quark loop contributions are non-zero and particularly large for
the induced pseudo-scalar form factor. | hep-lat |
Large center vortices and confinement in 3D Z(2) gauge theory: We study the role of large clusters of center vortices in producing
confinement in 3D Z(2) gauge theory. First, we modify each configuration of a
Monte Carlo-generated ensemble in the confined phase by removing the largest
cluster of center vortices, and show that the ensemble thus obtained does not
confine. Conversely, we show that removing all of the small clusters of center
vortices and leaving the largest one only, confinement is preserved, albeit
with a string tension significantly smaller than the original one. Remarkably,
also the string corrections due to the quantum fluctuations of the confining
flux tube are preserved by this transformation. | hep-lat |
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