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Temperature dependence of shear viscosity of $SU(3)$--gluodynamics
within lattice simulation: In this paper we study the shear viscosity temperature dependence of
$SU(3)$--gluodynamics within lattice simulation. To do so, we measure the
correlation functions of energy-momentum tensor in the range of temperatures
$T/T_c\in [0.9, 1.5]$. To extract the values of shear viscosity we used two
approaches. The first one is to fit the lattice data with some physically
motivated ansatz for the spectral function with unknown parameters and then
determine shear viscosity. The second approach is to apply the Backus-Gilbert
method which allows to extract shear viscosity from the lattice data
nonparametrically. The results obtained within both approaches agree with each
other. Our results allow us to conclude that within the temperature range
$T/T_c \in [0.9, 1.5]$ SU(3)--gluodynamics reveals the properties of a strongly
interacting system, which cannot be described perturbatively, and has the ratio
$\eta/s$ close to the value ${1}/{4\pi}$ in $N = 4$ Supersymmetric Yang-Mills
theory. | hep-lat |
Perturbative renormalization of moments of quark momentum, helicity and
transversity distributions with overlap and Wilson fermions: Using overlap as well as Wilson fermions, we have computed the one-loop
renormalization factors of ten non-singlet operators which measure the third
moment of quark momentum and helicity distributions (the lowest two having been
computed in a previous paper), as well as the lowest three moments of the $g_2$
structure function and the lowest two non-trivial moments of the $h_1$
transversity structure function (plus the tensor charge). These factors are
needed to extract physical observables from Monte Carlo simulations of the
corresponding matrix elements.
An exact chiral symmetry is maintained in our calculations with overlap
fermions, and its most important consequence here is that the operators
measuring $g_2$ do not show any of the power-divergent mixings with operators
of lower dimension which are present in the Wilson case. Many of our results
for Wilson fermions are also new; for the remaining ones, we agree with the
literature except in one case. The computations have been carried out using the
symbolic language FORM, in a general covariant gauge, which turns out also to
be useful in checking the gauge-invariance of the final results. | hep-lat |
Roper Resonance in 2+1 Flavor QCD: The low-lying even-parity states of the nucleon are explored in lattice QCD
using the PACS-CS collaboration 2+1-flavor dynamical-QCD gauge-field
configurations made available through the International Lattice Datagrid
(ILDG). The established correlation-matrix approach is used, in which various
fermion source and sink smearings are utilized to provide an effective basis of
interpolating fields to span the space of low-lying energy eigenstates. Of
particular interest is the nature of the first excited state of the nucleon,
the $N{1/2}^{+}$ Roper resonance of $P_{11}$ pion-nucleon scattering. The Roper
state of the present analysis approaches the physical mass, displaying
significant chiral curvature at the lightest quark mass. These full QCD
results, providing the world's first insight into the nucleon mass spectrum in
the light-quark regime, are significantly different from those of quenched QCD
and provide interesting insights into the dynamics of QCD. | hep-lat |
P-wave heavy-light mesons using NRQCD and D234: The masses of S- and P-wave heavy-light mesons are computed in quenched QCD
using a classically and tadpole-improved action on anisotropic lattices. Of
particular interest are the splittings among P-wave states, which have not yet
been resolved experimentally; even the ordering of these states continues to be
discussed in the literature. The present work leads to upper bounds for these
splittings, and is suggestive, but not conclusive, about the ordering. | hep-lat |
Non-perturbative renormalization of left-left four-fermion operators in
quenched lattice QCD: We define a family of Schroedinger Functional renormalization schemes for the
four-quark multiplicatively renormalizable operators of the $\Delta F = 1$ and
$\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization
with quenched Wilson quarks, we compute non-perturbatively the renormalization
group running of these operators in the continuum limit in a large range of
renormalization scales. Continuum limit extrapolations are well controlled
thanks to the implementation of two fermionic actions (Wilson and Clover). The
ratio of the renormalization group invariant operator to its renormalized
counterpart at a low energy scale, as well as the renormalization constant at
this scale, is obtained for all schemes. | hep-lat |
Quark mass dependence of the low-lying charmed mesons at one loop in
HH$χ$PT: We study the light and heavy quark mass dependence of the low-lying charmed
mesons in the framework of one-loop HH$\chi$PT. The low energy constants are
determined by analyzing the available lattice data from different LQCD
simulations. Model selection tools are implemented to determine the relevant
parameters as required by data with a higher precision. Discretization and
other effects due to the charm quark mass setting are discussed. | hep-lat |
Exact Chiral Fermions and Finite Density on Lattice: Any mu^2-divergence is shown analytically to be absent for a class of actions
for Overlap and Domain Wall Fermions with nonzero chemical potential. All such
actions are, however, shown to violate the chiral invariance. While the
parameter M of these actions can be shown to be irrelevant in the continuum
limit, as expected, it is shown numerically that the continuum limit can be
reached with relatively coarser lattices for M in the range of 1.5-1.6. | hep-lat |
Antisymmetric and other subleading corrections to scaling in the local
potential approximation: For systems in the universality class of the three-dimensional Ising model we
compute the critical exponents in the local potential approximation (LPA), that
is, in the framework of the Wegner-Houghton equation. We are mostly interested
in antisymmetric corrections to scaling, which are relatively poorly studied.
We find the exponent for the leading antisymmetric correction to scaling
$\omega_A \approx 1.691$ in the LPA. This high value implies that such
corrections cannot explain asymmetries observed in some Monte Carlo
simulations. | hep-lat |
Lattice QCD investigation of a doubly-bottom $\bar{b} \bar{b} u d$
tetraquark with quantum numbers $I(J^P) = 0(1^+)$: We use lattice QCD to investigate the spectrum of the $\bar{b} \bar{b} u d$
four-quark system with quantum numbers $I(J^P) = 0(1^+)$. We use five different
gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one
at the physical pion mass, and treat the heavy $\bar{b}$ quark within the
framework of lattice nonrelativistic QCD. Our work improves upon previous
similar computations by considering in addition to local four-quark
interpolators also nonlocal two-meson interpolators and by performing a
L\"uscher analysis to extrapolate our results to infinite volume. We obtain a
binding energy of $(-128 \pm 24 \pm 10) \, \textrm{MeV}$, corresponding to the
mass $(10476 \pm 24 \pm 10) \, \textrm{MeV}$, which confirms the existence of a
$\bar{b} \bar{b} u d$ tetraquark that is stable with respect to the strong and
electromagnetic interactions. | hep-lat |
Stable solvers for real-time Complex Langevin: This study explores the potential of modern implicit solvers for stochastic
partial differential equations in the simulation of real-time complex Langevin
dynamics. Not only do these methods offer asymptotic stability, rendering the
issue of runaway solution moot, but they also allow us to simulate at
comparatively largeLangevin time steps, leading to lower computational cost. We
compare different ways of regularizing the underlying path integral and
estimate the errors introduced due to the finite Langevin time. Based on that
insight, we implement benchmark (non-)thermal simulations of the quantum
anharmonic oscillator on the canonical Schwinger-Keldysh contour of short
real-time extent. | hep-lat |
Note on the Lattice Fermion Chiral Symmetry Group: The group structure of the variant chiral symmetry discovered by Luscher in
the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is
shown that the group contains an infinite number of linearly independent
symmetry generators, and the Lie algebra is given explicitly. CP is an
automorphism of the chiral group, and the CP transformation properties of the
symmetry generators is found. Features of the currents associated with these
symmetries are discussed, including the fact that some different, non-commuting
symmetry generators lead to the same Noether current. These strange features
occur in all implementations of lattice fermions based on the Ginsparg-Wilson
relation, including overlap, domain-wall, and perfect-action chiral fermions.
The conclusions are illustrated in a solvable example, free overlap fermions. | hep-lat |
Intrinsic quark transverse momentum in the nucleon from lattice QCD: A better understanding of transverse momentum (k_T-) dependent quark
distributions in a hadron is needed to interpret several experimentally
observed large angular asymmetries and to clarify the fundamental role of gauge
links in non-abelian gauge theories. Based on manifestly non-local gauge
invariant quark operators we introduce process-independent k_T-distributions
and study their properties in lattice QCD. We find that the longitudinal and
transverse momentum dependence approximately factorizes, in contrast to the
behavior of generalized parton distributions. The resulting quark
k_T-probability densities for the nucleon show characteristic dipole
deformations due to correlations between intrinsic k_T and the quark or nucleon
spin. Our lattice calculations are based on N_f=2+1 mixed action propagators of
the LHP collaboration. | hep-lat |
Singularities of QCD in the complex chemical potential plane: We study the thermodynamic singularities of QCD in the complex chemical
potential plane by a numerical simulation of lattice QCD, and discuss a method
to understand the nature of the QCD phase transition at finite density from the
information of the singularities. The existence of singular points at which the
partition function (Z) vanishes is expected in the complex plane. These are
called Lee-Yang zeros or Fisher zeros. We investigate the distribution of these
singular points using the data obtained by a simulation of two-flavor QCD with
p4-improved staggered quarks. The convergence radius of a Taylor expansion of
ln Z in terms of the chemical potential is also discussed. | hep-lat |
Longitudinal and transverse meson correlators in the deconfined phase
from the lattice: It has long been known that QCD undergoes a deconfining phase transition at
high temperature. One of the consequent features of this new, quark-gluon phase
is that hadrons become unbounded. In this talk meson correlation functions at
non-zero momentum are studied in the deconfined phase using the Maximum Entropy
Method. | hep-lat |
A new lattice measurement for potentials between static SU(3) sources: In this article, a new calculation of static potentials between sources of
different representations in SU(3) gauge group is presented. The results of
author's previous study \cite{Deld00} at the smallest lattice spacing
$a_{s}\simeq0.11$~ fm are shown to have been affected by finite volume effects.
Within statistical errors, the new results obtained here are still in agreement
with both, Casimir scaling and flux tube counting. There is also no
contradiction to the results obtained in Ref.~ \cite{Bali00} which however
exclude flux counting. | hep-lat |
Magnetic properties of light nuclei from lattice QCD: After a short review of Lattice QCD methodology and techniques, I summarize
recent results of Lattice QCD calculations of the interactions of nucleons and
light nuclei with magnetic fields at pion masses of 805 MeV and 450 MeV.
Interestingly, the magnetic moments are found to be consistent with the
experimental values when given in terms of natural nuclear magnetons. The very
low-energy cross section for $np\rightarrow d\gamma$ is calculated and found to
agree with the experimental measurement. First calculations of the magnetic
polarizabilities of light nuclei are presented, with a large isovector
polarizability observed for the nucleon at these heavier pion masses. | hep-lat |
Reweighting Lefschetz Thimbles: We present a novel reweighting technique to calculate the relative weights in
the Lefschetz thimble decomposition of a path integral. Our method is put to
work using a $U(1)$ one-link model providing for a suitable testing ground and
sharing many features with realistic gauge theories with fermions at finite
density. We discuss prospects and future challenges to our method. | hep-lat |
Abelian Dyons in the Maximal Abelian Projection of SU(2) Gluodynamics: Correlations of the topological charge Q, the electric current J^e and the
magnetic current J^m in SU(2) lattice gauge theory in the Maximal Abelian
projection are investigated. It occurs that the correlator <<QJ^e J^m>> is
nonzero for a wide range of values of the bare charge. It is shown that: (i)
the abelian monopoles in the Maximal Abelian projection are dyons which carry
fluctuating electric charge; (ii) the sign of the electric charge e(x)
coincides with that of the product of the monopole charge m(x) and the
topological charge density Q(x). | hep-lat |
Extracting excited states from lattice QCD: the Roper resonance: We present a new method for extracting excited states from a single two-point
correlation function calculated on the lattice. Our method simply combines the
correlation function evaluated at different time slices so as to ``subtract''
the leading exponential decay (ground state) and to give access to the first
excited state. The method is applied to a quenched lattice study (volume = 24^3
x 64, beta = 6.2, 1/a = 2.55 GeV) of the first excited state of the nucleon
using the local interpolating operator O = [uT C gamma5 d] u. The results are
consistent with the identification of our extracted excited state with the
Roper resonance N'(1440). The switching of the level ordering with respect to
the negative-parity partner of the nucleon, N*(1535), is not seen at the
simulated quark masses and, basing on crude extrapolations, is tentatively
expected to occur close to the physical point. | hep-lat |
Electromagnetic properties of doubly charmed baryons in Lattice QCD: We compute the electromagnetic properties of \Xi_cc baryons in 2+1 flavor
Lattice QCD. By measuring the electric charge and magnetic form factors of
\Xi_cc baryons, we extract the magnetic moments, charge and magnetic radii as
well as the \Xi_cc \Xi_cc \rho coupling constant, which provide important
information to understand the size, shape and couplings of the doubly charmed
baryons. We find that the two heavy charm quarks drive the charge radii and the
magnetic moment of \Xi_cc to smaller values as compared to those of, e.g., the
proton. | 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 |
Quenched hadron spectroscopy with improved staggered quark action: We investigate light hadron spectroscopy with an improved quenched staggered
quark action. We compare the results obtained with an improved gauge plus an
improved quark action, an improved gauge plus standard quark action, and the
standard gauge plus standard quark action. Most of the improvement in the
spectroscopy results is due to the improved gauge sector. However, the improved
quark action substantially reduces violations of Lorentz invariance, as
evidenced by the meson dispersion relations. | hep-lat |
Non-perturbative improvement of bilinears in unquenched QCD: We describe how the improvement of quark bilinears generalizes from quenched
to unquenched QCD, and discuss which of the additional improvement constants
can be determined using Ward Identities. | hep-lat |
In search of a scaling scalar glueball: Anisotropic lattices are an efficient means of studying the glueballs of QCD,
however problems arise with simulations of the lightest, scalar state. The mass
is strongly dependent on the lattice spacing, even when a mean-field improved
gluon action is used. The nature and cause of these errors are discussed and
the scaling properties of the scalar from different lattice actions are
presented. | hep-lat |
Finite size scaling in CP(N-1) models: Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic
boundary conditions are investigated by means of the $1/N$ expansion and by
Monte Carlo simulations. Analytic and numerical results for magnetic
susceptibility and correlation length are compared and found to agree for small
volumes. For large volumes a discrepancy is found and explained as an effect of
the physical bound state extension. The leading order finite size effects on
the Abelian string tension are computed and compared with simulations finding
agreement. Finite size dependence of topological quantities is also discussed. | hep-lat |
Determination of the mass anomalous dimension for $N_f=12$ and $N_f=9$
SU($3$) gauge theories: We show the numerical simulation result for the mass anomalous dimension of
the SU($3$) gauge theory coupled to $N_f = 12$ fundamental fermions. We use two
independent methods, namely the step scaling method and the hyperscaling method
of the Dirac mode number, to determine the anomalous dimension in the vicinity
of the infrared fixed point of the theory. We show the continuum extrapolations
keeping the renormalized coupling constant as a reference in both analyses.
Furthermore, some recent works seems to suggest the lower boundary of the
conformal window of the SU($3$) gauge theory exists between $N_f=8$ and $10$.
We also briefly report our new project, in which the numerical simulation of
the SU($3$) gauge theory coupled to $N_f=9$ fundamental fermions has been
performed. | hep-lat |
Contribution of the charm quark to the ΔI=1/2 rule: We report on the progress of our ongoing project to quantify the role of the
charm quark in the non-leptonic decay of a kaon into two pions. The effect of
its associated mass scale in the dynamics underlying the \Delta I = 1/2 rule
can be studied by monitoring the dependence of kaon decay amplitudes on the
charm quark mass using an effective \Delta S = 1 weak Hamiltonian. In contrast
to commonly used approaches the charm quark is kept as an active degree of
freedom. Quenched results in the GIM limit have shown that a significant part
of the \Delta I = 1/2 enhancement is purely due to low-energy QCD effects.
Moving away from the GIM limit involves the computation of diagrams containing
closed quark loops which requires new variance reduction techniques in order to
determine the relevant weak effective low-energy couplings. We employ a
combination of low-mode averaging and stochastic volume sources in order to
compute these diagrams and observe a significant improvement in the statistical
signal. | hep-lat |
Spectrum of Mesons and Baryons with $b$ Quarks: We present highlights of the spectrum of mesons and baryons calculated using
NRQCD for heavy quarks and tadpole improved clover action for the light quarks. | hep-lat |
Instantaneous interquark potential in generalized Landau gauge in SU(3)
lattice QCD: a possible gauge for the quark potential model: We investigate "instantaneous interquark potential", an interesting
gauge-dependent quantity defined from the spatial correlator $<\mathrm{Tr}
[U_4^\dagger(s)U_4(s')]>$ of the temporal link-variable $U_4$, in detail in
generalized Landau gauge using SU(3) quenched lattice QCD. While the
instantaneous potential has no linear part in the Landau gauge, in the Coulomb
gauge, it is expressed by the Coulomb plus linear potential, where the slope is
2-3 times larger than the physical string tension, and the lowest energy state
is considered to be a gluon-chain state. Using the generalized Landau gauge, we
find that the instantaneous potential can be continuously described between the
Landau and the Coulomb gauges, and it approximately reproduces the physical
interquark potential in a specific intermediate gauge, which we call
"$\lambda_C$-gauge". This $\lambda_C$-gauge is expected to provide a
quark-potential-model picture, where dynamical gluons do not appear. We also
investigate $T$-length terminated Polyakov-line correlator and its
corresponding "finite-time potential" in generalized Landau gauge. | hep-lat |
Vacuum alignment and lattice artifacts: When a subgroup of the flavor symmetry group of a gauge theory is weakly
coupled to additional gauge fields, the vacuum tends to align such that the
gauged subgroup is unbroken. At the same time, the lattice discretization
typically breaks the flavor symmetry explicitly, and can give rise to new
lattice-artifact phases with spontaneously broken symmetries. We discuss the
interplay of these two phenomena, using chiral lagrangian techniques. Our first
example is two-flavor Wilson QCD coupled to electromagnetism. We also consider
examples of theories with staggered fermions, and demonstrate that recent
claims in the literature based on the use of staggered fermions are incorrect. | hep-lat |
Broken Symmetries from Minimally Doubled Fermions: Novel chirally symmetric fermion actions containing the minimum amount of
fermion doubling have been recently proposed in the literature. We study the
symmetries and renormalization of these actions and find that in each case,
discrete symmetries, such as parity and time-reversal, are explicitly broken.
Consequently, when the gauge interactions are included, these theories
radiatively generate relevant and marginal operators. Thus the restoration of
these symmetries and the approach to the continuum limit require the
fine-tuning of several parameters. With some assumptions, we show that this
behavior is unavoidable for actions displaying minimal fermion doubling. | hep-lat |
Proton and neutron electromagnetic form factors from lattice QCD: The electromagnetic form factors of the proton and the neutron are computed
within lattice QCD using simulations with quarks masses fixed to their physical
values. Both connected and disconnected contributions are computed. We analyze
two new ensembles of $N_f = 2$ and $N_f = 2 + 1 + 1$ twisted mass
clover-improved fermions and determine the proton and neutron form factors, the
electric and magnetic radii, and the magnetic moments. We use several values of
the sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure
ground state identification. Disconnected contributions are calculated to an
unprecedented accuracy at the physical point. Although they constitute a small
correction, they are non-negligible and contribute up to 15% for the case of
the neutron electric charge radius. | hep-lat |
Remarks on abelian dominance: We used a renormalisation group based smoothing to address two questions
related to abelian dominance. Smoothing drastically reduces short distance
fluctuations but it preserves the long distance physical properties of the
SU(2) configurations. This enabled us to extract the abelian heavy-quark
potential from time-like Wilson loops on Polyakov gauge projected
configurations. We obtained a very small string tension which is inconsistent
with the string tension extracted from Polyakov loop correlators. This shows
that the Polyakov gauge projected abelian configurations do not have a
consistent physical meaning. We also applied the smoothing on SU(2)
configurations to test how sensitive abelian dominance in the maximal abelian
gauge is to the short distance fluctuations. We found that on smoothed SU(2)
configurations the abelian string tension was about 30% smaller than the SU(2)
string tension which was unaffected by smoothing. This suggests that the
approximate abelian dominance found with the Wilson action is probably an
accident and it has no fundamental physical relevance. | hep-lat |
Entanglement entropy of SU(3) Yang-Mills theory: We calculate the entanglement entropy using a SU(3) quenched lattice gauge
simulation. We find that the entanglement entropy scales as $1/l^2$ at small
$l$ as in the conformal field theory. Here $l$ is the size of the system, whose
degrees of freedom is left after the other part are traced out. The derivative
of the entanglement entropy with respect to $l$ hits zero at about $l^{\ast} =
0.6 \sim 0.7$ [fm] and vanishes above the length. It may imply that the
Yang-Mills theory has the mass gap of the order of $1/l^{\ast}$. Within our
statistical errors, no discontinuous change can be seen in the entanglement
entropy. We discuss also a subtle point appearing in gauge systems when we
divide a system with cuts. | hep-lat |
't Hooft loop and the phases of SU(2) LGT: We analyze the vacuum structure of SU(2) lattice gauge theories in D=2,3,4,
concentrating on the stability of 't Hooft loops. High precision calculations
have been performed in D=3; similar results hold also for D=4 and D=2. We
discuss the impact of our findings on the continuum limit of Yang-Mills
theories. | hep-lat |
Real-Time-Evolution of Heavy Quarks in the Glasma: We introduce a novel real-time formulation of lattice NRQCD designed for
simulations in the background of an highly occupied gluon field. By evolving
quarks in the background of a dynamically evolving gluon field we computed the
time-evolution of heavy-quarkonium spectral functions as well as the static and
for finitely heavy quarks generalised potential. We conclude that the back
reaction of the quarks is necessary for any binding process. Here we discuss
the methodology, our results and the origin of the absence of a binding
process. | hep-lat |
Decay constants of B and D mesons from improved relativistic lattice QCD
with two flavours of sea quarks: We present a calculation of the B and D meson decay constants in lattice QCD
with two (Nf=2) flavours of light dynamical quarks, using an O(a)-improved
Wilson action for both light and heavy quarks and a renormalization-group
improved gauge action. Simulations are made at three values of lattice spacing
a=0.22, 0.16, 0.11 fm and four values of sea quark mass in the range m_PS/m_V
\~= 0.8-0.6. Our estimate for the continuum values of the decay constants are
fBd = 208(10)(11) MeV, fBs = 250(10)(13)(^{+8}_{-0}) MeV, fDd = 225(14)(14)
MeV, fDs = 267(13)(17)(^{+10}_{-0}) MeV for Nf=2 where the statistical and
systematic errors are separately listed, and the third error for fBs and fDs
show uncertainty of determination of strange quark mass. We also carry out a
set of quenched simulations using the same action to make a direct examination
of sea quark effects. Taking the ratio of results for Nf=2 and Nf=0, we obtain
fb^{Nf=2}/fb^{Nf=0} = 1.11(6), fbs^{Nf=2}/fbs^{Nf=0} = 1.14(5),
fd^{Nf=2}/\fd^{Nf=0} = 1.03(6), fds^{Nf=2}/\fds^{Nf=0} = 1.07(5). They show a
10-15% increase in the Nf=2 results over those of Nf=0 for the B meson decay
constants, while evidence for such a trend is statistically less clear for the
D meson decay constants. | hep-lat |
Lambda-parameter of lattice QCD with the overlap-Dirac operator: We compute the ratio $\Lambda_L/\Lambda_{\bar{MS}}$ between the scale
parameter $\Lambda_L$, associated with a lattice formulation of QCD using the
overlap-Dirac operator, and $\Lambda_{\bar{MS}}$ of the $\bar{\rm MS}$
renormalization scheme. To this end, the necessary one-loop relation between
the lattice coupling $g_0$ and the coupling renormalized in the $\bar{{\rm
MS}}$ scheme is calculated, using the lattice background field technique. | hep-lat |
Behavior and finite-size effects of the sixth order cumulant in the
three-dimensional Ising universality class: The high-order cumulants of conserved charges are suggested to be sensitive
observables to search for the critical point of Quantum Chromodynamics (QCD).
This has been calculated to the sixth order in experiments. Corresponding
theoretical studies on the sixth order cumulant are necessary. Based on the
universality of the critical behavior, we study the temperature dependence of
the sixth order cumulant of the order parameter using the parametric
representation of the three-dimensional Ising model, which is expected to be in
the same universality class as QCD. The density plot of the sign of the sixth
order cumulant is shown on the temperature and external magnetic field plane.
We found that at non-zero external magnetic field, when the critical point is
approached from the crossover side, the sixth order cumulant has a negative
valley. The width of the negative valley narrows with decreasing external
field. Qualitatively, the trend is similar to the result of Monte Carlo
simulation on a finite-size system. Quantitatively, the temperature of the sign
change is different. Through Monte Carlo simulation of the Ising model, we
calculated the sixth order cumulant of different sizes of systems. We discuss
the finite-size effects on the temperature at which the cumulant changes sign. | hep-lat |
Simulating Yang-Mills theories with a complex coupling: We propose a novel simulation strategy for Yang-Mills theories with a complex
coupling, based on the Lefschetz thimble decomposition. We envisage, that the
approach developed in the present work, can also be adapted to QCD at finite
density, and real time simulations.
Simulations with Lefschetz thimbles offer a potential solution to sign
problems in Monte Carlo calculations within many different models with complex
actions. We discuss the structure of Generalized Lefschetz thimbles for pure
Yang-Mills theories with a complex gauge coupling $\beta$ and show how to
incorporate the gauge orbits. We propose to simulate such theories on the union
of the tangential manifolds to the relevant Lefschetz thimbles attached to the
critical manifolds of the Yang-Mills action. We demonstrate our algorithm on a
(1+1)-dimensional U(1) model and discuss how, starting from the main thimble
result, successive subleading thimbles can be taken into account via a
reweighting approach. While we face a residual sign problem, our novel approach
performs exponentially better than the standard reweighting approach. | hep-lat |
D-branes, Wilson Bags, and Coherent Topological Charge Structure in QCD: Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based
topological charge operator have revealed a laminar structure in the QCD vacuum
consisting of extended, thin, coherent, locally 3-dimensional sheets of
topological charge embedded in 4D space, with opposite sign sheets interleaved.
Studies of localization properties of Dirac eigenmodes have also shown evidence
for the delocalization of low-lying modes on effectively 3-dimensional
surfaces. In this talk, I review some theoretical ideas which suggest the
possibility of 3-dimensionally coherent topological charge structure in
4-dimensional gauge theory and provide a possible interpretation of the
observed structure. I begin with Luscher's ``Wilson bag'' integral over the
3-index Chern-Simons tensor. The analogy with a Wilson loop as a charged world
line in 2-dimensional $CP^{N-1}$ sigma models suggests that the Wilson bag
surface represents the world volume of a physical membrane. The large-N chiral
Lagrangian arguments of Witten also indicate the existence of multiple
``k-vacuum'' states with discontinuous transitions between k-vacua at $\theta=$
odd multiples of $\pi$. The domain walls between these vacua have the
properties of a Wilson bag surface. Finally, I review the AdS/CFT duality view
of $\theta$ dependence in QCD. The dual realtionship between topological charge
in gauge theory and Ramond-Ramond charge in type IIA string theory suggests
that the coherent topological charge sheets observed on the lattice are the
holographic image of wrapped D6 branes. | hep-lat |
Perfect discretizations of differential operators: We investigate an approach for the numerical solution of differential
equations which is based on the perfect discretization of actions. Such perfect
discretizations show up at the fixed points of renormalization group
transformations. This technique of integrating out the high momentum degrees of
freedom with a path integral has been mainly used in lattice field theory,
therefore our study of its application to PDE's explores new possibilities. We
calculate the perfect discretized Laplace operator for several non-trivial
boundary conditions analytically and numerically. Then we construct a
parametrization of the perfect Laplace operator and we show that with this
parametrization discretization errors -- or computation time -- can be reduced
dramatically compared to the standard discretization. | hep-lat |
Deconfinement Phase Transition in Bosonic BMN Model at General Coupling: We present our analysis of the deconfinement phase transition in the bosonic
BMN matrix model. The model is investigated using a non-perturbative lattice
framework. We used the Polyakov loop as the order parameter to monitor the
phase transition, and the results were verified using the separatrix ratio. The
calculations are performed using a large number of colors and a broad range of
temperatures for all couplings. Our results indicate a first-order phase
transition in this theory for all the coupling values that connect the
perturbative and non-perturbative regimes of the theory. | hep-lat |
Berry phase in lattice QCD: We propose the lattice QCD calculation of the Berry phase which is defined by
the ground state of a single fermion. We perform the ground-state projection of
a single-fermion propagator, construct the Berry link variable on a
momentum-space lattice, and calculate the Berry phase. As the first
application, the first Chern number of the (2+1)-dimensional Wilson fermion is
calculated by the Monte Carlo simulation. | hep-lat |
Minimally doubled fermions and their renormalization: Minimally doubled fermions have been proposed as a strictly local
discretization of the QCD quark action, which also preserves chiral symmetry at
finite cut-off. We study the renormalization and mixing properties of two
particular realizations of minimally doubled fermions in lattice perturbation
theory at one loop, and we construct conserved axial currents which have a
simple form involving only nearest-neighbours sites. We also introduce a
notation which allows a unified description of the renormalization properties
of both actions. | 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 |
The pion form factor on the lattice at zero and finite temperature: We calculate the electromagnetic form factor of the pion in quenched lattice
QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is
used together with the consistently O(a) improved current. We calculate the
pion form factor for masses down to m_pi = 360 MeV, extract the charge radius,
and extrapolate toward the physical pion mass. In the second part, we discuss
results for the pion form factor and charge radius at 0.93 T_c and compare with
zero temperature results. | hep-lat |
Semi-leptonic decays of heavy mesons and the Isgur-Wise function in
quenched lattice QCD: The form factors for the semi-leptonic B->D and B->D* decays are evaluated in
quenched lattice QCD at two different values of the coupling, beta=6.0 and 6.2.
The action and the operators are fully O(a) non-perturbatively improved. The
slope of the Isgur-Wise function is evaluated, and found to be
rho^2=0.83^{+15+24}_{-11-1} (quoted errors are statistical and systematic
respectively). Ratios of form factors are evaluated and compared to
experimental determinations. | hep-lat |
Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical
Potential: We present results of a simulation of 2-flavor QCD on a 4x16^3 lattice using
p4-improved staggered fermions with bare quark mass m/T=0.4. Derivatives of the
thermodynamic grand canonical partition function Z(V,T,mu_u,mu_d) with respect
to chemical potentials mu_(u,d) for different quark flavors are calculated up
to sixth order, enabling estimates of the pressure and the quark number density
as well as the chiral condensate and various susceptibilities as functions of
mu_q = (mu_u + mu_d)/2 via Taylor series expansion. Furthermore, we analyze
baryon as well as isospin fluctuations and discuss the relation between the
radius of convergence of the Taylor series and the chiral critical point in the
QCD phase diagram. We argue that bulk thermodynamic observables do not, at
present, provide direct evidence for the existence of a chiral critical point
in the QCD phase diagram. Results are compared to high temperature perturbation
theory as well as a hadron resonance gas model. | hep-lat |
Taste non-Goldstone, flavor-charged pseudo-Goldstone boson masses in
staggered chiral perturbation theory: We calculate the masses of taste non-Goldstone pions and kaons in staggered
chiral perturbation theory through next-to-leading order in the standard power
counting. The results can be used to quantitatively understand taste violations
in existing lattice data generated with staggered fermions and to extract the
$u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the
experimentally observed spectrum. The expressions for the non-Goldstone masses
contain low-energy couplings unique to the non-Goldstone sector. With two
exceptions these enter as coefficients of analytic terms; all the new couplings
can be fixed by performing spectrum calculations. We report one-loop results
for the quenched case and the fully dynamical and partially quenched 1+1+1 and
2+1 flavor cases in the chiral SU(3) and SU(2) theories. | hep-lat |
Comparison of different source calculations in two-nucleon channel at
large quark mass: We investigate a systematic error coming from higher excited state
contributions in the energy shift of light nucleus in the two-nucleon channel
by comparing two different source calculations with the exponential and wall
sources. Since it is hard to obtain a clear signal of the wall source
correlation function in a plateau region, we employ a large quark mass as the
pion mass is 0.8 GeV in quenched QCD. We discuss the systematic error in the
spin-triplet channel of the two-nucleon system, and the volume dependence of
the energy shift. | hep-lat |
Moments of parton evolution probabilities on the lattice within the
Schroedinger functional scheme: We define, within the Schroedinger functional scheme (SF), the matrix
elements of the twist-2 operators corresponding to the first two moments of
non-singlet parton densities. We perform a lattice one-loop calculation that
fixes the relation between the SF scheme and other common schemes and shows the
main source of lattice artefacts. This calculation sets the basis for a
numerical evaluation of the non-perturbative running of parton densities. | hep-lat |
O(4) scaling analysis in two-flavor QCD at finite temperature and
density with improved Wilson quarks: We study the curvature of the chiral transition/crossover line between the
low-temperature hadronic phase and the high-temperature quark-gluon-plasma
phase at low densities, performing simulations of two-flavor QCD with improved
Wilson quarks. After confirming that the chiral order parameter defined by a
Ward-Takahashi identity is consistent with the scaling of the O(4) universality
class at zero chemical potential, we extend the scaling analysis to finite
chemical potential to determine the curvature of the chiral
transition/crossover line at low densities assuming the O(4) universality. To
convert the curvature in lattice units to that of the $T_c(\mu_B)$ in physical
units, we evaluate the lattice scale applying a gradient flow method. We find
$\kappa=0.0006(1)$ in the chiral limit, which is much smaller than that
obtained in (2+1)-flavor QCD with improved staggered quarks. | hep-lat |
Status of the MILC calculation of electromagnetic contributions to
pseudoscalar masses: We calculate pseudoscalar masses on gauge configurations containing the
effects of 2+1 flavors of dynamical asqtad quarks and quenched
electromagnetism. The lattice spacings vary from 0.12 to 0.06 fm. The masses
are fit with staggered chiral perturbation theory including NLO electromagnetic
terms. We attempt to extract the fit parameters for the electromagnetic
contributions, while taking into account the finite volume effects, and
extrapolate them to the physical limit. | hep-lat |
Spectroscopy of two dimensional N=2 Super Yang Mills theory: Albeit the standard model is the most successful model of particles physics,
it still has some theoretical shortcomings, for instance the hierarchy problem,
the absence of dark matter, etc. Supersymmetric extensions of the standard
model could be a possible solution to these problems. One of the building
blocks of these supersymmetric models are supersymmetric gauge theories. It is
expected that they exhibit interesting features like confinement, chiral
symmetry breaking, magnetic monopoles and the like. We present new results on
N=2 Super Yang Mills theory in two dimensions. The lattice action is derived by
a dimensional reduction of the N=1 Super Yang Mills theory in four dimensions.
By preserving the R symmetry of the four dimensional model we can exploit Ward
identities to fine tune our parameters of the model to obtain the chiral and
supersymmetric continuum limit. This allows us to calculate the mass spectrum
at the physical point and compare these results with effective field theories. | hep-lat |
Fast algorithms for simulating chiral fermions in U(1)lattice gauge
theory: In order to develop fast inversion algorithms we have used overlap solvers in
two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional
space-times dimensions has always been a testing ground for algorithms. By the
other side, motivated by our previews work that the two-grid algorithm converge
faster than the standard iterative methods for overlap inversion but not for
all quark masses, we thought to test this idea in less dimensions such as U(1)
gauge theory. Our main objective of this paper it is to implement and develop
the idea of a two level algorithm in a new algorithm coded in QCDLAB. This
implementation is presented in the preconditioned GMRESR algorithm, as our new
contribution in QCDLAB package. The preconditioned part of our algorithm,
different from the one of [18], is the approximation of the overlap operator
with the truncated overlap operator with finite N3 dimension. We have tested it
for 100 statistically independent configurations on 32 x 32 lattice background
U(1) field at coupling constant \b{eta}=1 and for different bare quark masses
mq = [0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1]. We have compared the
convergence history of the preconditioned GMRESR residual norm with another
overlap inverter of QCDLAB as an optimal one, such as SHUMR. We have shown that
our algorithm converges faster than SHUMR for different quark masses. Also, we
have demonstrated that it saves more time for light quarks compared to SHUMR
algorithm. Our algorithm is approximately independent from the quark mass. This
is a key result in simulations with chiral fermions in lattice theories. By the
other side, if we compare the results of [18] for quark mass 0.1 in SU(3),
results that our chosen preconditioned saves a factor of 2 but in U(1). Our
next step is to test this algorithm in SU(3) and to adopt it in parallel. | hep-lat |
Lattice QCD and heavy ion collisions: a review of recent progress: In the last few years, numerical simulations of QCD on the lattice have
reached a new level of accuracy. A wide range of thermodynamic quantities is
now available in the continuum limit and for physical quark masses. This allows
a comparison with measurements from heavy ion collisions for the first time.
Furthermore, calculations of dynamical quantities are also becoming available.
The combined effort from first principles and experiment allows us to gain an
unprecedented understanding of the properties of quark-gluon plasma. I will
review the state-of-the-art results from lattice simulations and connect them
to the experimental information from RHIC and the LHC. | hep-lat |
Hyper-Systolic Parallel Computing: A new class of parallel algorithms is introduced that can achieve a
complexity of O(n^3/2) with respect to the interprocessor communication, in the
exact computation of systems with pairwise mutual interactions of all elements.
Hitherto, conventional methods exhibit a communicational complexity of O(n^2).
The amount of computation operations is not altered for the new algorithm which
can be formulated as a kind of h-range problem, known from the mathematical
field of Additive Number Theory. We will demonstrate the reduction in
communicational expense by comparing the standard-systolic algorithm and the
new algorithm on the connection machine CM5 and the CRAY T3D. The parallel
method can be useful in various scientific and engineering fields like exact
n-body dynamics with long range forces, polymer chains, protein folding or
signal processing. | hep-lat |
Axial and tensor charge of the nucleon with dynamical fermions: We present preliminary results for the axial and tensor charge of the nucleon
obtained from simulations with N_f=2 clover fermions. A comparison with chiral
perturbation theory is attempted. | hep-lat |
Monte Carlo overrelaxation for SU(N) gauge theories: The standard approach to Monte Carlo simulations of SU(N) Yang-Mills theories
updates successive SU(2) subgroups of each SU(N) link. We follow up on an old
proposal of Creutz, to perform overrelaxation in the full SU(N) group instead,
and show that it is more efficient. | hep-lat |
Chromo-electric screening length in 2+1 flavor QCD: We study Polyakov loop as well as correlators of real and imaginary parts of
the Polyakov loop in 2+1 flavor QCD at finite temperature. We use hypercubic
(HYP) smearing to improve the signal in the lattice calculations and to obtain
reliable results for the correlators at large distances. From the large
distance behavior of the correlators we estimate the chromo-electric screening
length to be (0.38-44)/T. Furthermore, we show that the short distance
distortions due to HYP smearing do not affect the physics of interest | hep-lat |
A Critical Surface of Chiral-invariant System with Gauge Boson and
Fermions: In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and
four-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson
equation for the fermion self-energy function is studied on a lattice. We find
that a sensible infrared limit can be defined on a critical surface, which is
consistent with the critical line found in the continuum theory. | hep-lat |
Predictions from Lattice QCD: In the past year, we calculated with lattice QCD three quantities that were
unknown or poorly known. They are the $q^2$ dependence of the form factor in
semileptonic $D\to Kl\nu$ decay, the decay constant of the $D$ meson, and the
mass of the $B_c$ meson. In this talk, we summarize these calculations, with
emphasis on their (subsequent) confirmation by experiments. | hep-lat |
Flavor symmetry breaking in lattice QCD with a mixed action: We study the phase structure of mixed-action QCD with two Wilson sea quarks
and any number of chiral valence quarks (and ghosts), starting from the chiral
lagrangian. A priori, the effective theory allows for a rich phase structure,
including a phase with a condensate made of sea and valence quarks. In such a
phase, mass eigenstates would become admixtures of sea and valence fields, and
pure-sea correlation functions would depend on the parameters of the valence
sector, in contradiction with the actual setup of mixed-action simulations.
Using that the spectrum of the chiral Dirac operator has a gap for nonzero
quark mass we prove that spontaneous symmetry breaking of the flavor symmetries
can only occur within the sea sector. This rules out a mixed condensate, and
implies restrictions on the low-energy constants of the effective theory. | hep-lat |
Semileptonic B to D decays at nonzero recoil with 2+1 flavors of
improved staggered quarks: The Fermilab Lattice-MILC collaboration is completing a comprehensive program
of heavy-light physics on the MILC (2+1)-flavor asqtad ensembles with lattice
spacings as small as 0.045 fm and light-to-strange-quark mass ratios as low as
1/20. We use the Fermilab interpretation of the clover action for heavy valence
quarks and the asqtad action for light valence quarks. The central goal of the
program is to provide ever more exacting tests of the unitarity of the CKM
matrix. We give a progress report on one part of the program, namely the
analysis of the semileptonic decay B to D at both zero and nonzero recoil.
Although final results are not presented, we discuss improvements in the
analysis methods, the statistical errors, and the parameter coverage that we
expect will lead to a significant reduction in the final error for |V_cb| from
this decay channel. | hep-lat |
Detecting Dual Superconductivity in the Ground State of Gauge Theories -
II: A monopole creation operator is constructed: its vacuum expectation value is
an order parameter for dual superconductivity in that, if different from zero
it signals spontaneous breaking of the U(1) symmetry corresponding to monopole
charge conservation. The operator is tested on compact U(1) gauge theory on
lattice. For SU(2) gauge theory it clearly demonstrates that confinement is
produced by dual superconductivity. | hep-lat |
Pion Distribution Amplitudes in the Continuum Limit: We present a lattice-QCD calculation of the pion distribution amplitudes
using large-momentum effective theory (LaMET). Our calculation is carried out
using five ensembles with 2+1+1 flavors of highly improved staggered quarks
(HISQ), generated by MILC collaboration, at 310 MeV and 220 MeV pion mass with
0.06, 0.09, 0.12 and 0.15 fm lattice spacings. We use clover fermion action for
the valence quarks and tune the quark mass to match the lightest light and
strange masses in the sea. The resulting lattice matrix elements are
nonperturbatively renormalized in regularization-independent
momentum-subtraction (RI/MOM) scheme and extrapolated to the continuum. We
compare different approaches to extract the x-dependence of the pion
distribution amplitudes. | hep-lat |
On the lattice construction of electroweak gauge theory: Based on the Ginsparg-Wilson relation, a gauge invariant formulation of
electroweak SU(2)xU(1) gauge theory on the lattice is considered. If the
hypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge
fields, the theory consists of four left-handed SU(2) doublets and it is
possible, as in vector-like theories, to make the fermion measure defined
globally in all topological sectors of SU(2). We then try to incorporate U(1)
gauge field, following L\"uscher's reconstruction theorem. The global
integrability condition is proved for ``gauge loops'' in the space of the U(1)
gauge fields with arbitrary SU(2) gauge field fixed in the background. For
``non-gauge loops'', however, the proof is given so far only for the classical
SU(2) instanton backgrounds. | hep-lat |
A quadrature-based eigensolver with a Krylov subspace method for shifted
linear systems for Hermitian eigenproblems in lattice QCD: We consider a quadrature-based eigensolver to find eigenpairs of Hermitian
matrices arising in lattice quantum chromodynamics. To reduce the computational
cost for finding eigenpairs of such Hermitian matrices, we propose a new
technique for solving shifted linear systems with complex shifts by means of
the shifted CG method. Furthermore using integration paths along horizontal
lines corresponding to the real axis of the complex plane, the number of
iterations for the shifted CG method is also reduced. Some numerical
experiments illustrate the accuracy and efficiency of the proposed method by
comparison with a conventional method. | hep-lat |
Towards Radiative Transitions in Charmonium: We present preliminary calculations towards radiative transitions in
charmonium using anisotropic $N_f = 2 + 1$ dynamical ensembles generated by the
Hadron Spectrum Collaboration. With the use of newer technologies we aim to
investigate transitions between states, including potential exotic charmonium
states, lying higher in the spectrum than in previous studies. A crucial
ingredient in this work is the use of variationally optimised interpolating
operators which allow for a reliable determination of the three-point
correlation functions needed. Using these operators, we perform first
calculations of relevant three-point correlation functions before discussing
future directions. | hep-lat |
Implementation of C* boundary conditions in the Hybrid Monte Carlo
algorithm: In the study of QCD dynamics, C* boundary conditions are physically relevant
in certain cases. In this paper we study the implementation of these boundary
conditions in the lattice formulation of full QCD with staggered fermions. In
particular, we show that the usual even-odd partition trick to avoid the
redoubling of the fermion matrix is still valid in this case. We give an
explicit implementation of these boundary conditions for the Hybrid Monte Carlo
algorithm. | hep-lat |
Mass estimates of the SU(2) $0^{++}$ glueball from spectral methods: The estimation of the K\"all\'en-Lehmann spectral density from gauge
invariant lattice QCD two point correlation functions is proposed, and explored
via an inversion strategy based on Tikhonov regularisation. We test the method
on a mesonic toy model, showing that our methodology is competitive with the
traditional Maximum Entropy Method. As proof of concept the SU(2) glueball
spectrum for the quantum numbers $J^{PC}=0^{++}$ is investigated, for various
values of the lattice spacing, using the published data of arXiv:1910.07756.
Our estimates for the ground state mass are in good agreement with the
traditional approach, which is based on the large time exponential behaviour of
the correlation functions. Furthermore, the spectral density also contains
hints of excites states in the spectrum. Spectroscopic analysis of glueball
two-point functions therefore provides a straightforward and insightful
alternative to the traditional method based on the large time exponential
behaviour of the correlation functions. | hep-lat |
Present and future prospects for lattice QCD calculations of matrix
elements for nEDM: A status report on the calculations of the contribution of four CP violating
operators, the $\Theta$-term, the quark EDM, the chromo EDM and the Weinberg
operator to the neutron EDM are presented. At this time, there exit precise
physical results only for the quark EDM operator by the PNDME collaboration.
First results showing signal in the contributions of the $\Theta$-term and the
connected part of the chromo EDM operator have been presented. The challenge of
divergent mixing in the chromo EDM and Weinberg operators has motivated
calculations in the gradient flow scheme. While there has been steady progress,
the challenges remaining are large. Results with $O(50\%)$ uncertainty with
control over all systematic errors can be expected for the $\Theta$-term over
the next five years. Prediction of a timeline for progress on the chromo EDM
and the Weinberg operators will depend on when the renormalization and
divergent mixing of these operators is brought under control. The most
optimistic scenario is that the gradient flow scheme provides a solution to the
numerical signal and mixing problems for both the gluonic and quark operators. | hep-lat |
Glueballs on the three-sphere: We study the non-perturbative effects of the global features of the
configuration space for SU(2) gauge theory on the three-sphere. The strategy is
to reduce the full problem to an effective theory for the dynamics of the
low-energy modes. By explicitly integrating out the high-energy modes, the
one-loop correction to the effective hamiltonian is obtained. Imposing the
$\theta$ dependence through boundary conditions in configuration space
incorporates the non-perturbative effects of the non-contractable loops in the
full configuration space. After this we obtain the glueball spectrum of the
effective theory with a variational method. | hep-lat |
Discrete Symmetry Enhancement in Nonabelian Models and the Existence of
Asymptotic Freedom: We study the universality between a discrete spin model with icosahedral
symmetry and the O(3) model in two dimensions. For this purpose we study
numerically the renormalized two-point functions of the spin field and the four
point coupling constant. We find that those quantities seem to have the same
continuum limits in the two models. This has far reaching consequences, because
the icosahedron model is not asymptotically free in the sense that the coupling
constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in
the short distance limit. By universality this then also applies to the O(3)
model, contrary to the predictions of perturbation theory. | hep-lat |
Physical and unphysical effects in the mixed SU(2)/SO(3) gauge theory: We investigate possible problems with universality in lattice gauge theory
where a mixed fundamental SU(2) and SO(3)-invariant gauge group is used: the
(second order) finite temperature phase transition becomes involved with first
order effects with increased SO(3) coupling, and this first order effect has a
noticeable coupling dependence for small lattices. We produce evidence that the
first order transition is essentially bulk in nature as generally believed, and
that the finite temperature effects start to separate out from the lower end of
the bulk effects for a lattice of 8 sites in the finite temperature direction.
We strengthen our picture of the first order effects as artefacts by using an
improved action: this shifts the end point of the first order line away from
the fundamental SU(2) axis. | hep-lat |
Scaling behavior at the tricritical point in the fermion-gauge-scalar
model: We investigate a strongly coupled U(1) gauge theory with fermions and scalars
on the lattice and analyze whether the continuum limit might be a
renormalizable theory with dynamical mass generation. Most attention is paid to
the phase with broken chiral symmetry in the vicinity of the tricritical point
found in the model. There we investigate the scaling of the masses of the
composite fermion and of some bosonic bound states. As a by-product we confirm
the mean-field exponents at the endpoint in the U(1)-Higgs model, by analyzing
the scaling of the Fisher zeros. | hep-lat |
Thermal mass and dispersion relations of quarks in the deconfined phase
of quenched QCD: Temporal quark correlation functions are analyzed in quenched lattice QCD for
two values of temperature above the critical temperature (Tc) for
deconfinement, T=1.5Tc and 3Tc. A two-pole ansatz for the quark spectral
function is used to determine the bare quark mass and the momentum dependence
of excitation spectra on large lattices of size up to 128^3x16. The dependence
of the quark correlator on these parameters as well as the finite volume
dependence of the excitation energies are analyzed in detail in order to
examine the reliability of our analysis. Our results suggest the existence of
quasi-particle peaks in the quark spectrum. We furthermore find evidence that
the dispersion relation of the plasmino mode has a minimum at non-zero momentum
even in the non-perturbative region near Tc. We also elaborate on the
enhancement of the quark correlator near the chiral limit which is observed at
T=1.5Tc on about half of the gauge configurations. We attribute this to the
presence of near zero-modes of the fermion matrix that are associated with
non-trivial topology of the gauge configurations. | hep-lat |
Chiral transition and monopole percolation in lattice scalar QED with
quenched fermions: We study the interplay between topological observables and chiral and Higgs
transitions in lattice scalar QED with quenched fermions. Emphasis is put on
the chiral transition line and magnetic monopole percolation at strong gauge
coupling. We confirm that at infinite gauge coupling the chiral transition is
described by mean field exponents. We find a rich and complicated behaviour at
the endpoint of the Higgs transition line which hampers a satisfactory analysis
of the chiral transition. We study in detail an intermediate coupling, where
the data are consistent both with a trivial chiral transition clearly separated
from monopole percolation and with a chiral transition coincident with monopole
percolation, and characterized by the same critical exponent $\nu \simeq 0.65$.
We discuss the relevance (or lack thereof) of these quenched results to our
understanding of the \chupiv\ model. We comment on the interplay of magnetic
monopoles and fermion dynamics in more general contexts. | hep-lat |
Attractive $N$-$φ$ Interaction and Two-Pion Tail from Lattice QCD
near Physical Point: First results on the interaction between the $\phi$-meson and the nucleon
($N$) are presented based on the ($2+1$)-flavor lattice QCD simulations with
nearly physical quark masses. Using the HAL QCD method, the spacetime
correlation of the $N$-$\phi$ system in the spin 3/2 channel is converted into
the $N$-$\phi$ scattering phase shift through the interaction potential. The
$N$-$\phi$ potential appears to be a combination of a short-range attractive
core and a long-range attractive tail. The latter is found to be consistent
with the two-pion exchange (TPE) obtained from the interaction between a
color-dipole and the nucleon. The resultant scattering length and effective
range for $m_{\pi}=$ 146.4 MeV are $ a^{(3/2)}_0=-1.43(23)_{\rm
stat.}\left(^{+36}_{-06}\right)_{\rm syst.} {\rm fm}$ and $ r^{(3/2)}_{\rm
eff}=2.36(10)_{\rm stat.}\left(^{+02}_{-48}\right)_{\rm syst.} {\rm fm}$,
respectively. The magnitude of the scattering length is shown to have
nontrivial dependence of $m_{\pi}$ and is sensitive to the existence of the
long-range tail from TPE. | hep-lat |
Gluons in Two-Color QCD at High Baryon Density: Landau gauge longitudinal and transverse gluon propagators are studied in
lattice QCD with gauge group $SU(2)$ at varying temperature and quark density.
In particular, it is found that the longitudinal propagator decreases with
increasing quark chemical potential at all temperatures under study, whereas
the transverse propagator increases with increasing quark chemical potential at
$T<200$ MeV and does not depend on it at higher temperatures. The relative
strength of chromoelectric and chromomagnetic interactions is also discussed. | hep-lat |
Remark on the energy-momentum tensor in the lattice formulation of 4D
$\mathcal{N}=1$ SYM: In a recent paper, arXiv:1209.2473 \cite{Suzuki:2012gi}, we presented a
possible definition of the energy-momentum tensor in the lattice formulation of
the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory, that is
conserved in the quantum continuum limit. In the present Letter, we propose a
quite similar but somewhat different definition of the energy-momentum tensor
(that is also conserved in the continuum limit) which is superior in several
aspects: In the continuum limit, the origin of the energy automatically becomes
consistent with the supersymmetry and the number of renormalization constants
that require a (non-perturbative) determination is reduced to two from four,
the number of renormalization constants appearing in the construction in Ref.
\cite{Suzuki:2012gi}. | hep-lat |
Nature of the $a_1$ meson in lattice quantum chromodynamics studied with
chiral fermions: We study the $a_1$ meson using a quenched lattice quantum chromodynamics
simulation with the truncated overlap fermions formalism based on the domain
wall fermions. The obtained lightest mass of the $a_1$ meson, 1272(45) MeV, is
consistent with the experimental value for $a_1$(1260). Thus, $a_1$(1260) can
be identified to have a simple two-body constituent-quark structure. Our
quenched simulation result of $a_1$(1420) can not explain the experimental mass
value, which suggests $a_1$(1420) is not a simple $q\bar{q}$ two quark state. | hep-lat |
Lattice investigations of the chimera baryon spectrum in the Sp(4) gauge
theory: We report the results of lattice numerical studies of the Sp(4) gauge theory
coupled to fermions (hyperquarks) transforming in the fundamental and two-index
antisymmetric representations of the gauge group. This strongly-coupled theory
is the minimal candidate for the ultraviolet completion of composite Higgs
models that facilitate the mechanism of partial compositeness for generating
the top-quark mass. We measure the spectrum of the low-lying, half-integer
spin, bound states composed of two fundamental and one antisymmetric
hyperquarks, dubbed chimera baryons, in the quenched approximation. In this
first systematic, non-perturbative study, we focus on the three lightest
parity-even chimera-baryon states, in analogy with QCD, denoted as
$\Lambda_{\rm CB}$, $\Sigma_{\rm CB}$ (both with spin 1/2), and $\Sigma_{\rm
CB}^\ast$(with spin 3/2). The spin-1/2 such states are candidates of the top
partners. The extrapolation of our results to the continuum and
massless-hyperquark limit is performed using formulae inspired by QCD
heavy-baryon Wilson chiral perturbation theory. Within the range of hyperquark
masses in our simulations, we find that $\Sigma_{\mathrm{CB}}$ is not heavier
than $\Lambda_{\mathrm{CB}}$. | hep-lat |
A Study of Charmonium Systems across the Deconfinement Transition: We present results from lattice studies of charmonium systems near the
deconfinement transition temperature. On quenched isotropic lattices with
lattice spacings between 0.02 and 0.05 fm, bar{q} q systems with quark masses
close to the charm mass and with different spin-parity quantum numbers are
studied in the temperature range 0.9 Tc - 3 Tc. Results for temporal
correlators of local operators, and the spectral functions constructed from
them, are discussed. For the pseudoscalar and vector channels, the correlators
are observed to change very little across the deconfinement transition, unlike
in the case of the light quarks. | hep-lat |
Theoretical Developments in Lattice Gauge Theory for Applications in
Double-beta Decay Processes and Quantum Simulation: Double beta decays are rare nuclear processes that can occur in two modes:
two-neutrino double beta decay, observed in the Standard Model, and
neutrinoless double beta decay, a hypothetical process with profound
implications for Particle Physics. To draw reliable conclusions from their
experimental constraints, it is necessary to have accurate predictions of the
underlying hadronic interactions described by quantum chromodynamics (QCD), a
non-Abelian gauge theory with the symmetry group SU(3). QCD predictions require
non-perturbative methods for calculating observables, and lattice QCD (LQCD), a
numerical method based on QCD formulated on a finite space-time grid, is the
only reliable first-principles technique for obtaining quantitative results.
However, LQCD needs formal prescriptions to match numerical results with
observables. This thesis provides such prescriptions for double beta decays
using the finite volume effects in the LQCD framework. Matching relations that
connect two-nucleon double beta decay amplitudes to quantities accessible via
LQCD calculations, namely the nuclear matrix elements and two-nucleon energy
spectra in a finite volume are provided. The impact of uncertainties is
examined on the precision with which low-energy constants of the corresponding
effective field theories can be determined from future LQCD calculations.
Hamiltonian simulation of QCD is another non-perturbative method of solving
QCD which can be more suitable in some cases than the conventional LQCD. The
rise of tensor network methods and quantum simulation has made Hamiltonian
simulation of lattice gauge theories (LGTs) a reality. Towards the goal of
simulating QCD, a loop-string-hadron (LSH) formulation of an SU(3) LGT with
matter in 1+1 dimensions is developed in this thesis, motivated by recent
studies that showed the LSH formulation of an SU(2) LGT to be advantageous over
other formulations. | hep-lat |
Canonical Demon Monte Carlo Renormalization Group: We describe a new method to compute renormalized coupling constants in a
Monte Carlo renormalization group calculation. The method can be used for a
general class of models, e.g., lattice spin or gauge models. The basic idea is
to simulate a joint system of block spins and canonical demons. In contrast to
the Microcanonical Renormalization Group invented by Creutz et al. our method
does not suffer from systematical errors stemming from a simultaneous use of
two different ensembles. We present numerical results for the $O(3)$ nonlinear
$\sigma$-model. | hep-lat |
Equation of state for pure SU(3) gauge theory with renormalization group
improved action: A lattice study of the equation of state for pure SU(3) gauge theory using a
renormalization-group (RG) improved action is presented. The energy density and
pressure are calculated on a $16^3\times 4$ and a $32^3\times 8$ lattice
employing the integral method. Extrapolating the results to the continuum
limit, we find the energy density and pressure to be in good agreement with
those obtained with the standard plaquette action within the error of 3-4%. | hep-lat |
A Study of Meson Correlators at Finite Temperature: We present results for mesonic propagators in temporal and spatial directions
at T below and above the deconfining transition in quenched QCD. Anisotropic
lattices are used to get enough information in the temporal direction. We use
the Wilson fermion action for light quarks and Fermilab action for heavy
quarks. | hep-lat |
Mean-Field Gauge Interactions in Five Dimensions II. The Orbifold: We study Gauge-Higgs Unification in five dimensions on the lattice by means
of the mean-field expansion. We formulate it for the case of an SU(2) pure
gauge theory and orbifold boundary conditions along the extra dimension, which
explicitly break the gauge symmetry to U(1) on the boundaries. Our main result
is that the gauge boson mass computed from the static potential along
four-dimensional hyperplanes is nonzero implying spontaneous symmetry breaking.
This observation supports earlier data from Monte Carlo simulations [12]. | hep-lat |
Central Dominance and the Confinement Mechanism in Gluodynamics: New topological objects, which we call center monopoles, naturally arise in
the Maximal Center Projection of SU(3) gluodynamics. The condensate of the
center monopoles is the order parameter of the theory. | hep-lat |
Exploring the QCD phase diagram with three flavors of Möbius domain
wall fermions: We present an update on the study of the QCD phase transition with 3 flavors
of M\"obius domain wall fermions at zero baryon density. We performed
simulations on lattices of size $36^3\times12\times16$ and
$24^3\times12\times32$ with a variety of quark masses at a fixed lattice
spacing $a=0.1361(20)$ fm, which correspond to a temperature 121(2) MeV. By
analyzing the chiral condensate, chiral susceptibilitities and Binder cumulant
on $36^3\times12\times16$ lattices together with the result obtained from our
previous study on $24^3\times12\times16$ lattices, we identified a crossover
occurring at quark mass around $m_q^{\mathrm{\overline {MS}}}(2\, \mathrm{GeV})
\sim 3-4$ MeV for this temperature. Besides, we show the effects of residual
chiral symmetry breaking on chiral condensate and chiral susceptibilities
between $L_s=16$ and 32. | hep-lat |
Rediscovery of Numerical Lüscher's Formula from the Neural Network: We present that by predicting the spectrum in discrete space from the phase
shift in continuous space, the neural network can remarkably reproduce the
numerical L\"uscher's formula to a high precision. The model-independent
property of the L\"uscher's formula is naturally realized by the
generalizability of the neural network. This exhibits the great potential of
the neural network to extract model-independent relation between
model-dependent quantities, and this data-driven approach could greatly
facilitate the discovery of the physical principles underneath the intricate
data. | hep-lat |
Thermodynamics of heavy-light hadrons: Ratios of cumulants of conserved net charge fluctuations are sensitive to the
degrees of freedom that are carriers of the corresponding quantum numbers in
different phases of strong interaction matter. We calculate second and fourth
order cumulants of net charm and strange fluctuations and their correlations
with other conserved charges such as net baryon number and electric charge.
Simulation are performed on $N_\tau$=6 and 8 lattices using the Highly Improved
Staggered Quark (HISQ) action with a light to strange quark mass ratio of 1/20
and having charm quarks treated in the quenched approximation. Analysing
appropriate ratios of these cumulants we observe that both open strange and
charm hadrons start to get dissociated in the chiral crossover region. We
provide indirect evidence for the existence of additional, experimentally yet
unobserved open charm and strange hadrons from QCD thermodynamics. This is done
by comparing lattice QCD results to Hadron Resonance Gas (HRG) model
calculations performed with a hadron spectrum as listed in the Particle Data
Tables as well as with a spectrum predicted in the relativistic quark model and
observed in lattice QCD calculations. We also discuss the influence of these
experimentally yet unobserved states on the determination of freeze-out
temperature and chemical potentials from heavy ion collision experiments. We
found that including these additional states in the HRG model leads to a
systematic 5-8 MeV decrease in the freeze-out temperature of strange hadrons. | hep-lat |
Two-nucleon scattering in multiple partial waves: We determine scattering phase shifts for S,P,D, and F partial wave channels
in two-nucleon systems using lattice QCD methods. We use a generalization of
Luscher's finite volume method to determine infinite volume phase shifts from a
set of finite volume ground- and excited-state energy levels on two volumes,
V=(3.4 fm)^3 and V=(4.5 fm)^3. The calculations are performed in the
SU(3)-flavor limit, corresponding to a pion mass of approximately 800 MeV. From
the energy dependence of the phase shifts we are able to extract scattering
parameters corresponding to an effective range expansion. | hep-lat |
Determinant of a new fermionic action on a lattice - (I): We investigate, analytically and numerically, the fermion determinant of a
new action on a (1+1)-dimensional Euclidean lattice. In this formulation the
discrete chiral symmetry is preserved and the number of fermion components is a
half of that of Kogut-Susskind. In particular, we show that our fermion
determinant is real and positive for U(1) gauge group under specific
conditions, which correspond to gauge conditions on the infinite lattice. It is
also shown that the determinant is real and positive for SU(N) gauge group
without any condition. | hep-lat |
Estimating the Unquenched Strange Quark Mass from the Lattice Axial Ward
Identity: We present a determination of the strange quark mass for two flavours (nf=2)
of light dynamical quarks using the axial Ward identity. The calculations are
performed on the lattice using O(a) improved Wilson fermions and include a
fully non-perturbative determination of the renormalisation constant. In the
continuum limit we find in the MSbar scheme at 2GeV, ms = 111(6)(4)(6)MeV using
the force scale r0 = 0.467fm, where the first error is statistical, the second
and third are systematic due to the fit and scale uncertainties respectively.
Results are also presented for the light quark mass and the chiral condensate.
The corresponding results are also given for r0=0.5fm. | hep-lat |
SU(N) polynomial integrals and some applications: We use the method of the Weingarten functions to evaluate SU(N) integrals of
the polynomial type. As an application we calculate various one-link integrals
for lattice gauge and spin SU(N) theories. | hep-lat |
High-loop perturbative renormalization constants for Lattice QCD (I):
finite constants for Wilson quark currents: We present a high order perturbative computation of the renormalization
constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The
computational setup is the one provided by the RI'-MOM scheme. Three- and
four-loop expansions are made possible by Numerical Stochastic Perturbation
Theory. Results are given for various numbers of flavours and/or (within a
finite accuracy) for generic n_f up to three loops. For the case n_f=2 we also
present four-loop results. Finite size effects are well under control and the
continuum limit is taken by means of hypercubic symmetric Taylor expansions.
The main indetermination comes from truncation errors, which should be assessed
in connection with convergence properties of the series. The latter is best
discussed in the framework of Boosted Perturbation Theory, whose impact we try
to assess carefully. Final results and their uncertainties show that high-loop
perturbative computations of Lattice QCD RC's are feasible and should not be
viewed as a second choice. As a by-product, we discuss the perturbative
expansion for the critical mass, also for which results are for generic n_f up
to three loops, while a four-loop result is obtained for n_f=2. | hep-lat |
Multicanonical Spin Glass Simulations: We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass
model within the recently introduced multicanonical ensemble. Replica on
lattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate
is found, we are able to give a lower bound on the number of statistically
independent groundstates sampled. Temperature dependence of the energy, entropy
and other quantities of interest are easily calculable. In particular we report
the groundstate results. Computations involving the spin glass order parameter
are more tedious. Our data indicate that the large $L$ increase of the
ergodicity time is reduced to an approximately $V^3$ power law. Altogether the
results suggest that the multicanonical ensemble improves the situation of
simulations for spin glasses and other systems which have to cope with similar
problems of conflicting constraints. | hep-lat |
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