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The Lefschetz thimble and the sign problem: In this talk I review the proposal to formulate quantum field theories (QFTs)
on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations
of lattice QFTs affected by sign problem. First I will review the theoretical
justification of the approach, and comment on some open issues. Then, I will
review the algorithms that have been proposed and are being tested to represent
and simulate a lattice QFT on a Lefschetz thimble. In particular, I will review
the lessons from the very first models of QFTs that have been studied with this
approach. | hep-lat |
Correlation functions and critical behaviour on fluctuating geometries: We study the two-point correlation function in the model of branched polymers
and its relation to the critical behaviour of the model. We show that the
correlation function has a universal scaling form in the generic phase with the
only scale given by the size of the polymer. We show that the origin of the
singularity of the free energy at the critical point is different from that in
the standard statistical models. The transition is related to the change of the
dimensionality of the system. | hep-lat |
Two topics from lattice NRQCD at non-zero temperature: heavy quark mass
dependence and S-wave bottomonium states moving in a thermal bath: Using Non-Relativistic QCD (NRQCD), we study heavy quark mass dependence of
S-wave and P-wave bottomonium correlators for 0.42Tc <= T <= 2.09Tc and study
spectral functions of S-wave bottomonium states moving in a thermal bath at
these temperatures using Maximum Entropy Method with NRQCD kernel. For the
studied momentum range, the energy of moving states shows quadratic
momentum-dependence and the width of moving states does not show significant
changes as the momentum of bottomonium is increased. Also, we find that in
correlator ratios, the temperature effect is larger than the effect caused by
20% change in the bottom quark mass. | hep-lat |
On the possibility of the critical behavior of LGT in the area of
asymptotically large β: Coupling dependence on lattice spacing and size is estimated analytically at
\beta -> \infty region where for a->0 the critical area is shifted in
accordance with Callan-Symanzik relation. In considered approximation no trace
of critical behavior is found in this area. | hep-lat |
Impact of stout-link smearing in lattice fermion actions: The impact of stout-link smearing in lattice fermion actions is examined
through the consideration of the mass and renormalization functions of the
overlap quark propagator over a variety of smeared configurations. Up to six
sweeps of stout-link smearing are investigated. For heavy quark masses, the
quark propagator is strongly affected by the smearing procedure. For moderate
masses, the effect appears to be negligible. A small effect is seen for light
quark masses, where dynamical mass generation is suppressed through the
smearing procedure. | hep-lat |
Charmonium Potentials at Finite Temperature: The charmonium states at non-zero temperature are studied on anisotropic
lattices with 2 dynamical quark flavours. Non-local operators are used to
determine the Nambu-Bethe-Salpeter (NBS) wavefunctions via both conventional
fitting methods and the Maximum Entropy Method. The interquark potential is
determined from the solution of the Schrodinger equation, given the NBS
wavefunction as input following the HAL QCD method. We observe a temperature
dependent potential which becomes steeper as the temperature decreases. | hep-lat |
Quark Propagation in the Instantons of Lattice QCD: We quantitatively examine the extent to which instanton degress of freedom,
contained within standard Monte-carlo generated gauge-field configurations, can
maintain the characteristic features of the mass and renormalisation functions
of the non-perturbative quark propagator. We use over-improved stout-link
smearing to isolate instanton effects on the lattice. Using a variety of
measures, we illustrate how gauge fields consisting almost solely of
instanton-like objects are produced after only 50 sweeps of smearing. We find a
full vacuum, with a packing fraction more than three times larger than
phenomenological models predict. We calculate the overlap quark propagator on
these smeared configurations, and find that even at high levels of smearing the
majority of the characteristic features of the propagator are reproduced. We
thus conclude that instantons contained within standard Monte-carlo generated
gauge-field configurations are the degrees of freedom responsible for the
dynamical generation of mass observed in lattice QCD. | hep-lat |
Bottomonium above deconfinement in lattice nonrelativistic QCD: We study the temperature dependence of bottomonium for temperatures in the
range $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom
quark and full relativistic lattice QCD simulations for $N_f=2$ light flavors
on a highly anisotropic lattice. We find that the $\Upsilon$ is insensitive to
the temperature in this range, while the $\chi_b$ propagators show a crossover
from the exponential decay characterizing the hadronic phase to a power-law
behaviour consistent with nearly-free dynamics at $T \simeq 2 T_c$. | hep-lat |
SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane and Scaling
Along the Wilson Axis: We present further evidence for the bulk nature of the phase transition line
in the fundamental--adjoint action plane of SU(3) lattice gauge theory.
Computing the string tension and some glueball masses along the thermal phase
transition line of finite temperature systems with $N_t=4$, which was found to
join onto the bulk transition line at its endpoint, we find that the ratio
$\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the
$0^{++}$ glueball decreases as the endpoint of the bulk transition line is
approached, while the other glueball masses appear unchanged. This is
consistent with the notion that the bulk transition line ends in a critical
endpoint, with the continuum limit there being a $\phi^4$ theory with a
diverging correlation length only in the $0^{++}$ channel. We comment on the
implications for the scaling behavior along the fundamental or Wilson axis. | hep-lat |
Calculation of the running coupling in non-Abelian gauge theories from
Jarzynski's equality: We discuss the theoretical foundations of non-equilibrium Monte Carlo
simulations based on Jarzynski's equality and present, as an example of
application, the determination of the running coupling in the
Schr\"odinger-functional scheme. | hep-lat |
P-wave nucleon-pion scattering amplitude in the $Δ(1232)$ channel
from lattice QCD: We determine the $\Delta(1232)$ resonance parameters using lattice QCD and
the L\"uscher method. The resonance occurs in elastic pion-nucleon scattering
with $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is
performed with $N_f=2+1$ flavors of clover fermions on a lattice with $L\approx
2.8$ fm. The pion and nucleon masses are $m_\pi =255.4(1.6)$ MeV and
$m_N=1073(5)$ MeV, and the strong decay channel $\Delta \rightarrow \pi N$ is
found to be above the threshold. To thoroughly map out the energy-dependence of
the nucleon-pion scattering amplitude, we compute the spectra in all relevant
irreducible representations of the lattice symmetry groups for total momenta up
to $\vec{P}=\frac{2\pi}{L}(1,1,1)$, including irreps that mix $S$ and $P$
waves. We perform global fits of the amplitude parameters to up to 21 energy
levels, using a Breit-Wigner model for the $P$-wave phase shift and the
effective-range expansion for the $S$-wave phase shift. From the location of
the pole in the $P$-wave scattering amplitude, we obtain the resonance mass
$m_\Delta=1378(7)(9)$ MeV and the coupling $g_{\Delta\text{-}\pi
N}=23.8(2.7)(0.9)$. | hep-lat |
Running Gluon Mass from Landau Gauge Lattice QCD Propagator: The interpretation of the Landau gauge lattice gluon propagator as a massive
type bosonic propagator is investigated. Three different scenarios are
discussed: i) an infrared constant gluon mass; ii) an ultraviolet constant
gluon mass; iii) a momentum dependent mass. We find that the infrared data can
be associated with a massive propagator up to momenta $\sim 500$ MeV, with a
constant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon
propagator from the analysis, or 648(7) MeV, if the zero momentum gluon
propagator is included in the data sets. The ultraviolet lattice data is not
compatible with a massive type propagator with a constant mass. The scenario of
a momentum dependent gluon mass gives a decreasing mass with the momentum,
which vanishes in the deep ultraviolet region. Furthermore, we show that the
functional forms used to describe the decoupling like solution of the
Dyson-Schwinger equations are compatible with the lattice data with similar
mass scales. | hep-lat |
The S, U and Δρparameters in the Zaragoza proposal for lattice
chiral gauge fermions: Using the Zaragoza proposal for lattice chiral gauge fermions, the S, U and
\Delta\rho parameters have been calculated at one loop. It is shown that the
continuum values for these quantities can be reproduced without requiring
explicit fine tuning of counterterms. Furthermore, fermion fields doubling is
not necessary. To the best of our knowledge, the Zaragoza proposal is the only
scheme which has these properties. A necessary (although not sufficient)
symmetry is found to support the calculations. Previous results for some of
these parameters in other lattice chiral regularizations are revisited in the
light of this symmetry. | hep-lat |
The chromomagnetic operator on the lattice: We present our study of the renormalization of the chromomagnetic
operator,O(CM), which appears in the effective Hamiltonian describing Delta S =
1 transitions in and beyond the Standard Model. We have computed,
perturbatively to one-loop, the relevant Green's functions with two
(quark-quark) and three (quark-quark-gluon) external fields, at nonzero quark
masses, using both the lattice and dimensional regularizations. The
perturbative computation on the lattice is carried out using the maximally
twisted-mass action for the fermions, while for the gluons we employed the
Symanzik improved gauge action for different sets of values of the Symanzik
coefficients. We have identified all the operators which can possibly mix with
O(CM), including lower dimensional and non gauge invariant operators, and we
have calculated those elements of the mixing matrix which are relevant for the
renormalization of O(CM). We have also performed numerical lattice calculations
to determine non-perturbatively the mixings of the chromomagnetic operator with
lower dimensional operators, through proper renormalization conditions. For the
first time the 1/a**2-divergent mixing of the chromomagnetic operator with the
scalar density has been determined non-perturbatively with high precision.
Moreover, the 1/a-divergent mixing with the pseudoscalar density, due to the
breaking of parity within the twisted-mass regularization of QCD, has been
calculated non-perturbatively and found to be smaller than its one-loop
perturbative estimate. The QCD simulations have been carried out using the
gauge configurations produced by the European Twisted Mass Collaboration with
Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light
mass degenerate quarks, also the strange and charm quarks with masses close to
their physical values. | hep-lat |
General properties of logarithmically divergent one-loop lattice Feynman
integrals: We prove that logarithmically divergent one-loop lattice Feynman integrals
have the general form I(p,a) = f(p)log(aM)+g(p,M) up to terms which vanish for
lattice spacing a -> 0. Here p denotes collectively the external momenta and M
is an arbitrary mass scale. The f(p) is shown to be universal and to coincide
with the analogous quantity in the corresponding continuum integral
(regularized, e.g., by momentum cut-off). This is essential for universality of
the lattice QCD beta-function and anomalous dimensions of renormalized lattice
operators at one loop. The result and argument presented here are simplified
versions of ones given in arXiv:0709.0781. A noteworthy feature of the argument
here is that it does not involve Taylor expansion in external momenta, hence
infra-red divergences associated with that expansion do not arise. | hep-lat |
Hadronic Coupling Constants in Lattice QCD: We calculate the hadronic coupling constants $g_{NN\pi}$ and $g_{\rho\pi\pi}$
in QCD, including dynamical quarks in the framework of staggered fermions in
the lattice approach. For the nucleon--pion coupling we obtain $g_{NN\pi} =
13.8 \pm 5.8$, to be compared with the experimental value $13.13 \pm 0.07$. The
$\rho\pi\pi$ coupling has been analysed for two different sets of operators
with the averaged result $g_{\rho\pi\pi} = 4.2 \pm 1.9$ which is to be compared
with the experimental value $6.06 \pm 0.01$. | hep-lat |
Solution to new sign problems with Hamiltonian Lattice Fermions: We present a solution to the sign problem in a class of particle-hole
symmetric Hamiltonian lattice fermion models on bipartite lattices using the
idea of fermion bags. The solution remains valid when the particle-hole
symmetry is broken through a staggered chemical potential term. This solution
allows, for the first time, simulations of some massless four-fermion models
with minimal fermion doubling and with an odd number of fermion flavors using
ultra-local actions. One can thus study a variety of quantum phase transitions
that have remained unexplored so far due to sign problems. | hep-lat |
Convergence of chiral effective field theory: We formulate the expansion for the mass of the nucleon as a function of pion
mass within chiral perturbation theory using a number of different ultra-violet
regularisation schemes; including dimensional regularisation and various
finite-ranged regulators. Leading and next-to-leading order non-analytic
contributions are included through the standard one-loop Feynman graphs. In
addition to the physical nucleon mass, the expansion is constrained by recent,
extremely accurate, lattice QCD data obtained with two flavors of dynamical
quarks. The extent to which different regulators can describe the chiral
expansion is examined, while varying the range of quark mass over which the
expansions are matched. Renormalised chiral expansion parameters are recovered
from each regularisation prescription and compared. We find that the
finite-range regulators produce consistent, model-independent results over a
wide range of quark mass sufficient to solve the chiral extrapolation problem
in lattice QCD. | hep-lat |
Two-Baryon Systems with Twisted Boundary Conditions: We explore the use of twisted boundary conditions in extracting the nucleon
mass and the binding energy of two-baryon systems, such as the deuteron, from
Lattice QCD calculations. Averaging the results of calculations performed with
periodic and anti-periodic boundary conditions imposed upon the light-quark
fields, or other pair-wise averages, improves the volume dependence of the
deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L.
However, a twist angle of pi/2 in each of the spatial directions improves the
volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging
the binding energy with a random sampling of twist angles improves the volume
dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard
deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest
lattice volumes. Using the experimentally determined phase shifts and mixing
angles, we determine the expected energies of the deuteron states over a range
of cubic lattice volumes for a selection of twisted boundary conditions. | hep-lat |
Chiral Determinant as an Overlap of Two Vacua: The effective action induced by chiral fermions can be written, formally, as
an overlap of two states. These states are the Fock ground states of
Hamiltonians for fermions in even dimensional space with opposite sign mass
terms coupled to identical static vector potentials. A perturbative analysis of
the overlap in the continuum framework produces the correct anomaly for Abelian
gauge fields in two dimensions. When a lattice transfer matrix formalism is
applied in the direction perpendicular to a domain wall on which chiral
fermions live a lattice version of the overlap is obtained. The real part of
the overlap is nonperturbatively defined and previous work indicates that the
real part of the vacuum polarization tensor in four dimensions has the correct
continuum limit for a chiral theory. The phase of the overlap represents the
imaginary part of the chiral action and suffers from ambiguities. | hep-lat |
Effects of non-perturbatively improved dynamical fermions in UKQCD
simulations: We present results for QCD with 2 degenerate flavours of quark using a
non-perturbatively improved action on a lattice volume of $16^3\times32$ where
the bare gauge coupling and bare dynamical quark mass have been chosen to
maintain a fixed physical lattice spacing and volume (1.71 fm). By comparing
measurements from these matched ensembles, including quenched ones, we find
evidence of dynamical quark effects on the short distance static potential, the
scalar glueball mass and the topological susceptibility. There is little
evidence of effects on the light hadron spectrum over the range of quark masses
studied ($m_{\pi}/m_{\rho}\geq 0.60$). | hep-lat |
Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from
finite volume energy levels: A novel effective-field-theory-based approach is implemented for extracting
two-body scattering information from finite volume energies, serving as an
alternative to L\"uscher's method. By explicitly incorporating one-pion
exchange, the approach quantitatively accounts for effects related to left-hand
cuts and range corrections from the longest-range interactions. The method
utilizes the plane wave basis instead of the conventional partial wave
expansion, thereby also naturally including partial wave mixing effects
resulting from rotational symmetry breaking in a cubic box. Applied to the
lattice data for $DD^*$ scattering at a pion mass of 280 MeV, it reveals the
significant impact of the one-pion exchange on P-wave and S-wave phase shifts.
The pole position of the $T_{cc}(3875)^+$ state, extracted from the
finite-volume energy levels while taking into account left-hand cut effects,
range corrections, and partial-wave mixing, appears to be consistent with a
near-threshold resonance. | hep-lat |
Schwinger-Keldysh on the lattice: a faster algorithm and its application
to field theory: A new algorithm is developed allowing the Monte Carlo study of a 1 + 1
dimensional theory in real time. The main algorithmic development is to avoid
the explicit calculation of the Jacobian matrix and its determinant in the
update process. This improvement has a wide applicability and reduces the cost
of the update in thimble-inspired calculations from O(N^3) to less than O(N^2).
As an additional feature, the algorithm leads to improved Monte Carlo
proposals. We exemplify the use of the algorithm to the real time dynamics of a
scalar {\phi}^4 theory with weak and strong couplings. | hep-lat |
Test for a universal behavior of Dirac eigenvalues in the complex
Langevin method: We apply the complex Langevin (CL) method to a chiral random matrix theory
(ChRMT) at non-zero chemical potential and study the nearest neighbor spacing
(NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted
using an unfolding procedure for the Dirac eigenvalues obtained in the CL
method. For large quark mass, we find that the NNS distribution obeys the
Ginibre ensemble as expected. For small quark mass, the NNS distribution
follows the Wigner surmise for correct convergence case, while it follows the
Ginibre ensemble for wrong convergence case. The Wigner surmise is physically
reasonable from the chemical potential independence of the ChRMT. The Ginibre
ensemble is known to be favored in a phase quenched QCD at finite chemical
potential. Our result suggests a possibility that the originally universal
behavior of the NNS distribution is preserved even in the CL method for correct
convergence case. | hep-lat |
Polyakov loop effects on the phase diagram in strong-coupling lattice
QCD: We investigate the Polyakov loop effects on the QCD phase diagram by using
the strong-coupling (1/g^2) expansion of the lattice QCD (SC-LQCD) with one
species of unrooted staggered quark, including O}(1/g^4) effects. We take
account of the effects of Polyakov loop fluctuations in Weiss mean-field
approximation (MFA), and compare the results with those in the Haar-measure MFA
(no fluctuation from the mean-field). The Polyakov loops strongly suppress the
chiral transition temperature in the second-order/crossover region at small
chemical potential, while they give a minor modification of the first-order
phase boundary at larger chemical potential. The Polyakov loops also account
for a drastic increase of the interaction measure near the chiral phase
transition. The chiral and Polyakov loop susceptibilities have their peaks
close to each other in the second-order/crossover region. In particular in
Weiss MFA, there is no indication of the separated deconfinement transition
boundary from the chiral phase boundary at any chemical potential. We discuss
the interplay between the chiral and deconfinement dynamics via the bare quark
mass dependence of susceptibilities. | hep-lat |
A lattice regularization of Weyl fermions in a gravitational background: We report on a lattice fermion formulation with a curved domain-wall mass
term to nonperturbatively describe fermions in a gravitational background. In
our previous work in 2022, we showed under the time-reversal symmetry that the
edge-localized massless Dirac fermion appears on one and two-dimensional
spherical domain-walls and the spin connection is induced on the lattice in a
consistent way with continuum theory. In this work, we extend our study to the
Shamir type curved domain-wall fermions without the time-reversal symmetry. We
find in the free fermion case that a single Weyl fermion appears on the edge,
and feels gravity through the induced spin connection. With a topologically
nontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero
mode at the center where the gauge field is singular. | hep-lat |
Lattice real-time simulations with learned optimal kernels: We present a simulation strategy for the real-time dynamics of quantum
fields, inspired by reinforcement learning. It builds on the complex Langevin
approach, which it amends with system specific prior information, a necessary
prerequisite to overcome this exceptionally severe sign problem. The
optimization process underlying our machine learning approach is made possible
by deploying inherently stable solvers of the complex Langevin stochastic
process and a novel optimality criterion derived from insight into so-called
boundary terms. This conceptual and technical progress allows us to both
significantly extend the range of real-time simulations in 1+1d scalar field
theory beyond the state-of-the-art and to avoid discretization artifacts that
plagued previous real-time field theory simulations. Limitations of and
promising future directions are discussed. | hep-lat |
Double parton distributions in the nucleon from lattice QCD: We evaluate nucleon four-point functions in the framework of lattice QCD in
order to extract the first Mellin moment of double parton distributions (DPDs)
in the unpolarized proton. In this first study, we employ an nf = 2 + 1
ensemble with pseudoscalar masses of mpi = 355 MeV and mK = 441 MeV. The
results are converted to the scale mu = 2 GeV. Our calculation includes all
Wick contractions, and for almost all of them a good statistical signal is
obtained. We analyze the dependence of the DPD Mellin moments on the quark
flavor and the quark polarization. Furthermore, the validity of frequently used
factorization assumptions is investigated. | hep-lat |
Non-relativistic bound states in a finite volume: We derive general results for the mass shift of bound states with angular
momentum l >= 1 in a periodic cubic box in two and three spatial dimensions.
Our results have applications to lattice simulations of hadronic molecules,
halo nuclei, and Feshbach molecules. The sign of the mass shift can be related
to the symmetry properties of the state under consideration. We verify our
analytical results with explicit numerical calculations. Moreover, we comment
on the relations connecting the effective range parameter, the binding momentum
of a given state and the asymptotic normalization coefficient of the
corresponding wave function. We give explicit expressions for this relation in
the shallow binding limit. | hep-lat |
Lattice QCD Calculation of Electroweak Box Contributions to Superallowed
Nuclear and Neutron Beta Decays: We present the first lattice QCD calculation of the universal axial $\gamma
W$-box contribution $\square_{\gamma W}^{VA}$ to both superallowed nuclear and
neutron beta decays. This contribution emerges as a significant component
within the theoretical uncertainties surrounding the extraction of $|V_{ud}|$
from superallowed decays. Our calculation is conducted using two domain wall
fermion ensembles at the physical pion mass. To construct the nucleon 4-point
correlation functions, we employ the random sparsening field technique.
Furthermore, we incorporate long-distance contributions to the hadronic
function using the infinite-volume reconstruction method. Upon performing the
continuum extrapolation, we arrive at $\square_{\gamma
W}^{VA}=3.65(8)_{\mathrm{lat}}(1)_{\mathrm{PT}}\times10^{-3}$. Consequently,
this yields a slightly higher value of
$|V_{ud}|=0.97386(11)_{\mathrm{exp.}}(9)_{\mathrm{RC}}(27)_{\mathrm{NS}}$,
reducing the previous $2.1\sigma$ tension with the CKM unitarity to
$1.8\sigma$. Additionally, we calculate the vector $\gamma W$-box contribution
to the axial charge $g_A$, denoted as $\square_{\gamma W}^{VV}$, and explore
its potential implications. | hep-lat |
Phase structure of four flavor QCD in the T μplane from a new method
for simulations of lattice gauge theories at non zero baryon density: We review a method for numerical simulations of lattice gauge theories at
non-zero baryonic chemical potential we recently proposed. We first report on a
test of the method using a solvable model and then present results for the
phase structure of four flavour QCD. For the first time the region of chemical
potential up to 1.4 T_C is explored, finding a first order transition line. | hep-lat |
Light Quark Masses with Dynamical Wilson Fermions: We determine the masses of the light and the strange quarks in the
$\bar{MS}$-scheme using our high-statistics lattice simulation of QCD with
dynamical Wilson fermions. For the light quark mass we find
$m^{light}_{\bar{MS}}(2 GeV) = 2.7(2) MeV$, which is lower than in quenched
simulations. For the strange quark, in a sea of two dynamical light quarks, we
obtain $m^{strange}_{\bar{MS}}(2 GeV) = 140(20) MeV$. | hep-lat |
Core -- a New Method for Solving Hamiltonian Lattice Systems: The COntractor REnormalization group (CORE) approximation, a new method for
solving Hamiltonian lattice systems, is introduced. The approach combines
variational and contraction techniques with the real-space renormalization
group approach and is systematically improvable. Since it applies to lattice
systems of infinite extent, the method is suitable for studying critical
phenomena and phase structure; systems with dynamical fermions can also be
treated. The method is tested using the 1+1-dimensional Ising model. | hep-lat |
Phases at finite winding number of an Abelian lattice gauge theory: Pure gauge theories are rather different from theories with pure scalar and
fermionic matter, especially in terms of the nature of excitations. For
example, in scalar and fermionic theories, one can create ultra-local
excitations. For a gauge theory, such excitations need to be closed loops that
do not violate gauge invariance. In this proceedings, we present a study on the
condensation phenomenon associated with the string-like excitations of an
Abelian lattice gauge theory. These phenomena are studied through numerical
simulations of a $U(1)$ quantum link model in 2+1 dimensions in a ladder
geometry using matrix product states. In this proceedings, we show the
existence of ground states characterized by the presence of such string-like
excitations. These are caused due to the condensation of torelons. We also
study the relationship between the properties of the plaquettes in the ground
state and the presence of such condensation phenomenon. | hep-lat |
Quantum tunneling in the real-time path integral by the Lefschetz
thimble method: Quantum tunneling is mostly discussed in the Euclidean path integral
formalism using instantons. On the other hand, it is difficult to understand
quantum tunneling based on the real-time path integral due to its oscillatory
nature, which causes the notorious sign problem. We show that recent
development of the Lefschetz thimble method enables us to investigate this
issue numerically. In particular, we find that quantum tunneling occurs due to
complex trajectories, which are actually observable experimentally by using the
so-called weak measurement. | hep-lat |
Cutoff effects in twisted mass lattice QCD: We present a first numerical study of lattice QCD with O(a) improved Wilson
quarks and a chirally twisted mass term. Renormalized correlation functions are
derived from the Schroedinger functional and evaluated in an intermediate
space-time volume of size 0.75^3 x 1.5 fm^4. In the quenched approximation
precise results are then obtained with a moderate computational effort,
allowing for a detailed study of the continuum approach. The latter is
discussed in terms of observables which converge to meson masses and decay
constants in the limit of large space-time volume. In the O(a) improved theory
we find residual cutoff effects to be at the level of a few percent for lattice
spacings of about 0.1 fm. | hep-lat |
Excited state baryon spectroscopy from lattice QCD with spin
identification: Lattice QCD calculations are presented for the spectra of N* excited states
with spins up to J = 7/2. Ambiguities of the standard method of spin
identification are shown to be overcome by the use of lattice operators that
transform according to SU(2) symmetry restricted to the lattice. Such operators
are labeled by their continuum spins. Overlaps of the operators with the states
obtained by diagonalizing matrices of correlation functions provide a clear
link between continuum spins and lattice states, allowing spins to be
identified. Evidence for an approximate realization of rotational symmetry in
the N* spectrum is presented. In simulations with pion mass = 392 MeV, the
low-lying excited states of lattice QCD are found to have the same quantum
numbers as the states of SU(6)xO(3) symmetry. The lattice spectra are
inconsistent with either a quark-diquark model or parity doubling of states and
they suggest that the J = 1/2 Roper resonance may have a complex structure
consisting of contributions from L=0, 1 and 2. | hep-lat |
Three-particle finite-volume formalism for $π^+π^+ K^+$ and related
systems: We consider three-particle systems consisting of two identical particles and
a third that is different, with all being spinless. Examples include
$\pi^+\pi^+ K^+$ and $K^+K^+\pi^+$. We derive the formalism necessary to
extract two- and three-particle infinite-volume scattering amplitudes from the
spectrum of such systems in finite volume. We use a relativistic formalism
based on an all-orders diagrammatic analysis in generic effective field theory,
adopting the methodology used recently to study the case of three nondegenerate
particles. We present both a direct derivation, and also a cross-check based on
an appropriate limit and projection of the fully nondegenerate formalism. We
also work out the threshold expansions for the three-particle K matrix that
will be needed in practical applications, both for systems with two identical
particles plus a third, and also for the fully nondegenerate theory. | hep-lat |
Interplay between sign problem and Z_3 symmetry in three-dimensional
Potts model: We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models,
each with different number of states at each site on a 3-d lattice, by
extending the 3-d three-state Potts model. Comparing the ordinary Potts model
with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects
the sign problem and see how the deconfinement transition line changes in the
$\mu-\kappa$ plane as the number of states increases, where $\mu$ $(\kappa)$
plays a role of chemical potential (temperature) in the models. We find that
the sign problem is almost cured by imposing Z3 symmetry. This mechanism may
happen in Z3-symmetric QCD-like theory. We also show that the deconfinement
transition line has stronger $\mu$-dependence with respect to increasing the
number of states. | hep-lat |
K^0--\bar{K}^0 mixing in full lattice QCD: There are at least two methods to calculate $ B_K $ with staggered fermions:
one is the two spin trace formalism and the other is the one spin trace
formalism. We have performed numerical simulations on a $ 16^3 \times 40 $
lattice in full QCD with $ \beta = 5.7 $ and a dynamical quark mass 0.01 in
lattice units. We try various sources to select only the pseudo-Goldstone
bosons and compare the various results. | hep-lat |
Remarks on the quantum gravity interpretation of 4D dynamical
triangulation: We review some of the phenomenology in 4D dynamical triangulation and explore
its interpretation in terms of a euclidean effective action of the continuum
form $\intx \sqrt{g} [\mu -\frac{1}{16\pi G} R + \cdots]$. | hep-lat |
Phase Quenched Lattice QCD at Finite Density and Temperature: We simulate 3-flavour lattice QCD at finite quark-number chemical potential
mu in the phase-quenched approximation, close to the finite temperature
transition. Working close to the critical quark mass, we find no evidence for
the expected critical endpoint at small mu. We are performing further
simulations aimed at calculating the equation-of-state of this theory outside
of the superfluid domain, where its phase structure is expected to mimic the
full theory. | hep-lat |
Light hadron spectroscopy with O(a) improved dynamical fermions: We present the first results for the static quark potential and the light
hadron spectrum using dynamical fermions at $\beta=5.2$ using an O(a) improved
Wilson fermion action together with the standard Wilson plaquette action for
the gauge part. Sea quark masses were chosen such that the pseudoscalar-vector
mass ratio, m_PS/m_V$, varies from 0.86 to 0.67. Finite-size effects are
studied by using three different volumes, 8^3\cdot 24, 12^3\cdot 24 and
16^3\cdot 24. Comparing our results to previous ones obtained using the
quenched approximation, we find evidence for sea quark effects in quantities
like the static quark potential and the vector-pseudoscalar hyperfine
splitting. | hep-lat |
High-loop perturbative renormalization constants for Lattice QCD (II):
three-loop quark currents for tree-level Symanzik improved gauge action and
n_f=2 Wilson fermions: Numerical Stochastic Perturbation Theory was able to get three- (and even
four-) loop results for finite Lattice QCD renormalization constants. More
recently, a conceptual and technical framework has been devised to tame finite
size effects, which had been reported to be significant for (logarithmically)
divergent renormalization constants. In this work we present three-loop results
for fermion bilinears in the Lattice QCD regularization defined by tree-level
Symanzik improved gauge action and n_f=2 Wilson fermions. We discuss both
finite and divergent renormalization constants in the RI'-MOM scheme. Since
renormalization conditions are defined in the chiral limit, our results also
apply to Twisted Mass QCD, for which non-perturbative computations of the same
quantities are available. We emphasize the importance of carefully accounting
for both finite lattice space and finite volume effects. In our opinion the
latter have in general not attracted the attention they would deserve. | hep-lat |
Renormalization constants for $N_{\rm f}=2+1+1$ twisted mass QCD: We summarize recent non-perturbative results obtained for the renormalization
constants computed in the RI'-MOM scheme for $N_{\rm f}=2+1+1$ twisted mass
QCD. Our implementation employs the Iwasaki gauge action and four dynamical
degenerate twisted mass fermions. Renormalization constants for scalar,
pseudo-scalar, vector and axial operators, as well as the quark propagator
renormalization, are computed at three different values of the lattice spacing,
two different volumes and several values of the twisted mass. Our method allows
for a precise cross-check of the running, because of the particular proper
treatment of the hypercubic artifacts. Preliminary results for twist-2
operators are also presented. | 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 |
Unpolarized gluon distribution in the nucleon from lattice quantum
chromodynamics: In this study, we present a determination of the unpolarized gluon Ioffe-time
distribution in the nucleon from a first principles lattice quantum
chromodynamics calculation. We carry out the lattice calculation on a
$32^3\times 64$ ensemble with a pion mass of $358$ MeV and lattice spacing of
$0.094$ fm. We construct the nucleon interpolating fields using the
distillation technique, flow the gauge fields using the gradient flow, and
solve the summed generalized eigenvalue problem to determine the glounic matrix
elements. Combining these techniques allows us to provide a statistically
well-controlled Ioffe-time distribution and unpolarized gluon PDF. We obtain
the flow time independent reduced Ioffe-time pseudo-distribution, and calculate
the light-cone Ioffe-time distribution and unpolarized gluon distribution
function in the $\overline{\rm MS}$ scheme at $\mu = 2$ GeV, neglecting the
mixing of the gluon operator with the quark singlet sector. Finally, we compare
our results to phenomenological determinations. | hep-lat |
Lattice QCD constraints on the parton distribution functions of
${}^3\text{He}$: The fraction of the longitudinal momentum of ${}^3\text{He}$ that is carried
by the isovector combination of $u$ and $d$ quarks is determined using lattice
QCD for the first time. The ratio of this combination to that in the
constituent nucleons is found to be consistent with unity at the few-percent
level from calculations with quark masses corresponding to $m_\pi\sim 800$ MeV,
extrapolated to the physical quark masses. This constraint is consistent with,
and significantly more precise than, determinations from global nuclear parton
distribution function fits. Including the lattice QCD determination of the
momentum fraction in the nNNPDF global fitting framework results in the
uncertainty on the isovector momentum fraction ratio being reduced by a factor
of 2.5, and thereby enables a more precise extraction of the $u$ and $d$ parton
distributions in ${}^3\text{He}$. | hep-lat |
SO(2N) and SU(N) gauge theories: We present our preliminary results of SO(2N) gauge theories, approaching the
large-N limit. SO(2N) theories may help us to understand QCD at finite chemical
potential since there is an orbifold equivalence between SO(2N) and SU(N) gauge
theories at large-N and SO(2N) theories do not have the sign problem present in
QCD. We consider the string tensions, mass spectra, and deconfinement
temperatures in the SO(2N) pure gauge theories in 2+1 dimensions, comparing
them to their corresponding SU(N) theories. | hep-lat |
Multi-hadron interactions from lattice QCD: First-principles calculations of multi-hadron dynamics are a crucial goal in
lattice QCD. Significant progress has been achieved in developing,
implementing, and applying theoretical tools that connect finite-volume
quantities to their infinite-volume counterparts. Here, I review some recent
theoretical developments and numerical results regarding multi-particle
quantities in a finite volume. These results include $N\pi$ scattering, systems
of two and three mesons at maximal isospin, three-body resonances in a toy
model, and the formulation of effective theories in finite volume for
multi-nucleon systems. | hep-lat |
Lattice diffeomorphism invariance: We propose a lattice counterpart of diffeomorphism symmetry in the continuum.
A functional integral for quantum gravity is regularized on a discrete set of
space-time points, with fermionic or bosonic lattice fields. When the
space-time points are positioned as discrete points of a continuous manifold,
the lattice action can be reformulated in terms of average fields within local
cells and lattice derivatives. Lattice diffeomorphism invariance is realized if
the action is independent of the positioning of the space-time points. Regular
as well as rather irregular lattices are then described by the same action.
Lattice diffeomorphism invariance implies that the continuum limit and the
quantum effective action are invariant under general coordinate transformations
- the basic ingredient for general relativity. In our approach the lattice
diffeomorphism invariant actions are formulated without introducing a metric or
other geometrical objects as fundamental degrees of freedom. The metric rather
arises as the expectation value of a suitable collective field. As examples, we
present lattice diffeomorphism invariant actions for a bosonic non-linear
sigma-model and lattice spinor gravity. | hep-lat |
Thermal monopole condensation in QCD with physical quark masses: Thermal monopoles, identified after Abelian projection as magnetic currents
wrapping non-trivially around the thermal circle, are studied in $N_f = 2+1$
QCD at the physical point. The distribution in the number of wrappings, which
in pure gauge theories points to a condensation temperature coinciding with
deconfinement, points in this case to around 275 MeV, almost twice the QCD
crossover temperature $T_c$; similar indications emerge looking for the
formation of a percolating current cluster. The possible relation with other
non-perturbative phenomena observed above $T_c$ is discussed. | hep-lat |
A non-perturbative calculation of the mass of the Bc: We present a calculation of the mass of the 1S0 pseudoscalar anti-b c (Bc)
state using a non-perturbative measurement from quenched lattice QCD. We find
M_Bc = 6.386(9)(98)(15) GeV where the first error is statistical, the second
systematic due to the quark mass ambiguities and quenching and the third the
systematic error due to the estimation of mass of the eta_b. | hep-lat |
An estimate for the thermal photon rate from lattice QCD: We estimate the production rate of photons by the quark-gluon plasma in
lattice QCD. We propose a new correlation function which provides better
control over the systematic uncertainty in estimating the photon production
rate at photon momenta in the range {\pi}T/2 to 2{\pi}T. The relevant Euclidean
vector current correlation functions are computed with $N_{\mathrm f}$ = 2
Wilson clover fermions in the chirally-symmetric phase. In order to estimate
the photon rate, an ill-posed problem for the vector-channel spectral function
must be regularized. We use both a direct model for the spectral function and a
model-independent estimate from the Backus-Gilbert method to give an estimate
for the photon rate. | hep-lat |
Quark contribution to the proton spin from 2+1+1-flavor lattice QCD: We present the first chiral-continuum extrapolated up, down and strange quark
spin contribution to the proton spin using lattice QCD. For the connected
contributions, we use eleven ensembles of 2+1+1-flavor of Highly Improved
Staggered Quarks (HISQ) generated by the MILC Collaboration. They cover four
lattice spacings $a \approx \{0.15,0.12,0.09,0.06\}$ fm and three pion masses,
$M_\pi \approx \{315,220,135\}$ MeV, of which two are at the physical pion
mass. The disconnected strange calculations are done on seven of these
ensembles, covering the four lattice spacings but only one with the physical
pion mass. The disconnected light quark calculation was done on six ensembles
at two values of $M_\pi \approx \{315,220\}$ MeV. High-statistics estimates on
each ensemble for all three quantities allow us to quantify systematic
uncertainties and perform a simultaneous chiral-continuum extrapolation in the
lattice spacing and the light-quark mass. Our final results are $\Delta u
\equiv \langle 1 \rangle_{\Delta u^+} = 0.777(25)(30)$, $\Delta d \equiv
\langle 1 \rangle_{\Delta d^+} = -0.438(18)(30)$, and $\Delta s \equiv \langle
1 \rangle_{\Delta s^+} = -0.053(8)$, adding up to a total quark contribution to
proton spin of $\sum_{q=u,d,s} (\frac{1}{2} \Delta q) = 0.143(31)(36)$. The
second error is the systematic uncertainty associated with the chiral-continuum
extrapolation. These results are obtained without model assumptions and are in
good agreement with the recent COMPASS analysis $0.13 < \frac{1}{2} \Delta
\Sigma < 0.18$, and with the $\Delta q$ obtained from various global analyses
of polarized beam or target data. | hep-lat |
Large N: I review some of the things we have learned about large N gauge theories (and
QCD at N=oo) from lattice calculations in recent years. I point to some open
problems. | hep-lat |
Gauge-fixing approach to lattice chiral gauge theories: We review the status of our recent work on the gauge-fixing approach to
lattice chiral gauge theories. New numerical results in the reduced version of
a model with a U(1) gauge symmetry are presented which strongly indicate that
the factorization of the correlation functions of the left-handed neutral and
right-handed charged fermion fields, which we established before in
perturbation theory, holds also nonperturbatively. | hep-lat |
Nucleon Structure in Lattice QCD using twisted mass fermions: We present results on the nucleon form factors and moments of generalized
parton distributions obtained within the twisted mass formulation of lattice
QCD. We include a discussion of lattice artifacts by examining results at
different volumes and lattice spacings. We compare our results with those
obtained using different discretization schemes and to experiment. | hep-lat |
N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one
exact supersymmetry: We formulate ${\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two
dimensional transverse lattice using supersymmetric discrete light cone
quantization in the large-$N_c$ limit. This formulation is free of fermion
species doubling. We are able to preserve one supersymmetry. We find a rich,
non-trivial behavior of the mass spectrum as a function of the coupling
$g\sqrt{N_c}$, and see some sort of "transition" in the structure of a bound
state as we go from the weak coupling to the strong coupling. Using a toy model
we give an interpretation of the rich behavior of the mass spectrum. We present
the mass spectrum as a function of the winding number for those states whose
color flux winds all the way around in one of the transverse directions. We use
two fits to the mass spectrum and the one that has a string theory
justification appears preferable. For those states whose color flux is
localized we present an extrapolated value for $m^2$ for some low energy bound
states in the limit where the numerical resolution goes to infinity. | hep-lat |
The Chiral Condensate of One-Flavor QCD and the Dirac Spectrum at
θ=0: In a sector of fixed topological charge, the chiral condensate has a
discontinuity given by the Banks-Casher formula also in the case of one-flavor
QCD. However, at fixed \theta-angle, the chiral condensate remains constant
when the quark mass crosses zero. To reconcile these contradictory
observations, we have evaluated the spectral density of one-flavor QCD at
\theta=0. For negative quark mass, it becomes a strongly oscillating function
with a period that scales as the inverse space-time volume and an amplitude
that increases exponentially with the space-time volume. As we have learned
from QCD at nonzero chemical potential, if this is the case, an alternative to
the Banks-Casher formula applies, and as we will demonstrate in this talk, for
one-flavor QCD this results in a continuous chiral condensate. A special role
is played by the topological zero modes which have to be taken into account
exactly in order to get a finite chiral condensate in the thermodynamic limit. | hep-lat |
The strange quark contribution to the spin of the nucleon: Quark line disconnected matrix elements of an operator, such as the axial
current, are difficult to compute on the lattice. The standard method uses a
stochastic estimator of the operator, which is generally very noisy. We discuss
and develop further our alternative approach using the Feynman-Hellmann theorem
which involves only evaluating two-point correlation functions. This is applied
to computing the contribution of the quark spin to the nucleon and in
particular for the strange quark. In this process we also pay particular
attention to the development of an SU(3) flavour breaking expansion for singlet
operators. | hep-lat |
Spectrum of the open QCD flux tube and its effective string description: I perform a high precision measurement of the static quark-antiquark
potential in three-dimensional ${\rm SU}(N)$ gauge theory with $N=2$ to 6. The
results are compared to the effective string theory for the QCD flux tube and I
obtain continuum limit results for the string tension and the non-universal
leading order boundary coefficient, including an extensive analysis of all
types of systematic uncertainties. The magnitude of the boundary coefficient
decreases with increasing $N$, but remains non-vanishing in the large-$N$
limit. I also test for the presence of possible contributions from rigidity or
massive modes and compare the results for the string theory parameters to data
for the excited states. | hep-lat |
Nuclear force in Lattice QCD: We perform the quenched lattice QCD analysis on the nuclear force
(baryon-baryon interactions). We employ $20^3\times 24$ lattice at $\beta=5.7$
($a\simeq 0.19$ fm) with the standard gauge action and the Wilson quark action
with the hopping parameters $\kappa=0.1600, 0.1625, 0.1650$, and generate about
200 gauge configurations. We measure the temporal correlators of the two-baryon
system which consists of heavy-light-light quarks. We extract the inter-baryon
force as a function of the relative distance $r$. We also evaluate the
contribution to the nuclear force from each ``Feynman diagram'' such as the
quark-exchange diagram individually, and single out the roles of Pauli-blocking
effects or quark exchanges in the inter-baryon interactions. | hep-lat |
Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the
Green's Function: Analytical and numerical methods are applied to principal chiral models on a
two-dimensional lattice and their predictions are tested and compared. New
techniques for the strong coupling expansion of SU(N) models are developed and
applied to the evaluation of the two-point correlation function. The
momentum-space lattice propagator is constructed with precision O(\beta^{10})
and an evaluation of the correlation length is obtained for several different
definitions. Three-loop weak coupling contributions to the internal energy and
to the lattice $\beta$ and $\gamma$ functions are evaluated for all N, and the
effect of adopting the ``energy'' definition of temperature is computed with
the same precision. Renormalization-group improved predictions for the
two-point Green's function in the weak coupling ( continuum ) regime are
obtained and successfully compared with Monte Carlo data. We find that strong
coupling is predictive up to a point where asymptotic scaling in the energy
scheme is observed. Continuum physics is insensitive to the effects of the
large N phase transition occurring in the lattice model. Universality in N is
already well established for $N \ge 10$ and the large N physics is well
described by a ``hadronization'' picture. | hep-lat |
Effects of the anomaly on the QCD chiral phase transition: We study a lattice field theory described by two flavors of massless
staggered fermions interacting with U(1) gauge fields in the strong coupling
limit. We show that the lattice model has a $SU(2)\times SU(2)\times U(1)$
chiral symmetry and can be used to model the two-flavor QCD chiral phase
transition in the absence of the anomaly. It is also possible to add a coupling
to this model which breaks the chiral symmetry to $SU(2)\times SU(2)$ and thus
mimics the effects of the anomaly in two-flavor QCD. We construct an efficient
directed loop algorithm to study such a model. We show that the chiral phase
transition in our model is first order in the absence of the anomaly, while it
becomes second order with O(4) exponents when the anomaly is turned on. | hep-lat |
Running Coupling and the Lambda-Parameter from SU(3) Lattice Simulations: We present new results on the static qq-potential from high statistics
simulations on 32^4 and smaller lattices, using the standard Wilson beta = 6.0,
6.4, and 6.8. Within our statistical errors we do not observe any finite size
effects affecting the potential values, on varying the spatial lattice extent
from 0.9fm up to 3.3fm. We are able to see and quantify the running of the
coupling from the Coulomb behaviour of the interquark force. From this we
extract the ratio \sqrt{sigma}/Lambda_L. We demonstrate that scaling violations
on the string tension can be considerably reduced by introducing effective
coupling schemes, which allow for a safe extrapolation of \Lambda_L to its
continuum value. Both methods yield consistent values for Lambda: Lambda_MSbar
= 0.558_{-0.007}^{+0.017}\sqrt{sigma} = 246_{-3}^{+7}MeV. At the highest energy
scale attainable to us we find alpha(5 GeV) = 0.150(3) | hep-lat |
Domain Decomposition method on GPU cluster: Pallalel GPGPU computing for lattice QCD simulations has a bottleneck on the
GPU to GPU data communication due to the lack of the direct data exchanging
facility. In this work we investigate the performance of quark solver using the
restricted additive Schwarz (RAS) preconditioner on a low cost GPU cluster. We
expect that the RAS preconditioner with appropriate domaindecomposition and
task distribution reduces the communication bottleneck. The GPU cluster we
constructed is composed of four PC boxes, two GPU cards are attached to each
box, and we have eight GPU cards in total. The compute nodes are connected with
rather slow but low cost Gigabit-Ethernet. We include the RAS preconditioner in
the single-precision part of the mixedprecision nested-BiCGStab algorithm and
the single-precision task is distributed to the multiple GPUs. The benchmarking
is done with the O(a)-improved Wilson quark on a randomly generated gauge
configuration with the size of $32^4$. We observe a factor two improvment on
the solver performance with the RAS precoditioner compared to that without the
preconditioner and find that the improvment mainly comes from the reduction of
the communication bottleneck as we expected. | hep-lat |
Deflated BiCGStab for linear equations in QCD problems: The large systems of complex linear equations that are generated in QCD
problems often have multiple right-hand sides (for multiple sources) and
multiple shifts (for multiple masses). Deflated GMRES methods have previously
been developed for solving multiple right-hand sides. Eigenvectors are
generated during solution of the first right-hand side and used to speed up
convergence for the other right-hand sides. Here we discuss deflating
non-restarted methods such as BiCGStab. For effective deflation, both left and
right eigenvectors are needed. Fortunately, with the Wilson matrix, left
eigenvectors can be derived from the right eigenvectors. We demonstrate for
difficult problems with kappa near kappa_c that deflating eigenvalues can
significantly improve BiCGStab. We also will look at improving solution of
twisted mass problems with multiple shifts. Projecting over previous solutions
is an easy way to reduce the work needed. | hep-lat |
Electroweak three-body decays in the presence of two- and three-body
bound states: Recently, formalism has been derived for studying electroweak transition
amplitudes for three-body systems both in infinite and finite volumes. The
formalism provides exact relations that the infinite-volume amplitudes must
satisfy, as well as a relationship between physical amplitudes and
finite-volume matrix elements, which can be constrained from lattice QCD
calculations. This formalism poses additional challenges when compared with the
analogous well-studied two-body equivalent one, including the necessary step of
solving integral equations of singular functions. In this work, we provide some
non-trivial analytical and numerical tests on the aforementioned formalism. In
particular, we consider a case where the three-particle system can have
three-body bound states as well as bound states in the two-body subsystem. For
kinematics below the three-body threshold, we demonstrate that the scattering
amplitudes satisfy unitarity. We also check that for these kinematics the
finite-volume matrix elements are accurately described by the formalism for
two-body systems up to exponentially suppressed corrections. Finally, we verify
that in the case of the three-body bound state, the finite-volume matrix
element is equal to the infinite-volume coupling of the bound state, up to
exponentially suppressed errors. | hep-lat |
One dimensional supersymmetric Yang-Mills theory with 16 supercharges: We report on numerical simulations of one dimensional maximally
supersymmetric SU(N) Yang-Mills theory, by using the lattice action with two
exact supercharges. Based on the gauge/gravity duality, the gauge theory
corresponds to N D0-branes system in type IIA superstring theory at finite
temperature. We aim to verify the gauge/gravity duality numerically by
comparing our results of the gauge side with analytic solutions of the gravity
side. First of all, by examining the supersymmetric Ward-Takahashi relation, we
show that supersymmetry breaking effects from the cut-off vanish in the
continuum limit and our lattice theory has the desired continuum limit. Then,
we find that, at low temperature, the black hole internal energy obtained from
our data is close to the analytic solution of the gravity side. It suggests the
validity of the duality. | hep-lat |
Confined Charged Particles in C-periodic Volumes: Charged particles in an Abelian Coulomb phase are non-local infraparticles
that are surrounded by a cloud of soft photons which extends to infinity.
Gauss' law prevents the existence of charged particles in a periodic volume. In
a $C$-periodic volume, which is periodic up to charge conjugation, on the other
hand, charged particles can exist. This includes vortices in the $3$-d
XY-model, magnetic monopoles in $4$-d $\mathrm{U}(1)$ gauge theory, as well as
protons and other charged particles in QCD coupled to QED. In four dimensions
non-Abelian charges are confined. Hence, in an infinite volume non-Abelian
infraparticles cost an infinite amount of energy. However, in a $C$-periodic
volume non-Abelian infraparticles (whose energy increases linearly with the box
size) can indeed exist. Investigating these states holds the promise of
deepening our understanding of confinement. | hep-lat |
Toward solving the sign problem with path optimization method: We propose a new approach to circumvent the sign problem in which the
integration path is optimized to control the sign problem. We give a trial
function specifying the integration path in the complex plane and tune it to
optimize the cost function which represents the seriousness of the sign
problem. We call it the path optimization method. In this method, we do not
need to solve the gradient flow required in the Lefschetz-thimble method and
then the construction of the integration-path contour arrives at the
optimization problem where several efficient methods can be applied. In a
simple model with a serious sign problem, the path optimization method is
demonstrated to work well; the residual sign problem is resolved and precise
results can be obtained even in the region where the global sign problem is
serious. | hep-lat |
Scaling studies of QCD with the dynamical HISQ action: We study the lattice spacing dependence, or scaling, of physical quantities
using the highly improved staggered quark (HISQ) action introduced by the
HPQCD/UKQCD collaboration, comparing our results to similar simulations with
the asqtad fermion action. Results are based on calculations with lattice
spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical
HISQ quarks. The strange and charm quark masses are near their physical values,
and the light-quark mass is set to 0.2 times the strange-quark mass. We look at
the lattice spacing dependence of hadron masses, pseudoscalar meson decay
constants, and the topological susceptibility. In addition to the commonly used
determination of the lattice spacing through the static quark potential, we
examine a determination proposed by the HPQCD collaboration that uses the decay
constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the
lattice artifacts in the HISQ simulations are much smaller than those in the
asqtad simulations at the same lattice spacings and quark masses. | hep-lat |
Confinement-Deconfinement transition and $Z_2$ symmetry in $Z_2+$Higgs
theory: We study the Polyakov loop and the $Z_2$ symmetry in the lattice $Z_2+$Higgs
theory in 4D Euclidean space using Monte Carlo simulations. The results show
that this symmetry is realised in the Higgs symmetric phase for large number of
temporal lattice sites. To understand the dependence on the number of temporal
sites, we consider a one dimensional model by keeping terms of the original
action corresponding to a single spatial site. In this approximation the
partition function can be calculated exactly as a function of the Polyakov
loop. The resulting free energy is found to have the $Z_2$ symmetry in the
limit of large temporal sites. We argue that this is due to $Z_2$ invariance as
well as dominance of the distribution or density of states corresponding to the
action. | hep-lat |
Proton decay matrix element on the lattice with physical pion mass: Proton decay is one of possible signatures of baryon number violation, which
has to exist to explain the baryon asymmetry and the existence of nuclear
matter. Proton decays must be mediated through effective low-energy baryon
number violating operators made of three quarks and a lepton. We calculate
matrix elements of these operators between the proton and various meson final
states using the direct method. We report on preliminary results of matrix
element calculation done with the 2+1 dynamical flavor domain wall fermions at
the physical point for the first time. | hep-lat |
Deriving exact results for Ising-like models from the cluster variation
method: The cluster variation method (CVM) is an approximation technique which
generalizes the mean field approximation and has been widely applied in the
last decades, mainly for finding accurate phase diagrams of Ising-like lattice
models. Here we discuss in which cases the CVM can yield exact results,
considering: (i) one-dimensional systems and strips (in which case the method
reduces to the transfer matrix method), (ii) tree-like lattices and (iii) the
so-called disorder points of euclidean lattice models with competitive
interactions in more than one dimension. | hep-lat |
Measurement of hybrid content of heavy quarkonia using lattice NRQCD: Using lowest-order lattice NRQCD to create heavy meson propagators and
applying the spin-dependent interaction, $c_B^{}
\frac{-g}{2m_q}\vec\sigma\cdot\vec{B}$, at varying intermediate time slices, we
compute the off-diagonal matrix element of the Hamiltonian for the
quarkonium-hybrid two-state system. Thus far, we have results for one set of
quenched lattices with an interpolation in quark mass to match the bottomonium
spectrum. After diagonalization of the two-state Hamiltonian, we find the
ground state of the $\Upsilon$ to show a $0.0035(1)c_B^2$ (with $c_B^2 \sim
1.5-3.1$) probability admixture of hybrid, $|b\bar{b}g>$. | hep-lat |
Pion form factor with twisted mass QCD: The pion form factor is calculated using quenched twisted mass QCD with
beta=6.0 and maximal twisting angle omega=pi/2. Two pion masses and several
values of momentum transfer are considered. The momentum averaging procedure of
Frezzotti and Rossi is used to reduce lattice spacing errors, and numerical
results are consistent with the expected O(a) improvement. | hep-lat |
Chiral Lattice Gauge Theories from Warped Domain Walls and
Ginsparg-Wilson Fermions: We propose a construction of a 2-dimensional lattice chiral gauge theory. The
construction may be viewed as a particular limit of an infinite warped
3-dimensional theory. We also present a "single-site'' construction using
Ginsparg-Wilson fermions which may avoid, in both 2 and 4 dimensions, the
problems of waveguide-Yukawa models. | hep-lat |
Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD
with Wilson or Ginsparg-Wilson quarks: We derive the asymptotic lattice spacing dependence
$a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ relevant for spectral quantities of
lattice QCD, when using Wilson, O$(a)$ improved Wilson or Ginsparg-Wilson
quarks. We give some examples for the spectra encountered for $\hat{\Gamma}_i$
including the partially quenched case, mixed actions and using two different
discretisations for dynamical quarks. This also includes maximally twisted mass
QCD relying on automatic O$(a)$ improvement. At O$(a^2)$, all cases considered
have $\min_i\hat{\Gamma}_i\gtrsim -0.3$ if $N_\mathrm{f}\leq 4$, which ensures
that the leading order lattice artifacts are not severely logarithmically
enhanced in contrast to the O$(3)$ non-linear sigma model [1,2]. However, we
find a very dense spectrum of these leading powers, which may result in major
pile-ups and cancellations. We present in detail the computational strategy
employed to obtain the 1-loop anomalous dimensions already used in [3]. | hep-lat |
Exact calculation of disconnected loops: We present an implementation of the disconnected diagram contributions to
quantities such as the flavor-singlet pseudoscalar meson mass which are
accelerated by GPGPU technology utilizing the NVIDIA CUDA platform. To enable
the exact evaluation of the disconnected loops we use a $16^3 \times 32$
lattice and $N_f=2$ Wilson fermions simulated by the SESAM Collaboration. The
disconnected loops are also computed using stochastic methods with several
noise reduction techniques.
In particular, we analyze various dilution schemes as well as the recently
proposed truncated s olver method. We find consistency among the different
methods used for the determination of the $\eta^\prime$ mass, albeit that the
gauge noise for the ensemble studied is large. We also find that the effect of
'dilution' d oes not go beyond that of optimal statistical noise in many cases.
It has been observed, however, that spin dilution does have a significant
effect for some quantities studied. | hep-lat |
Light hadronic physics using domain wall fermions in quenched lattice
QCD: In the past year domain wall fermion simulations have moved from exploratory
stages to the point where systematic effects can be studied with different
gauge couplings, volumes, and lengths in the fifth dimension. Results are
presented here for the chiral condensate, the light hadron spectrum, and the
strange quark mass. We focus especially on the pseudoscalar meson mass and show
that, in small volume, the correlators used to compute it can be contaminated
to different degrees by topological zero modes. In large volume a nonlinear
extrapolation to the chiral limit, e.g. as expected from quenched chiral
perturbation theory, is needed in order to have a consistent picture of low
energy chiral symmetry breaking effects. | hep-lat |
Flux representation of an effective Polyakov loop model for QCD
thermodynamics: We discuss an effective Polyakov loop model for QCD thermodynamics with a
chemical potential. Using high temperature expansion techniques the partition
sum is mapped exactly onto the partition sum of a flux model. In the flux
representation the complex action problem is resolved and a simulation with
worm-type algorithms becomes possible also at finite chemical potential. | hep-lat |
The beta function and equation of state for QCD with two flavors of
quarks: We measure the pressure and energy density of two flavor QCD in a wide range
of quark masses and temperatures. The pressure is obtained from an integral
over the average plaquette or psi-bar-psi. We measure the QCD beta function,
including the anomalous dimension of the quark mass, in new Monte Carlo
simulations and from results in the literature. We use it to find the
interaction measure, E-3p, yielding non-perturbative values for both the energy
density E and the pressure p. uuencoded compressed PostScript file Revised
version should work on more PostScript printers. | hep-lat |
A study of the (m,d,N)=(1,3,2) Lifshitz point and of the three-
dimensional XY universality class by high-temperature bivariate series for
the XY models with anisotropic competing interactions: High-temperature bivariate expansions have been derived for the two-spin
correlation-function in a variety of classical lattice XY (planar rotator)
models in which spatially isotropic interactions among first-neighbor spins
compete with spatially isotropic or anisotropic (in particular uniaxial)
interactions among next-to-nearest-neighbor spins. The expansions, calculated
for cubic lattices of dimension d=1,2 and 3, are expressed in terms of the two
variables K1=J1/kT and K2=J2/kT, where J1 and J2 are the nearest-neighbor and
the next-to-nearest-neighbor exchange couplings, respectively. This report
deals in particular with the properties of the d=3 uniaxial XY model (ANNNXY
model) for which the bivariate expansions have been computed through the 18-th
order, thus extending by 12 orders the results so far available and making a
study of this model possible over a wide range of values of the competition
parameter R=J2/J1. | hep-lat |
$ξ/ξ_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models: Effective Polyakov line actions are a powerful tool to study the finite
temperature behaviour of lattice gauge theories. They are much simpler to
simulate than the original lattice model and are affected by a milder sign
problem, but it is not clear to which extent they really capture the rich
spectrum of the original theories. We propose here a simple way to address this
issue based on the so called second moment correlation length $\xi_{2nd}$. The
ratio $\xi/\xi_{2nd}$ between the exponential correlation length and the second
moment one is equal to 1 if only a single mass is present in the spectrum, and
it becomes larger and larger as the complexity of the spectrum increases. Since
both $\xi$ and $\xi_{2nd}$ are easy to measure on the lattice, this is a cheap
and efficient way to keep track of the spectrum of the theory. As an example of
the information one can obtain with this tool we study the behaviour of
$\xi/\xi_{2nd}$ in the confining phase of the ($D=3+1$) $\mathrm{SU}(2)$ gauge
theory and show that it is compatible with 1 near the deconfinement transition,
but it increases dramatically as the temperature decreases. We also show that
this increase can be well understood in the framework of an effective string
description of the Polyakov loop correlator. This non-trivial behaviour should
be reproduced by the Polyakov loop effective action; thus, it represents a
stringent and challenging test of existing proposals and it may be used to
fine-tune the couplings and to identify the range of validity of the
approximations involved in their construction. | hep-lat |
Numerical simulations with two flavours of twisted-mass Wilson quarks
and DBW2 gauge action: Discretisation errors in two-flavour lattice QCD with Wilson-quarks and DBW2
gauge action are investigated by comparing numerical simulation data at two
values of the bare gauge coupling. Both non-zero and zero twisted mass values
are considered. The results, including also data from simulations using the
Wilson plaquette gauge action, are compared to next-to-leading order chiral
perturbation theory formulas. | hep-lat |
4d Simplicial Quantum Gravity: Matter Fields and the Corresponding
Effective Action: Four-dimensional simplicial quantum gravity is modified either by coupling it
to U(1) gauge fields or by introducing a measure weighted by the orders of the
triangles. Strong coupling expansion and Monte Carlo simulations are used.
Although the two modifications of the standard pure-gravity model are
apparently very distinct, they produce strikingly similar results, as far as
the geometry of random manifolds is concerned. In particular, for an
appropriate choice of couplings, the branched polymer phase is replaced by a
crinkled phase, characterized by the susceptibility exponent $\gamma < 0$ and
the fractal dimension $d_H > 2$. The quasi-equivalence between the two models
is exploited to get further insight into the extended phase diagram of the
theory. | hep-lat |
Magnetic polarizability of hadrons from lattice QCD: We extract the magnetic polarizability from the quadratic response of a
hadron's mass shift in progressively small static magnetic fields. The
calculation is done on a 24x12x12x24 lattice at a = 0.17 fm with an improved
gauge action and the clover quark action. The results are compared to those
from experiments and models where available. | hep-lat |
Curvature of the pseudocritical line in (2+1)-flavor QCD with HISQ
fermions: We study QCD with (2+1)-HISQ fermions at nonzero temperature and nonzero
imaginary baryon chemical potential. Monte Carlo simulations are performed
using the MILC code along the line of constant physics with a light to strange
mass ratio of $m_l/m_s=1/20$ on lattices up to $48^3 \times 12$ to check for
finite cutoff effects. We determine the curvature of the pseudocritical line
extrapolated to the continuum limit. | hep-lat |
Bosonic color-flavor transformation for the special unitary group: We extend Zirnbauer's color-flavor transformation in the bosonic sector to
the color group SU(N_c). Because the flavor group U(N_b, N_b) is non-compact,
the algebraic method by which the original color-flavor transformation was
derived leads to a useful result only for 2N_b \le N_c. Using the character
expansion method, we obtain a different form of the transformation in the
extended range N_b \le N_c. This result can also be used for the color group
U(N_c). The integrals to which the transformation can be applied are of
relevance for the recently proposed boson-induced lattice gauge theory. | hep-lat |
Charged Pion Polarizability from the Lattice: Direct evaluation of charged particle polarizabilities on the lattice is
quite difficult. However, a short cut for charged pion polarizability - the
Das, Mathur, Okubo Sum Rule - can readily be calculated using lattice
techniques. A phenomenological model has been developed to fit the time
behavior of the propagators in this expression. Numerical systematics are
discussed and some preliminary results are presented. | hep-lat |
Chiral condensate from the Banks-Casher relation: We report on our ongoing project of determining the chiral condensate of
two-flavor QCD from the Banks-Casher relation. We compute the mode number of
the O(a)-improved Wilson-Dirac operator for several values of \Lambda, and we
discuss different fitting strategies to extract the chiral condensate from its
mass and \Lambda dependence. Our preliminary results haven been obtained at two
different lattice spacings by using CLS-configurations. | hep-lat |
Thermal Correlators in the ρ channel of two-flavor QCD: We present a lattice QCD calculation with two dynamical flavors of the
isovector vector correlator in the high-temperature phase. We analyze the
correlator in terms of the associated spectral function, for which we review
the theoretical expectations. In our main analysis, we perform a fit for the
difference of the thermal and vacuum spectral functions, and we use an exact
sum rule that constrains this difference. We also perform a direct fit for the
thermal spectral function, and obtain good agreement between the two analyses
for frequencies below the two-pion threshold. Under the assumption that the
spectral function is smooth in that region, we give an estimate of the
electrical conductivity. | hep-lat |
Power corrections from decoupling of the charm quark: Decoupling of heavy quarks at low energies can be described by means of an
effective theory as shown by S. Weinberg in Ref. [1]. We study the decoupling
of the charm quark by lattice simulations. We simulate a model, QCD with two
degenerate charm quarks. In this case the leading order term in the effective
theory is a pure gauge theory. The higher order terms are proportional to
inverse powers of the charm quark mass $M$ starting at $M^{-2}$. Ratios of
hadronic scales are equal to their value in the pure gauge theory up to power
corrections. We show, by precise measurements of ratios of scales defined from
the Wilson flow, that these corrections are very small and that they can be
described by a term proportional to $M^{-2}$ down to masses in the region of
the charm quark mass. | hep-lat |
$d^\ast (2380)$ dibaryon from lattice QCD: The $\Delta\Delta$ dibaryon resonance $d^\ast (2380)$ with $(J^P, I)=(3^+,
0)$ is studied theoretically on the basis of the 3-flavor lattice QCD
simulation with heavy pion masses ($m_\pi =679, 841$ and $1018$ MeV). By using
the HAL QCD method, the central $\Delta$-$\Delta$ potential in the ${}^7S_3$
channel is obtained from the lattice data with the lattice spacing $a\simeq
0.121$ fm and the lattice size $L\simeq 3.87$ fm. The resultant potential shows
a strong short-range attraction, so that a quasi-bound state corresponding to
$d^\ast (2380)$ is formed with the binding energy $25$-$40$ MeV below the
$\Delta\Delta$ threshold for the heavy pion masses. The tensor part of the
transition potential from $\Delta\Delta$ to $NN$ is also extracted to
investigate the coupling strength between the $S$-wave $\Delta\Delta$ system
with $J^P=3^+$ and the $D$-wave $NN$ system. Although the transition potential
is strong at short distances, the decay width of $d^\ast (2380)$ to $NN$ in the
$D$-wave is kinematically suppressed, which justifies our single-channel
analysis at the range of the pion mass explored in this study. | hep-lat |
Dilaton EFT from p-regime to RMT in the $ε$-regime: New results are reported from tests of a low-energy effective field theory
(EFT) that includes a dilaton field to describe the emergent light scalar with
${ 0^{++} }$ quantum numbers in the strongly coupled near-conformal gauge
theory with a massless fermion flavor doublet in the two-index symmetric
(sextet) representation of the SU(3) color gauge group. In the parlor of
walking --- based on the observed light scalar, the small $\beta$-function at
strong coupling, and the large anomalous scale dimension of the chiral
condensate --- the dilaton EFT hypothesis is introduced to test if it explains
the slowly changing nearly scale invariant physics that connects the
asymptotically free UV fixed point and the far-infrared scale of chiral
symmetry breaking. The characteristic dilaton EFT signatures of scale symmetry
breaking are probed in this report in the small Compton wavelength limit of
Goldstone bosons relative to the size of the lattice volume (p-regime) and in
the limit when the Goldstone wavelength exceeds the size of the volume
($\epsilon$-regime). Random matrix theory (RMT) analysis of the dilaton EFT is
applied to the lowest part of the Dirac spectrum in the $\epsilon$-regime to
directly test predictions for the fundamental EFT parameters. The predictions,
sensitive to the choice of the dilaton potential, were limited before to the
p-regime, using extrapolations from far above the chiral limit with untested
uncertainties. The dilaton EFT analysis of the $\epsilon$-regime was first
suggested in \cite{Fodor:2019vmw}, with some results presented at this
conference and with our continued post-conference analysis added to stimulate
discussions. | hep-lat |
Quark propagator from an improved staggered action in Laplacian and
Landau gauges: Studies of gauge dependent quantities are afflicted with Gribov copies, but
Laplacian gauge fixing provides one possible solution to this problem. We
present results for the lattice quark propagator in both Landau and Laplacian
gauges using standard and improved staggered quark actions. The standard
Kogut-Susskind action has errors of \oa{2} while the improved ``Asqtad'' action
has \oa{4}, \oag{2}{2} errors and this improvement is seen in the quark
propagator. We demonstrate the application of tree-level corrections to these
actions and see that Landau and Laplacian gauges produce very similar results.
In addition, we test an ansatz for the quark mass function, with promising
results. In the chiral limit, the infrared quark mass, $M(q^2 = 0)$ is found to
be $260\pm 20$ MeV. | hep-lat |
SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A
HYPERSPHERICAL BOUNDARY: A recently developed model of random walks on a $D$-dimensional
hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is
used to study polymer growth near a $D$-dimensional attractive hyperspherical
boundary. The model determines the fraction $P(\kappa)$ of the polymer adsorbed
on this boundary as a function of the attractive potential $\kappa$ for all
values of $D$. The adsorption fraction $P(\kappa)$ exhibits a second-order
phase transition with a nontrivial scaling coefficient for $0<D<4$, $D\neq 2$,
and exhibits a first-order phase transition for $D>4$. At $D=4$ there is a
tricritical point with logarithmic scaling. This model reproduces earlier
results for $D=1$ and $D=2$, where $P(\kappa)$ scales linearly and
exponentially, respectively. A crossover transition that depends on the radius
of the adsorbing boundary is found. | hep-lat |
Some exact results on the QCD critical point: We show, in a model-independent manner, that the QCD critical point can
appear only inside the pion condensation phase of the phase-quenched QCD as
long as the contribution of flavor-disconnected diagrams is negligible. The
sign problem is known to be maximally severe in this region, implying that the
QCD critical point is reachable by the present lattice QCD techniques only if
there is an enhancement of the flavor-disconnected contribution at finite
baryon chemical potential. | hep-lat |
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