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Matrix elements relevant for Delta I=1/2 rule and epsilon-prime from
Lattice QCD with staggered fermions: We perform a study of matrix elements relevant for the Delta I=1/2 rule and
the direct CP-violation parameter epsilon-prime from first principles by
computer simulation in Lattice QCD. We use staggered (Kogut-Susskind) fermions,
and employ the chiral perturbation theory method for studying K to 2 Pi decays.
Having obtained a reasonable statistical accuracy, we observe an enhancement of
the Delta I=1/2 amplitude, consistent with experiment within our large
systematic errors. Finite volume and quenching effects have been studied and
were found small compared to noise. The estimates of epsilon-prime are hindered
by large uncertainties associated with operator matching. In this paper we
explain the simulation method, present the results and address the systematic
uncertainties. | hep-lat |
Neutron electric dipole moment on the lattice: We carry out a feasibility study toward a lattice QCD calculation of the
neutron electric dipole moment (NEDM) in the presence of the $\theta$ term
using two different approaches. In the first method, we calculate the CP-odd
electromagnetic form factor $F_3$, which becomes the NEDM in the zero momentum
transfer limit. At the first order in $\theta$, we derive a formula connecting
the lattice three-point function to the CP-odd electromagnetic form factor. In
the second method we directly extract the NEDM from the energy difference
between spin-up and spin-down neutron states in the presence of a constant
electric field, without expanding a small but non-zero $\theta$. We test both
approaches numerically, employing the domain-wall quark action with the RG
improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times
32\times 16$ lattice, and further applying the second method to the clover
quark action at a similar lattice spacing and nucleon mass. We obtain good
signals from both approaches. In particular the second method works well with
both fermion formulations. | hep-lat |
Determination of $s$- and $p$-wave $I=1/2$ $Kπ$ scattering amplitudes
in $N_{\mathrm{f}}=2+1$ lattice QCD: The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes are
calculated using a single ensemble of anisotropic lattice QCD gauge field
configurations with $N_{\mathrm{f}} = 2+1$ flavors of dynamical Wilson-clover
fermions at $m_{\pi} = 230\mathrm{MeV}$. A large spatial extent of $L =
3.7\mathrm{fm}$ enables a good energy resolution while partial wave mixing due
to the reduced symmetries of the finite volume is treated explicitly.The
$p$-wave amplitude is well described by a Breit-Wigner shape with parameters
$m_{K^{*}}/m_{\pi} = 3.808(18)$ and $g^{\mathrm{BW}}_{K^{*}K\pi} = 5.33(20)$
which are insensitive to the inclusion of $d$-wave mixing and variation of the
$s$-wave parametrization. An effective range description of the near-threshold
$s$-wave amplitude yields $m_{\pi}a_0 = -0.353(25)$. | hep-lat |
Correlation functions in lattice formulations of quantum gravity: We compare different models of a quantum theory of four-dimensional lattice
gravity based on Regge's original proposal. From Monte Carlo simulations we
calculate two-point functions between geometrical quantities and estimate the
masses of the corresponding interaction particles. | hep-lat |
The topological susceptibility in finite temperature QCD and axion
cosmology: We study the topological susceptibility in 2+1 flavor QCD above the chiral
crossover transition temperature using Highly Improved Staggered Quark action
and several lattice spacings, corresponding to temporal extent of the lattice,
$N_\tau=6,8,10$ and $12$. We observe very distinct temperature dependences of
the topological susceptibility in the ranges above and below $250$ MeV. While
for temperatures above $250$ MeV, the dependence is found to be consistent with
dilute instanton gas approximation, at lower temperatures the fall-off of
topological susceptibility is milder. We discuss the consequence of our results
for cosmology wherein we estimate the bounds on the axion decay constant and
the oscillation temperature if indeed the QCD axion is a possible dark matter
candidate. | hep-lat |
Inclusive hadronic decay rate of the $τ$ lepton from lattice QCD: Inclusive hadronic decays of the $\tau$ lepton are very interesting from the
phenomenological point of view since they give access to the CKM matrix
elements $V_{ud}$ and $V_{us}$. In this paper, for the first time, by employing
the HLT method for hadronic smeared spectral densities we compute on the
lattice the inclusive decay rate of the processes $\tau \to X_{ud}\, \nu_\tau$,
where $X_{ud}$ is a generic hadronic state with $\bar{u} d$ flavor quantum
numbers. Our computation, which avoids any recourse to OPE and/or perturbative
approximations, is carried out in isospin symmetric $N_{f}=2+1+1$ lattice QCD
at physical quark masses, using ensembles produced by the ETMC at three lattice
spacings and two volumes. All uncertainties, except for isospin breaking
effects, are taken into account and a result with a subpercent error is
obtained for $|V_{ud}|$, which is nicely consistent with the current world
average. These findings validate our approach and also motivate the inclusion
of isospin breaking corrections and its extension to the inclusive decay $\tau
\to X_{us}\, \nu_\tau$, paving the way towards a high-precision first
principles determination of $|V_{us}|$ and $|V_{ud}|$ from inclusive $\tau$
decay. | hep-lat |
Exploring the HMC trajectory-length dependence of autocorrelation times
in lattice QCD: We study autocorrelation times of physical observables in lattice QCD as a
function of the molecular dynamics trajectory length in the hybrid Monte-Carlo
algorithm. In an interval of trajectory lengths where energy and reversibility
violations can be kept under control, we find a variation of the integrated
autocorrelation times by a factor of about two in the quantities of interest.
Trajectories longer than conventionally used are found to be superior both in
the Nf=0 and Nf=2 examples considered here. We also provide evidence that they
lead to faster thermalization of systems with light quarks. | hep-lat |
Strong isospin violation and chiral logarithms in the baryon spectrum: We present a precise lattice QCD calculation of the contribution to the
neutron-proton mass splitting arising from strong isospin breaking,
$m_n-m_p|_{QCD}=2.32\pm0.17$ MeV. We also determine $m_{\Xi^-} -
m_{\Xi^0}|_{QCD} = 5.44\pm0.31$ MeV. The calculation is performed at three
values of the pion mass, with several values of the quark mass splitting and
multiple lattice volumes, but only a single lattice spacing and an estimate of
discretization errors. The calculations are performed on the anisotropic
clover-Wilson ensembles generated by the Hadron Spectrum Collaboration. The
omega-baryon mass is used to set the scale $a_t^{-1}=6111\pm127$ MeV, while the
kaon masses are used to determine the value of the light-quark mass spitting.
The nucleon mass splitting is then determined as a function of the pion mass.
We observe, for the first time, conclusive evidence for non-analytic light
quark mass dependence in lattice QCD calculations of the baryon spectrum. When
left as a free parameter, the fits prefer a nucleon axial coupling of
$g_A=1.24(56)$. To highlight the presence of this chiral logarithm in the
nucleon mass splitting, we also compute the isospin splitting in the
cascade-baryon system which is less sensitive to chiral dynamics. Finally, we
update the best lattice QCD determination of the CP-odd pion-nucleon coupling
that would arise from a non-zero QCD theta-term, $\bar{g}_0 / (\sqrt{2}f_\pi) =
(14.7\pm1.8\pm1.4) \cdot 10^{-3} \bar{\theta}$.
The original lattice QCD correlation functions, analysis results and
extrapolated quantities are packaged in HDF5 files made publicly available
including a simple Python script to access the numerical results, construct
effective mass plots along with our analysis results, and perform the
extrapolations of various quantities determined in this work. | hep-lat |
Disconnected Quark Loop Contributions to Nucleon Structure: We calculate the disconnected contribution to isoscalar nucleon charges for
scalar, axial and tensor channels of light and strange quarks. The calculation
has been done with the Clover valence quarks on the MILC $N_f=2+1+1$ HISQ
lattices whose light quark masses corresponding to the pion masses of 305 MeV
and 217 MeV at $a \approx 0.12$ fm and 312 MeV at $a \approx 0.09$ fm.
All-mode-averaging technique is used for the evaluation two-point functions.
Disconnected quark loops are estimated by using the truncated solver method
with Gaussian random noise sources. Contamination from the excited states is
removed by fitting the results of various source-sink separations and operator
insertions to the formula including up to the first excited state,
simultaneously. | hep-lat |
Recent progress in applying lattice QCD to kaon physics: Standard lattice calculations in kaon physics are based on the evaluation of
matrix elements of local operators between two single-hadron states or a
single-hadron state and the vacuum. Recent progress in lattice QCD has gone
beyond these standard observables. I will review the status and prospects of
lattice kaon physics with an emphasis on non-leptonic $K\to\pi\pi$ decay and
long-distance processes including $K^0$-$\overline{K^0}$ mixing and rare kaon
decays. | hep-lat |
$m_c$ (and $m_b$) from lattice QCD: Quark mass determinations based on lattice QCD simulations have continued to
make strides in recent years. Here I review that progress with a focus on
developments computing the charm (and bottom) quark masses since the 2015
edition of CHARM. These advances have resulted in groups now quoting
(sub-)percent-level precision for these quantities, and, importantly, using a
variety of techniques subject to differing systematic uncertainties.
Improvements to quantify the effects of QED are also now being included. I will
highlight three of the strategies being used to determine $m_c$ at this level
of precision. | hep-lat |
NRQCD and Static Systems -- A General Variational Approach: We present initial results from Monte Carlo simulations of NRQCD-light,
static-light, and NRQCD-NRQCD mesons, using a variational technique (MOST), as
part of our ongoing calculation of the $f_{B}$ decay constant. The basis states
for the variational calculation are quark-antiquark operators separated by all
possible relative distances not equivalent under the cubic group (for example,
for a $20^{3}$ lattice there are 286 operators). The efficacy of the method is
demonstrated by the good plateaus obtained for the ground state and the clean
extraction of the wave functions of the ground and first radially excited
state. | hep-lat |
Chern-Simons term in the 4-dimensional SU(2) Higgs Model: Using Seiberg's definition for the geometric charge in SU(2) lattice gauge
theory, we have managed to apply it also to the Chern-Simons term. We checked
the periodic structure and determined the Chern-Simons density on small
lattices $L^4$ and $L^3 \times 2,\, 4$ with $L=4,\, 6,\mbox{ and }8$ near the
critical region in the SU(2) Higgs model. The data indicate that tunneling is
increased at high temperature. | hep-lat |
Meron-Cluster Solution of Fermion and Other Sign Problems: Numerical simulations of numerous quantum systems suffer from the notorious
sign problem. Important examples include QCD and other field theories at
non-zero chemical potential, at non-zero vacuum angle, or with an odd number of
flavors, as well as the Hubbard model for high-temperature superconductivity
and quantum antiferromagnets in an external magnetic field. In all these cases
standard simulation algorithms require an exponentially large statistics in
large space-time volumes and are thus impossible to use in practice.
Meron-cluster algorithms realize a general strategy to solve severe sign
problems but must be constructed for each individual case. They lead to a
complete solution of the sign problem in several of the above cases. | hep-lat |
High-Precision c and b Masses, and QCD Coupling from Current-Current
Correlators in Lattice and Continuum QCD: We extend our earlier lattice-QCD analysis of heavy-quark correlators to
smaller lattice spacings and larger masses to obtain new values for the c mass
and QCD coupling, and, for the first time, values for the b mass:
m_c(3GeV,n_f=4)=0.986(6)GeV, alpha_msb(M_Z,n_f=5)=0.1183(7), and
m_b(10GeV,n_f=5)=3.617(25)GeV. These are among the most accurate determinations
by any method. We check our results using a nonperturbative determination of
the mass ratio m_b(mu,n_f)/m_c(mu,n_f); the two methods agree to within our 1%
errors and taken together imply m_b/m_c=4.51(4). We also update our previous
analysis of alpha_msb from Wilson loops to account for revised values for r_1
and r_1/a, finding a new value alpha_\msb(M_Z,n_f=5)=0.1184(6); and we update
our recent values for light-quark masses from the ratio m_c/m_s. Finally, in
the Appendix, we derive a procedure for simplifying and accelerating
complicated least-squares fits. | hep-lat |
Exploring quark transverse momentum distributions with lattice QCD: We discuss in detail a method to study transverse momentum dependent parton
distribution functions (TMDs) using lattice QCD. To develop the formalism and
to obtain first numerical results, we directly implement a bi-local quark-quark
operator connected by a straight Wilson line, allowing us to study T-even,
"process-independent" TMDs. Beyond results for x-integrated TMDs and quark
densities, we present a study of correlations in x and transverse momentum. Our
calculations are based on domain wall valence quark propagators by the LHP
collaboration calculated on top of gauge configurations provided by MILC with
2+1 flavors of asqtad-improved staggered sea quarks. | hep-lat |
Cutoff effects in the O(N) sigma model at large N: The computation of the step scaling function for the finite size mass-gap in
the O(N) sigma model at large N is reviewed. Practically exact nonperturbative
results become available for both finite and vanishing lattice spacing. We use
them as a testbed to investigate standard procedures of continuum extrapolation
in lattice field theory. | hep-lat |
Rare $B$ decays using lattice QCD form factors: In this write-up we review and update our recent lattice QCD calculation of
$B \to K^*$, $B_s \to \phi$, and $B_s \to K^*$ form factors [arXiv:1310.3722].
These unquenched calculations, performed in the low-recoil kinematic regime,
provide a significant improvement over the use of extrapolated light cone sum
rule results. The fits presented here include further kinematic constraints and
estimates of additional correlations between the different form factor shape
parameters. We use these form factors along with Standard Model determinations
of Wilson coefficients to give Standard Model predictions for several
observables [arXiv:1310.3887]. The modest improvements to the form factor fits
lead to improved determinations of $F_L$, the fraction of longitudinally
polarized vector mesons, but have little effect on most other observables. | hep-lat |
Toward dense QCD in quantum computers: Lattice QCD at nonzero baryon density is a big challenge in hadron physics.
In this presentation, I discuss the quantum computation of lattice gauge theory
at nonzero density. I show some benchmark results of the Schwinger model
obtained by the quantum adiabatic algorithm and the quantum variational
algorithm. | hep-lat |
The lower moments of nucleon structure functions in lattice QCD with
physical quark masses: We present results for the nucleon structure functions and form factors
obtained from 2+1 flavor lattice QCD with physical light quark masses
($m_{\pi}=135$ MeV) in a large spatial extent of about 10 fm. Our calculations
are performed with the PACS10 gauge configurations generated by the PACS
Collaboration with the six stout-smeared ${\mathscr{O}}(a)$ improved
Wilson-clover quark action and Iwasaki gauge action at $\beta=1.82$ and $2.00$
corresponding to lattice spacings of $0.085$ fm and $0.064$ fm respectively.
The lower moments of structure functions, $\langle x \rangle_{u-d}$ and
$\langle x \rangle_{\Delta u - \Delta d}$ given by the twist-2 operators being
properly renormalized, are evaluated in the $\overline{\rm MS}$ scheme at the
renormalization scale of 2 GeV only at $\beta=1.82$, since the renormalization
factors at $\beta=2.00$ have not yet determined nonperturbatively in the RI/MOM
scheme. Instead, at two lattice spacings, we evaluate appropriate ratios of
$g_{A}/g_{V}$ and $\langle x \rangle_{u-d}/\langle x \rangle_{\Delta u -\Delta
d}$, which are not renormalized in the continuum limit. These quantities thus
can be directly compared with the experimental data without the
renormalization. | hep-lat |
The dual sector of the φ^4 Theory in 4D: The one-component $\lambda\phi^4$ theory in four dimensions in the
spontaneously broken symmetry phase has a non-trivial, non-perturbative sector
which can be studied by means of a duality transformation of its Ising limit.
Duality maps this theory to a model of interacting membranes. Physical states
correspond to membrane excitations. The way this non-perturbative behaviour can
be reconciled with the triviality of the theory in its continuum limit is
discussed. | hep-lat |
Color Dynamics in External Fields: We investigate the vacuum dynamics of U(1), SU(2), and SU(3) lattice gauge
theories in presence of external (chromo)magnetic fields, both in (3+1) and
(2+1) dimensions. We find that the critical coupling for the phase transition
in compact U(1) gauge theory is independent of the strength of an external
magnetic field. On the other hand we find that, both in (3+1) and (2+1)
dimensions, the deconfinement temperature for SU(2) and SU(3) gauge systems in
a constant abelian chromomagnetic field decreases when the strength of the
applied field increases. We conclude that the dependence of the deconfinement
temperature on the strength of an external constant chromomagnetic field is a
peculiar feature of non abelian gauge theories and could be useful to get
insight into color confinement. | hep-lat |
Lattice QCD determination of states with spin 5/2 or higher in the
spectrum of nucleons: Energies for excited isospin 1/2 states that include the nucleon are computed
using quenched, anisotropic lattices. Baryon interpolating field operators that
are used include nonlocal operators that provide $G_2$ irreducible
representations of the octahedral group. The decomposition of spin 5/2 or
higher states is realized for the first time in a lattice QCD calculation. We
observe patterns of degenerate energies in the irreducible representations of
the octahedral group that correspond to the subduction of the continuum spin
5/2 or higher. | hep-lat |
Machine Learning Trivializing Maps: A First Step Towards Understanding
How Flow-Based Samplers Scale Up: A trivializing map is a field transformation whose Jacobian determinant
exactly cancels the interaction terms in the action, providing a representation
of the theory in terms of a deterministic transformation of a distribution from
which sampling is trivial. Recently, a proof-of-principle study by Albergo,
Kanwar and Shanahan [arXiv:1904.12072] demonstrated that approximations of
trivializing maps can be `machine-learned' by a class of invertible,
differentiable neural models called \textit{normalizing flows}. By ensuring
that the Jacobian determinant can be computed efficiently, asymptotically exact
sampling from the theory of interest can be performed by drawing samples from a
simple distribution and passing them through the network. From a theoretical
perspective, this approach has the potential to become more efficient than
traditional Markov Chain Monte Carlo sampling techniques, where
autocorrelations severely diminish the sampling efficiency as one approaches
the continuum limit. A major caveat is that it is not yet understood how the
size of models and the cost of training them is expected to scale. As a first
step, we have conducted an exploratory scaling study using two-dimensional
$\phi^4$ with up to $20^2$ lattice sites. Although the scope of our study is
limited to a particular model architecture and training algorithm, initial
results paint an interesting picture in which training costs grow very quickly
indeed. We describe a candidate explanation for the poor scaling, and outline
our intentions to clarify the situation in future work. | hep-lat |
Rare decay B -> K ll form factors from lattice QCD: We calculate, for the first time using unquenched lattice QCD, form factors
for the rare decay B -> Kll in and beyond the Standard Model. Our lattice QCD
calculation utilizes a nonrelativistic QCD formulation for the b valence
quarks, the highly improved staggered quark formulation for the light valence
quarks, and employs the MILC 2+1 asqtad ensembles. The form factor results,
based on the z expansion, are valid over the full kinematic range of q^2. We
construct the ratios f0/f+ and fT/f+, which are useful in constraining new
physics and verifying effective theory form factor symmetry relations. We also
discuss the calculation of Standard Model observables. | hep-lat |
A complete non-perturbative renormalization prescription for quasi-PDFs: In this work we present, for the first time, the non-perturbative
renormalization for the unpolarized, helicity and transversity quasi-PDFs, in
an RI' scheme. The proposed prescription addresses simultaneously all aspects
of renormalization: logarithmic divergences, finite renormalization as well as
the linear divergence which is present in the matrix elements of fermion
operators with Wilson lines. Furthermore, for the case of the unpolarized
quasi-PDFs, we describe how to eliminate the unwanted mixing with the twist-3
scalar operator. We utilize perturbation theory for the one-loop conversion
factor that brings the renormalization functions to the MS-scheme at a scale of
2 GeV. We also explain how to improve the estimates on the renormalization
functions by eliminating lattice artifacts. The latter can be computed in
one-loop perturbation theory and to all orders in the lattice spacing. We apply
the methodology for the renormalization to an ensemble of twisted mass fermions
with Nf=2+1+1 dynamical light quarks, and a pion mass of around 375 MeV. | hep-lat |
Excited states in the full QCD hadron spectrum on a $16^3 \times 40$
lattice: We report the hadron mass spectrum obtained on a $16^3 \times 40$ lattice at
$\beta = 5.7$ using two flavors of staggered fermions with $m a = 0.01$. We
calculate the masses of excited states that have the same quantum numbers as
the $\pi$, $\rho$ and $N$. They are obtained by a combined analysis of the
hadron correlators from sources of size $16^3$ and $8^3$. We also report on the
hadron spectrum for a wide range of valence quark masses. | hep-lat |
Renormalisation of lattice currents and the calculation of decay
constants for dynamical staggered fermions: A numerical calculation of the lattice staggered renormalisation constants at
$\beta = 5.35$, $m = 0.01$ is presented. It is seen that there are considerable
non-perturbative effects present. As an application the vector decay constant
$f_\rho$ is estimated. (LAT92 contribution, one LATEX file with 3 postscript
figures appended.) | hep-lat |
Quenched QCD at finite temperature with chiral Fermions: We study physics at temperatures just above the QCD phase transition (Tc)
using chiral (overlap) Fermions in the quenched approximation of lattice QCD.
Exact zero modes of the overlap Dirac operator are localized and their
frequency of occurrence drops with temperature. This is closely related to
axial U(1) symmetry, which remains broken up to 2Tc. After subtracting the
effects of these zero modes, chiral symmetry is restored, as indicated by the
behavior of the chiral condensate. The pseudoscalar and vector screening masses
are close to ideal gas values. | hep-lat |
A method to measure the antikaon-nucleon scattering length in lattice
QCD: We propose a method to determine the isoscalar \bar K N scattering length on
the lattice. Our method represents the generalization of L\"uscher's approach
in the presence of inelastic channels (complex scattering length). In addition,
the proposed approach allows one to find the position of the S-matrix pole
corresponding the the Lambda(1405) resonance. | hep-lat |
Light hadron masses with 4-GeV cutoff and L=2.4fm: We discuss preliminary results from our quenched light hadron mass
calculation on a $48^3 \times 64$ lattice at the coupling of $\beta = 6.5$.
Staggered quarks with masses of $m_q = 0.01, 0.005, 0.0025$ and $0.00125$ are
used. | hep-lat |
Exploring a hidden symmetry with electrically charged quarks: It is usual to study confinement via quantum chromodynamics (QCD) alone. The
deconfinement transition of the pure gauge theory (i.e. with static quarks) is
then characterized by the breaking of center symmetry. Center vortices offer an
intuitive and quantitative description of the transition. Dynamical quarks
explicitly break center symmetry, and the phase transition becomes a crossover.
However, it may be misleading to study QCD in isolation. Quarks also carry
fractional electric charge. This bestows the Standard Model with a global
center symmetry that combines color center phases with an appropriate
electromagnetic phase. Is this symmetry relevant to confinement? We begin our
investigation by studying a 2-color model of QCD with half-integer electrically
charged quarks. | hep-lat |
Continuum limit of the leading order HQET form factor in $B_s \to
K\ellν$ decays: We discuss the computation of form factors for semi-leptonic decays of $\rm
B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of
the static $\rm B_s$ form factors we demonstrate that after non-perturbative
renormalization the continuum limit can be taken with confidence. The resulting
precision is of interest for extractions of $V_{\rm ub}$. The size of the
corrections of order $1/m_{\rm b}$ is just estimated at present but it is
expected that their inclusion does not pose significant difficulties. | hep-lat |
Non-Perturbative Gauge-Higgs Unification in Five Dimensions: We study the phase diagram and mass spectrum of an $SU(2)$ Gauge-Higgs
Unification scenario on a five-dimensional orbifold.We observe spontaneous
symmetry breaking within the Higgs phase of the theory and, in the vicinity of
a newly discovered phase, we find that the ratio of Higgs to gauge boson masses
takes a Standard Model-like value. Precisely in this region of the phase
diagram, we observe dimensional reduction via localisation. | hep-lat |
Numerical methods for the sign problem in Lattice Field Theory: The great majority of algorithms employed in the study of lattice field
theory are based on Monte Carlo's importance sampling method, i.e. on
probability interpretation of the Boltzmann weight. Unfortunately in many
theories of interest one cannot associated a real and positive weight to every
configuration, that is because their action is explicitly complex or because
the weight is multiplied by some non positive term. In this cases one says that
the theory on the lattice is affected by the sign problem. An outstanding
example of sign problem preventing a quantum field theory to be studied, is QCD
at finite chemical potential. Whenever the sign problem is present, standard
Monte Carlo methods are problematic to apply and, in general, new approaches
are needed to explore the phase diagram of the complex theory. Here we will
review three of the main candidate methods to deal with the sign problem,
namely complex Langevin dynamics, Lefschetz thimbles and density of states
method. We will first study complex Langevin dynamics, combined with the gauge
cooling method, on the one-dimensional Polyakov line model, and then we will
apply it to pure gauge Yang-Mills theory with a topological theta-term. It
follows a comparison between complex Langevin dynamics and the Lefschetz
thimbles method on three toy models, which are the quartic model, the U(1)
one-link model with a mu dependent determinant, and the SU(2) non abelian
one-link model with complex beta parameter. Lastly, we introduce the density of
state method, based on the LLR algorithm, and we will employ it in the study of
the relativistic Bose gas at finite chemical potential. | hep-lat |
Lattice Study of the Extent of the Conformal Window in Two-Color
Yang-Mills Theory: We perform a lattice calculation of the Schr\"odinger functional running
coupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the
fundamental representation. The aim of this work is to determine whether the
above theory has an infrared fixed point. Due to sensitivity of the $SF$
renormalized coupling to the tuning of the fermion bare mass we were unable to
reliably extract the running coupling for stronger bare couplings. | hep-lat |
Semileptonic form factor ratio B_s->D_s/B->D and its application to
BR(B^0_s->μ^+μ^-): We present a (2+1)-flavor lattice QCD calculation of the form factor ratio
between the semileptonic decays $\bar{B}^0_s \to D^+_sl^-\bar{\nu} $ and
$\bar{B}^0 \to D^+l^-\bar{\nu} $. This ratio is an important theoretical input
to the hadronic determination of the $B$ meson fragmentation fraction ratio
$f_s/f_d$ which enters in the measurement of $\mathrm{BR}(B^0_s\to
\mu^+\mu^-)$. Small lattice spacings and high statistics enable us to simulate
the decays with a dynamic final $D$ meson of small momentum and reliably
extract the hadronic matrix elements at nonzero recoil. We report our
preliminary result for the form factor ratio at the corresponding momentum
transfer of the two decays $f_0^{(s)}(M^2_\pi)/f_0^{(d)}(M^2_K)$. | hep-lat |
Thermodynamical quantities for overlap fermions with chemical potential: Recently a formulation of overlap fermions at finite density based on an
analytic continuation of the sign function was proposed. We study this proposal
by analyzing the energy and number densities for free fermions as a function of
the chemical potential and the temperature. Our results show that overlap
fermions with chemical potential give rise to the correct continuum behavior. | hep-lat |
Controlling Excited-State Contributions with Distillation in Lattice QCD
Calculations of Nucleon Isovector Charges $g_S^{u-d}$, $g_A^{u-d}$,
$g_T^{u-d}$: We investigate the application of the distillation smearing approach, and the
use of the variational method with an extended basis of operators facilitated
by this approach, on the calculation of the nucleon isovector charges
$g_S^{u-d}$, $g_A^{u-d}$, and $g_T^{u-d}$. We find that the better sampling of
the lattice enabled through the use of distillation yields a substantial
reduction in the statistical uncertainty in comparison with the use of
alternative smearing methods, and furthermore, appears to offer better control
over the contribution of excited-states compared to use of a single, local
interpolating operator. The additional benefit arising through the use of the
variational method in the distillation approach is less dramatic, but
nevertheless significant given that it requires no additional Dirac inversions. | hep-lat |
Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite
Temperature: We examine the eigenvalues and eigenvectors of the staggered Dirac operator
on thermal ensembles created in QCD with two flavours of staggered quarks. We
see that across the phase transition a gap opens in the spectrum. For finite
volume lattices in the low-temperature phase the eigenvectors are extended, but
generic field configurations in the high temperature phase give rise to
localized eigenstates. We examine measures of the stability of such
localization and find that at finite volumes localization occurs through Mott's
mechanism of the formation of mobility edges. However, the band gap between the
localized and extended states seem to scale to zero in the limit of large
volume. | hep-lat |
Monopole and instanton effects on connected and disconnected
correlations for scalar density: This study investigates the effects on the connected and disconnected
correlations for the scalar density that are induced by created monopoles and
instantons in the QCD vacuum. To reveal the effects, we add a monopole and
anti-monopole pair in the gauge field configurations in \textit{SU}(3) by
applying the monopole creation operator to the vacuum. We vary the magnetic
charges of the monopole and anti-monopole and increase the number of monopoles
and anti-monopoles in the configurations. The Dirac operator of overlap
fermions preserves the exact chiral symmetry in lattice gauge theory and exact
zero-modes exist in its spectrum. The eigenvalues and eigenvectors of the
overlap Dirac operator have been calculated using these configurations, and the
numbers of instantons and anti-instantons which are created by these additional
monopoles and anti-monopoles have been estimated from the numbers of
topological charges in our previous studies. In this study, we demonstrate the
preliminary results that instantons and monopoles influence the masses that are
evaluated from the connected and disconnected correlation functions for the
scalar density using low-lying eigenvalues and eigenvectors of the overlap
Dirac operator. | hep-lat |
Critical point phase transition for finite temperature 3-flavor QCD with
non-perturbatively O($a$) improved Wilson fermions at $N_{\rm t}=10$: We study the finite temperature phase structure for three-flavor QCD with a
focus on locating the critical point which separates crossover and first order
phase transition region in the chiral regime of the Columbia plot. In this
study, we employ the Iwasaki gauge action and the non-perturvatively O($a$)
improved Wilson-Clover fermion action. We discuss the finite size scaling
analysis including the mixing of magnetization-like and energy-like
observables. We carry out the continuum extrapolation of the critical point
using newly generated data at $N_{\rm t}=8$, $10$ and estimate the upper bound
of the critical pseudo-scalar meson mass $m_{\rm PS,E} \lesssim 170 {\rm MeV}$
and the critical temperature $T_{\rm E}=134(3){\rm MeV}$. Our estimate of the
upper bound is derived from the existence of the critical point as an edge of
the 1st order phase transition while that of the staggered-type fermions is
based on its absence. | hep-lat |
Chiral condensate, susceptibilities, critical coupling and indices in
QED$_4$: We measure chiral susceptibilities in the Coulomb phase of noncompact QED$_4$
in $8^4, 10^4$ and $12^4$ lattices. The MFA approach allows simulations in the
chiral limit which are therefore free from arbitrary mass extrapolations. Using
the critical couplings extracted from these calculations, we study the critical
behaviour of the chiral condensate, which we find in disagreement with the
predictions of logarithmically improved scalar Mean Field theory. | hep-lat |
Quark number susceptibility at high temperature: We use three dimensional reduced effective field theory (EQCD) and lattice
calculations to determine the quark number susceptibility of QCD at high
temperature. We find our results to agree well with known perturbative
expansion as well as with other lattice data. | hep-lat |
Angular momentum content of the rho-meson in lattice QCD: The variational method allows one to study the mixing of interpolators with
different chiral transformation properties in the non-perturbatively determined
physical state. It is then possible to define and calculate in a
gauge-invariant manner the chiral as well as the partial wave content of the
quark-antiquark component of a meson in the infrared, where mass is generated.
Using a unitary transformation from the chiral basis to the LSJ basis one may
extract a partial wave content of a meson. We present results for the ground
state of the rho-meson using quenched simulations as well as simulations with
two dynamical quarks, all for lattice spacings close to 0.15 fm. We point out
that these results indicate a simple 3S1-wave composition of the rho-meson in
the infrared, like in the SU(6) flavor-spin quark model. | hep-lat |
The Kaon B-parameter in Mixed Action Chiral Perturbation Theory: We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a
partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and
staggered sea quarks. We find that the resulting expression is similar to that
in the continuum, and in fact has only two additional unknown parameters. At
one-loop order, taste-symmetry violations in the staggered sea sector only
contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the
masses of taste-singlet sea-sea mesons. Lattice discretization errors also give
rise to an analytic term which shifts the tree-level value of B_K by an amount
of O(a^2). This term, however, is not strictly due to taste-breaking, and is
therefore also present in the expression for B_K for pure G-W lattice fermions.
We also present a numerical study of the mixed B_K expression in order to
demonstrate that both discretization errors and finite volume effects are small
and under control on the MILC improved staggered lattices. | hep-lat |
Moments of generalized parton distributions and quark angular momentum
of the nucleon: The internal structure of hadrons is important for a variety of topics,
including the hadron form factors, proton spin and spin asymmetry in polarized
proton scattering.
For a systematic study generalized parton distributions (GPDs) encode
important information on hadron structure in the entire impact parameter space.
We report on a computation of nucleon GPDs based on simulations with two
dynamical non-perturbatively improved Wilson quarks with pion masses down to
350MeV. We present results for the total angular momentum of quarks with chiral
extrapolation based on covariant baryon chiral perturbation theory. | hep-lat |
Fermions obstruct dimensional reduction in hot QCD: We have studied, for the first time, screening masses obtained from
glueball-like correlators in Quantum Chromodynamics with four light dynamical
flavours of quarks in the temperature range 1.5T_c < T < 3T_c, where T_c is the
temperature at which the chiral transition occurs. We have also studied
pion-like and sigma-like screening masses, and found that they are degenerate
in the entire range of T. These obstruct perturbative dimensional reduction
since the lowest glueball screening mass is heavier than them. Extrapolation of
our results suggests that this obstruction may affect the entire range of
temperature expected to be reached even at the Large Hadron Collider. | 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 |
Probing the Region of Massless Quarks in Quenched Lattice QCD using
Wilson Fermions: We study the spectrum of $H(m)=\gamma_5 W(-m)$ with $W(m)$ being the
Wilson-Dirac operator on the lattice with bare mass equal to $m$. The
background gauge fields are generated using the SU(3) Wilson action at
$\beta=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of
$H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is
massless in this whole region. | hep-lat |
Spectral Analysis of Causal Dynamical Triangulations via Finite Element
Method: We examine the dual graph representation of simplicial manifolds in Causal
Dynamical Triangulations (CDT) as a mean to build observables, and propose a
new representation based on the Finite Element Methods (FEM). In particular,
with the application of FEM techniques, we extract the (low-lying) spectrum of
the Laplace-Beltrami (LB) operator on the Sobolev space $H^1$ of scalar
functions on piecewise flat manifolds, and compare them with corresponding
results obtained by using the dual graph representation. We show that, besides
for non-pathological cases in two dimensions, the dual graph spectrum and
spectral dimension do not generally agree, neither quantitatively nor
qualitatively, with the ones obtained from the LB operator on the continuous
space. We analyze the reasons of this discrepancy and discuss its possible
implications on the definition of generic observables built from the dual graph
representation. | hep-lat |
Higgs mechanism in five-dimensional gauge theories: Lattice simulations of five-dimensional gauge theories on an orbifold
revealed that there is spontaneous symmetry breaking. Some of the
extra-dimensional components of the gauge field play the role of a Higgs field
and some of the four-dimensional components become massive gauge bosons. The
effect is confirmed by computing the Coleman-Weinberg potential with a cutoff.
We compare the results of this computation with the lattice data. | hep-lat |
Nuclear Physics Review: Anchoring low-energy nuclear physics to the fundamental theory of strong
interactions remains an outstanding challenge. I review the current progress
and challenges of the endeavor to use lattice QCD to bridge this connection.
This is a particularly exciting time for this line of research as demonstrated
by the spike in the number of different collaborative efforts focussed on this
problem and presented at this conference. I first digress and discuss the 2013
Ken Wilson Award. | hep-lat |
The three-loop beta function in SU(N) lattice gauge theories: We calculate the third coefficient of the lattice $\beta$ function in pure
Yang-Mills theory. We make use of a computer code for solving perturbation
theory analytically on the lattice. We compute the divergent integrals by using
a method based on a Taylor expansion of the integrand in powers of the external
momenta in $4 - \epsilon$ dimensions. Our results are in agreement with a
previous calculation by M. L\"uscher and P. Weisz where the authors used a
different technique. We also show how this new coefficient modifies the scaling
function on the lattice in both the standard and energy schemes. In particular
we show that asymptotic scaling is extremely well achieved in the energy
scheme. | hep-lat |
A note on the vacuum structure to lattice Euclidean quantum gravity: It is shown that the ground state or vacuum to the lattice Euclidean quantum
gravity is significantly different from the ground states to the well-known
vacua in QED, QCD, et cetera. In the case of the lattice Euclidean quantum
gravity, the long-wavelength scale vacuum structure is similar to that in QED,
moreover the quantum fluctuations to gravity are very reduced in comparison
with the situation in QED. But the small scale (of the order of the lattice
scale) vacuum structure to gravity is significantly different from that to the
long-wavelength scales: the fluctuation values of geometrical degrees of
freedom (tetrads) are commensurable with theirs most probable values. | hep-lat |
Composite flavor-singlet scalar in twelve-flavor QCD: We report the calculation of the flavor-singlet scalar in the SU(3) gauge
theory with the degenerate twelve fermions in the fundamental representation
using a HISQ-type action at a fixed $\beta$. In order to reduce the large
statistical error coming from the vacuum-subtracted disconnected correlator, we
employ a noise reduction method and a large number of configurations. We
observe that the flavor-singlet scalar is lighter than the pion in this theory
from the calculations with the fermion bilinear and gluonic operators. This
peculiar feature is considered to be due to the infrared conformality of this
theory, and it is a promissing signal for a walking technicolor, where a light
composite Higgs boson is expected to emerge by approximate conformal dynamics. | hep-lat |
Landau gauge gluon and ghost propagators from two-flavor lattice QCD at
T > 0: In this contribution we extend our unquenched computation of the Landau gauge
gluon and ghost propagators in lattice QCD at non-zero temperature. The study
was aimed at providing input for investigations employing continuum functional
methods. We show data which correspond to pion mass values between 300 and 500
MeV and are obtained for a lattice size 32**3 x 12. The longitudinal and
transversal components of the gluon propagator turn out to change smoothly
through the crossover region, while the ghost propagator exhibits only a very
weak temperature dependence. For a pion mass of around 400 MeV and the
intermediate temperature value of approx. 240 MeV we compare our results with
additional data obtained on a lattice with smaller Euclidean time extent N_t =
8, 10 and find a reasonable scaling behavior. | hep-lat |
A numerical and theoretical study of multilevel performance for
two-point correlator calculations: An investigation of the performance of the multilevel algorithm in the
approach to criticality has been undertaken using the Ising model, performing
simulations across a range of temperatures. Numerical results show that the
performance of multilevel in this system deteriorates as the correlation length
is increased with respect to the lattice size. The statistical error of the
longest correlator in the system is reduced in a multilevel setup when the
correlation length is less than one-tenth of the lattice size, while for longer
correlation lengths multilevel performs more poorly than a computer-time
equivalent single level algorithm. A theoretical model of this performance
scaling is outlined, and shows remarkable accuracy when compared to numerical
results. This theoretical model may be applied to other systems with more
complex spectra to predict if multilevel techniques are likely to result in
improved statistics. | hep-lat |
SU(4) lattice gauge theory with decuplet fermions: Schrödinger
functional analysis: We complete a program of study of SU(N) gauge theories coupled to two flavors
of fermions in the two-index symmetric representation by performing numerical
simulations in SU(4). The beta function, defined and calculated via the
Schr\"odinger functional, runs more slowly than the two-loop perturbative
result. The mass anomalous dimension levels off in strong coupling at a value
of about 0.45, rendering this theory unsuitable for walking technicolor. A
large-N comparison of this data with results from SU(2) and SU(3) reveals
striking regularities. | hep-lat |
Irregular parameter dependence of numerical results in tensor
renormalization group analysis: We study the parameter dependence of numerical results obtained by the tensor
renormalization group. We often observe an irregular behavior as the parameters
are varied with the method, which makes it difficult to perform the numerical
derivatives in terms of the parameter. With the use of two-dimensional Ising
model we explicitly show that the sharp cutoff used in the truncated singular
value decomposition causes this unwanted behavior when the level crossing
happens between singular values below and above the truncation order as the
parameters are varied. We also test a smooth cutoff, instead of the sharp one,
as a truncation scheme and discuss its effects. | hep-lat |
Quantum Field Theories with Tensor Renormalization Group: We report recent progress on the application of the tensor renormalization
group (TRG) to quantum field theories pursued by the Tsukuba group. We explain
how to treat the scalar, fermion, and gauge theories with the TRG method
presenting the results for the phase transitions in the (3+1)-dimensional
((3+1)$d$) complex $\phi^4$ theory at finite density, (1+1)$d$ pure U(1)
lattice gauge theory with a $\theta$ term, (3+1)$d$ Nambu--Jona-Lasinio model
at finite density and (1+1)$d$ and (2+1)$d$ Hubbard models at an arbitrary
chemical potential. It is demonstrated that the TRG method is free from the
sign problem in practical calculations and applicable to the four-dimensional
models. | hep-lat |
Lattice Gauge Fixing, Gribov Copies and BRST Symmetry: We show that a modification of the BRST lattice quantization allows to
circumvent an old paradox, formulated by Neuberger, related to lattice Gribov
copies and non-perturbative BRST invariance. In the continuum limit the usual
BRST formulation is recovered. | hep-lat |
Multi-block/multi-core SSOR preconditioner for the QCD quark solver for
K computer: We study the algorithmic optimization and performance tuning of the Lattice
QCD clover-fermion solver for the K computer. We implement the L\"uscher's SAP
preconditioner with sub-blocking in which the lattice block in a node is
further divided to several sub-blocks to extract enough parallelism for the
8-core CPU SPARC64$^{\mathrm{TM}}$ VIIIfx of the K computer. To achieve a
better convergence property we use the symmetric successive over-relaxation
(SSOR) iteration with {\it locally-lexicographical} ordering for the sub-blocks
in obtaining the block inverse. The SAP preconditioner is included in the
single precision BiCGStab solver of the nested BiCGStab solver. The single
precision part of the computational kernel are solely written with the SIMD
oriented intrinsics to achieve the best performance of the \SPARC on the K
computer. We benchmark the single precision BiCGStab solver on the three
lattice sizes: $12^3\times 24$, $24^3\times 48$ and $48^3\times 96$, with
fixing the local lattice size in a node at $6^3\times 12$. We observe an ideal
weak-scaling performance from 16 nodes to 4096 nodes. The performance of a
computational kernel exceeds 50% efficiency, and the single precision BiCGstab
has $\sim26% susutained efficiency. | hep-lat |
Light hadron masses with a tadpole-improved next-nearest-neighbour
lattice fermion action: Calculations of hadron masses are done in quenched approximation using gauge
field and fermion actions which are both corrected for discretization errors to
$O(a^2)$ at the classical level and which contain tadpole improvement factors.
The fermion action has both nearest-neighbour and next-nearest-neighbour
couplings in the kinetic and Wilson terms. Simulations done at lattice spacings
of $0.27$ and $0.4$fm yield hadron masses which are already quite close to
experimental values. The results are compared to Wilson action calculations
done at comparable lattice spacings. | hep-lat |
Perfect Lattice Actions for the Gross-Neveu Model: We apply the method of Hasenfratz and Niedermayer to analytically construct
perfect lattice actions for the Gross--Neveu model. In the large $N$ limit
these actions display an exactly perfect scaling, i.e. cut-off artifacts are
completely eliminated even at arbitrarily short correlation length. Also the
energy spectrum coincides with the spectrum in the continuum and continuous
translation and rotation symmetries are restored in physical observables. This
is the first (analytic) construction of an exactly perfect lattice action at
finite correlation length. | hep-lat |
Asymptotic scaling in the two-dimensional $SU(3)$ $σ$-model at
correlation length $4 \times 10^5$: We carry out a high-precision simulation of the two-dimensional $SU(3)$
principal chiral model at correlation lengths $\xi$ up to $\approx\! 4 \times
10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. We extrapolate the
finite-volume Monte Carlo data to infinite volume using finite-size-scaling
theory, and we discuss carefully the systematic and statistical errors in this
extrapolation. We then compare the extrapolated data to the
renormalization-group predictions. For $\xi \gtapprox 10^3$ we observe good
asymptotic scaling in the bare coupling; at $\xi \approx 4 \times 10^5$ the
nonperturbative constant is within 2--3\% of its predicted limiting value. | hep-lat |
Precise Determinations of the Decay Constants of B and D mesons: Recently we studied the B, Bs, D and Ds meson decay constants using various
treatments for the heavy quark. For B mesons, we determined fB, fBs, and fBs/fB
with NRQCD bottom quarks. We then combined the ratio fBs/fB and another very
precise determination from HPQCD for fBs using heavy HISQ quarks, and extracted
fB with 2% total errors. We also calculated fD, fDs, and fDs/fD using HISQ
charm quarks. Here we review our results and briefly discuss their implications
for the determination of the CKM matrix elements |Vcd| and |Vcs|. | hep-lat |
Status of the Finite Temperature Electroweak Phase Transition on the
Lattice: I review the status of non-perturbative investigations of the finite
temperature electroweak phase transition by means of lattice simulations. | hep-lat |
Leading Isospin Breaking effects in nucleon and $Δ$ masses: We present a lattice calculation of the leading corrections to the masses of
nucleons and $\Delta$ resonances. These are obtained in QCD+QED at $1$st order
in the Isospin Breaking parameters $\alpha_{EM}$, the electromagnetic coupling,
and $\frac{{\hat{m}}_d - {\hat{m}}_u}{\Lambda_{QCD}}$, coming from the mass
difference between $u$ and $d$ quarks. | hep-lat |
Form factors for semi-leptonic B decays: We report on form factors for the B->K l^+ l^- semi-leptonic decay process.
We use several lattice spacings from a=0.12 fm down to 0.06 fm and a variety of
dynamical quark masses with 2+1 flavors of asqtad quarks provided by the MILC
Collaboration. These ensembles allow good control of the chiral and continuum
extrapolations. The b-quark is treated as a clover quark with the Fermilab
interpretation. We update our results for f_\parallel and f_\perp, or,
equivalently, f_+ and f_0. In addition, we present new results for the tensor
form factor f_T. Model independent results are obtained based upon the
z-expansion. | hep-lat |
Strong-coupling expansion of lattice O(N) sigma models: We report progress in the computation and analysis of strong-coupling series
of two- and three-dimensional ${\rm O}(N)$ $\sigma$ models. We show that,
through a combination of long strong-coupling series and judicious choice of
observables, one can compute continuum quantities reliably and with a precision
at least comparable with the best available Monte Carlo data. | hep-lat |
Critical exponents of a three dimensional O(4) spin model: By Monte Carlo simulation we study the critical exponents governing the
transition of the three-dimensional classical O(4) Heisenberg model, which is
considered to be in the same universality class as the finite-temperature QCD
with massless two flavors. We use the single cluster algorithm and the
histogram reweighting technique to obtain observables at the critical
temperature. After estimating an accurate value of the inverse critical
temperature $\Kc=0.9360(1)$, we make non-perturbative estimates for various
critical exponents by finite-size scaling analysis. They are in excellent
agreement with those obtained with the $4-\epsilon$ expansion method with
errors reduced to about halves of them. | hep-lat |
An ideal toy model for confining, walking and conformal gauge theories:
the O(3) sigma model with theta-term: A toy model is proposed for four dimensional non-abelian gauge theories
coupled to a large number of fermionic degrees of freedom. As the number of
flavors is varied the gauge theory may be confining, walking or conformal. The
toy model mimicking this feature is the two dimensional O(3) sigma model with a
theta-term. For all theta the model is asymptotically free. For small theta the
model is confining in the infra red, for theta = pi the model has a non-trivial
infra red fixed point and consequently for theta slightly below pi the coupling
walks. The first step in investigating the notoriously difficult systematic
effects of the gauge theory in the toy model is to establish non-perturbatively
that the theta parameter is actually a relevant coupling. This is done by
showing that there exist quantities that are entirely given by the total
topological charge and are well defined in the continuum limit and are
non-zero, despite the fact that the topological susceptibility is divergent.
More precisely it is established that the differences of connected correlation
functions of the topological charge (the cumulants) are finite and non-zero and
consequently there is only a single divergent parameter in Z(theta) but
otherwise it is finite. This divergent constant can be removed by an
appropriate counter term rendering the theory completely finite even at theta >
0. | hep-lat |
A lattice calculation of the pion form factor with Ginsparg-Wilson-type
fermions: Results for Monte Carlo calculations of the electromagnetic vector and scalar
form factors of the pion in a quenched simulation are presented. We work with
two different lattice volumes up to a spatial size of 2.4 fm at a lattice
spacing of 0.148 fm. The pion form factors in the space-like region are
determined for pion masses down to 340 MeV. | hep-lat |
'Bs --> Ds l nu' near zero recoil in and beyond the Standard Model: We compute the normalization of the form factor entering the Bs --> Ds l nu
decay amplitude by using numerical simulations of QCD on the lattice. From our
study with Nf=2 dynamical light quarks, and by employing the maximally twisted
Wilson quark action, we obtain in the continuum limit G(1) = 1.052(46). We also
compute the scalar and tensor form factors in the region near zero recoil and
find f0(t0)/f+(t0)=0.77(2), fT(t0,mb)/f+(t0)=1.08(7), for t0=11.5 GeV^2. These
latter results are useful for searching the effects of physics beyond the
Standard Model in Bs --> Ds l nu decays. Our results for the similar form
factors relevant to the non-strange case indicate that the method employed here
can be used to achieve the precision determination of the B --> D l nu decay
amplitude as well. | hep-lat |
A direct relation between confinement and chiral symmetry breaking in
temporally odd-number lattice QCD: In the lattice QCD formalism, we derive a gauge-invariant analytical relation
connecting the Polyakov loop and the Dirac modes on a temporally odd-number
lattice, where the temporal lattice size is odd, with the normal (nontwisted)
periodic boundary condition. This analytical relation indicates that low-lying
Dirac modes have little contribution to the Polyakov loop. Using lattice QCD
simulations, we numerically confirm the analytical relation and the negligible
contribution of low-lying Dirac modes to the Polyakov loop at the quenched
level, i.e., the Polyakov loop is almost unchanged by removing low-lying
Dirac-mode contribution from the QCD vacuum generated by lattice QCD in both
confinement and deconfinement phases. Thus, we conclude that there is no
one-to-one correspondence between confinement and chiral symmetry breaking in
QCD. As a new method, modifying the Kogut-Susskind formalism, we develop a
method for spin-diagonalizing the Dirac operator on the temporally odd-number
lattice. | hep-lat |
Physics from the lattice: glueballs in QCD; topology; SU(N) for all N: Lectures given at the Isaac Newton Institute, NATO-ASI School on
"Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July,
1997. | hep-lat |
Perturbation theory predictions and Monte Carlo simulations for the 2-d
O(n) non-linear sigma-model: By using the results of a high-statistics (O(10^7) measurements) Monte Carlo
simulation we test several predictions of perturbation theory on the O(n)
non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on
large enough lattices to have a good control on finite-size effects. The
magnetic susceptibility and three different definitions of the correlation
length are measured. We check our results with large-n expansions as well as
with standard formulae for asymptotic freedom up to 4 loops in the standard and
effective schemes.
For this purpose the weak coupling expansions of the energy up to 4 loops for
the standard action and up to 3 loops for the Symanzik action are calculated.
For the O(3) model we have used two different effective schemes and checked
that they lead to compatible results. A great improvement in the results is
obtained by using the effective scheme based on the energy at 3 and 4 loops. We
find that the O(8) model follows very nicely (within few per mille) the
perturbative predictions. For the O(3) model an acceptable agreement (within
few per cent) is found. | hep-lat |
A simple approach towards the sign problem using path optimisation: We suggest an approach for simulating theories with a sign problem that
relies on optimisation of complex integration contours that are not restricted
to lie along Lefschetz thimbles. To that end we consider the toy model of a
one-dimensional Bose gas with chemical potential. We identify the main
contribution to the sign problem in this case as coming from a nearest
neighbour interaction and approximately cancel it by an explicit deformation of
the integration contour. We extend the obtained expressions to more general
ones, depending on a small set of parameters. We find the optimal values of
these parameters on a small lattice and study their range of validity. We also
identify precursors for the onset of the sign problem. A fast method of
evaluating the Jacobian related to the contour deformation is proposed and its
numerical stability is examined. For a particular choice of lattice parameters,
we find that our approach increases the lattice size at which the sign problem
becomes serious from $L \approx 32$ to $L \approx 700$. The efficient
evaluation of the Jacobian ($O(L)$ for a sweep) results in running times that
are of the order of a few minutes on a standard laptop. | hep-lat |
Colorful plane vortices and Chiral Symmetry Breaking in $SU(2)$ Lattice
Gauge Theory: We investigate plane vortices with color structure. The topological charge
and gauge action of such colorful plane vortices are studied in the continuum
and on the lattice. These configurations are vacuum to vacuum transitions
changing the winding number between the two vacua, leading to a topological
charge $Q=-1$ in the continuum. After growing temporal extent of these
vortices, the lattice topological charge approaches $-1$ and the index theorem
is fulfilled. We analyze the low lying modes of the overlap Dirac operator in
the background of these colorful plane vortices and compare them with those of
spherical vortices. They show characteristic properties for spontaneous chiral
symmetry breaking. | hep-lat |
Anomalous Fermion Number Non-Conservation on the Lattice: The anomaly for the fermion number current is calculated on the lattice in a
simple prototype model with an even number of fermion doublets. | hep-lat |
The Renormalization Group and Dynamical Triangulations: A block spin renormalization group approach is introduced which can be
applied to dynamical triangulations in any dimension. | hep-lat |
Trivializing maps, the Wilson flow and the HMC algorithm: In lattice gauge theory, there exist field transformations that map the
theory to the trivial one, where the basic field variables are completely
decoupled from one another. Such maps can be constructed systematically by
integrating certain flow equations in field space. The construction is worked
out in some detail and it is proposed to combine the Wilson flow (which
generates approximately trivializing maps for the Wilson gauge action) with the
HMC simulation algorithm in order to improve the efficiency of lattice QCD
simulations. | hep-lat |
The static energy of a quark-antiquark pair from Laplacian eigenmodes: We test a method for computing the static quark-antiquark potential in
lattice QCD, which is not based on Wilson loops, but where the trial states are
formed by eigenvector components of the covariant lattice Laplace operator. The
runtime of this method is significantly smaller than the standard Wilson loop
calculation, when computing the static potential not only for on-axis, but also
for many off-axis quark-antiquark separations, i.e., when a fine spatial
resolution is required. We further improve the signal by using multiple
eigenvector pairs, weighted with Gaussian profile functions of the eigenvalues,
providing a basis for a generalized eigenvalue problem (GEVP), as it was
recently introduced to improve distillation in meson spectroscopy. We show
results with the new method for the static potential with dynamical fermions
and demonstrate its efficiency compared to traditional Wilson loop
calculations. The method presented here can also be applied to compute hybrid
or tetra-quark potentials and to static-light systems. | hep-lat |
Static quark anti-quark interactions at non-zero temperature from
lattice QCD: We present results on the in-medium interactions of static quark anti-quark
pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the
extraction of spectral information from Wilson line correlators in Coulomb
gauge using four complementary methods. Our results indicate that on HISQ
lattices, the position of the dominant spectral peak associated with the
real-part of the interquark potential remains unaffected by temperature. This
is in contrast to prior work in quenched QCD and we present follow up
comparisons to newly generated quenched ensembles. | hep-lat |
Perturbative calculations for the HISQ action: the gluon action at
$O(N_fα_sa^2)$: We present a new (and general) algorithm for deriving lattice Feynman rules
which is capable of handling actions as complex as the Highly Improved
Staggered Quark (HISQ) action. This enables us to perform a perturbative
calculation of the influence of dynamical HISQ fermions on the perturbative
improvement of the gluonic action in the same way as we have previously done
for asqtad fermions. We find the fermionic contributions to the radiative
corrections in the L\"uscher-Weisz gauge action to be somewhat larger for HISQ
fermions than for asqtad. | hep-lat |
A new fermion Hamiltonian for lattice gauge theory: We formulate Hamiltonian vector-like lattice gauge theory using the overlap
formula for the spatial fermionic part, $H_f$. We define a chiral charge, $Q_5$
which commutes with $H_f$, but not with the electric field term. There is an
interesting relation between the chiral charge and the fermion energy with
consequences for chiral anomalies. | hep-lat |
Lattice Models of Quantum Gravity: Standard Regge Calculus provides an interesting method to explore quantum
gravity in a non-perturbative fashion but turns out to be a CPU-time demanding
enterprise. One therefore seeks for suitable approximations which retain most
of its universal features. The $Z_2$-Regge model could be such a desired
simplification. Here the quadratic edge lengths $q$ of the simplicial complexes
are restricted to only two possible values $q=1+\epsilon\sigma$, with
$\sigma=\pm 1$, in close analogy to the ancestor of all lattice theories, the
Ising model. To test whether this simpler model still contains the essential
qualities of the standard Regge Calculus, we study both models in two
dimensions and determine several observables on the same lattice size. In order
to compare expectation values, e.g. of the average curvature or the Liouville
field susceptibility, we employ in both models the same functional integration
measure. The phase structure is under current investigation using mean field
theory and numerical simulation. | hep-lat |
Hadronic vacuum polarization with C* boundary conditions: We present a progress report on the calculation of the connected hadronic
contribution to the muon g-2 with C* boundary conditions. For that purpose we
use a QCD gauge ensemble with 3+1 flavors and two QCD+QED gauge ensembles with
1+2+1 flavors of dynamical quarks generated by the RC* collaboration. We detail
the calculation of the vector mass and elaborate on both statistical and
systematic errors. | hep-lat |
Delta I = 3/2, K to Pi Pi Decays with a Nearly Physical Pion Mass: The Delta I = 3/2 K to Pi Pi decay amplitude is calculated on RBC/UKQCD 32^3
x 64, L_s=32 dynamical lattices with 2+1 flavors of domain wall fermions using
the DSDR and Iwasaki gauge action. The calculation is performed with a single
pion mass (m_pi=141.9(2.3) MeV, partially quenched) and kaon mass
(m_K=507.4(8.5) MeV) which are nearly physical, and with nearly energy
conserving kinematics. Antiperiodic boundary conditions in two spatial
directions are used to give the two pions non-zero ground state momentum.
Results for time separations of 20, 24, 28 and 32 between the kaon and two-pion
sources are computed and an error weighted average is performed to reduce the
error. We find prelimenary results for Re(A_2)=1.396(081)_stat(160)_sys x
10^(-8) GeV and Im(A_2) = -8.46(45)_stat(1.95)_sys x 10^(-13) GeV. | hep-lat |
Colorful vortex intersections in SU(2) lattice gauge theory and their
influencs on chiral properties: We introduce topological non-trivial colorful regions around intersection
points of two perpendicular vortex pairs and investigate their influence on
topological charge density and eigenmodes of the Dirac operator. With
increasing distance between the vortices the eigenvalues of the lowest modes
decrease. We show that the maxima and minima of the chiral densities of the low
modes follow mainly the distributions of the topological charge densities. The
topological non-trivial color structures lead in some low modes to distinct
peaks in the chiral densities. The other low modes reflect the topological
charge densities of the intersection points. | hep-lat |
First experience with classical-statistical real-time simulations of
anomalous transport with overlap fermions: We present first results of classical-statistical real-time simulations of
anomalous transport phenomena with overlap fermions. We find that even on small
lattices overlap fermions reproduce the real-time anomaly equation with much
better precision than Wilson-Dirac fermions on an order of magnitude larger
lattices. The difference becomes much more pronounced for quickly changing
electromagnetic fields, especially if one takes into account the back-reaction
of fermions on electromagnetism. As test cases, we consider chirality pumping
in parallel electric and magnetic fields and mixing between the plasmon and the
Chiral Magnetic Wave. | hep-lat |
Magnetic properties of the nucleon in a uniform background field: We present results for the magnetic moment and magnetic polarisability of the
neutron and the magnetic moment of the proton. These results are calculated
using the uniform background field method on 32^3 x 64 dynamical QCD lattices
provided by the PACS-CS collaboration as part of the ILDG. We use a uniform
background magnetic field quantised by the periodic spatial volume. We
investigate ways to improve the effective energy plots used to calculate
magnetic polarisabilities, including the use of correlation matrix techniques
with various source smearings. | hep-lat |
The order of the phase transition in 3d U(1)+Higgs theory: We study the order of the phase transition in the 3d U(1)+Higgs theory, which
is the Ginzburg-Landau theory of superconductivity. We confirm that for small
scalar self-coupling the transition is of first order. For large scalar
self-coupling the transition ceases to be of first order, and a non-vanishing
scalar mass suggests that the transition may even be of higher than second
order. | hep-lat |
Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD: We investigate the Dirac eigenvalue spectrum ($\rho(\lambda,m_l)$) to study
the microscopic origin of axial anomaly in high temperature phase of QCD. We
propose novel relations between the derivatives ($\partial^n
\rho(\lambda,m_l)/\partial m_l^n$) of the Dirac eigenvalue spectrum with
respect to the quark mass ($m_l$) and the $(n+1)$-point correlations among the
eigenvalues ($\lambda$) of the massless Dirac operator. Based on these
relations, we present lattice QCD results for $\partial^n
\rho(\lambda,m_l)/\partial m_l^n$ ($n=1, 2, 3$) with $m_l$ corresponding to
pion masses $m_\pi=160-55$ MeV, and at a temperature of about 1.6 times the
chiral phase transition temperature. Calculations were carried out using
(2+1)-flavors of highly improved staggered quarks and the tree-level Symanzik
gauge action with the physical strange quark mass, three lattice spacings
$a=0.12, 0.08, 0.06$ fm, and lattices having aspect ratios $4-9$. We find that
$\rho(\lambda\to0,m_l)$ develops a peaked structure. This peaked structure,
which arises due to non-Poisson correlations within the infrared part of the
Dirac eigenvalue spectrum, becomes sharper as $a\to0$, and its amplitude is
proportional to $m_l^2$. After continuum and chiral extrapolations, we find
that the axial anomaly remains manifested in two-point correlation functions of
scalar and pseudo-scalar mesons in the chiral limit. We demonstrate that the
behavior of $\rho(\lambda\to0,m_l)$ is responsible for it. | hep-lat |
Monte Carlo approach to the string/M-theory: It has long been conjectured that certain supersymmetric Yang-Mills (SYM)
theories provide us with nonperturbative formulations of the string/M-theory.
Although the supersymmetry (SUSY) on lattice is notoriously difficult in
general, for a class of theories important for the string/M-theory various
lattice and non-lattice methods, which enable us to study them on computers,
have been proposed by now. In this talk, firstly I explain how SYM and
string/M-theory are related. Then I explain why the lattice SUSY is difficult
in general, and how the difficulties are solved in theories related to
string/M-theory. Then I review the status of the simulations. It is explained
that some stringy effects are correctly incorporated in SYM. Furthermore,
concrete values can be obtained from the SYM side, even when a direct
calculation on the string theory side is impossible by the state-of-the-art
techniques. We also comment on other recent developments, including the
membrane mini-revolution in 2008 and simulation of the matrix model formulation
of the string theory. | hep-lat |
Asymptotic scaling from strong coupling: Strong-coupling analysis of two-dimensional chiral models, extended to 15th
order, allows for the identification of a scaling region where known continuum
results are reproduced with great accuracy, and asymptotic scaling predictions
are fulfilled. The properties of the large-$N$ second-order phase transition
are quantitatively investigated. | hep-lat |
Polyakov loops and spectral properties of the staggered Dirac operator: We study the spectrum of the staggered Dirac operator in SU(2) gauge fields
close to the free limit, for both the fundamental and the adjoint
representation. Numerically we find a characteristic cluster structure with
spacings of adjacent levels separating into three scales. We derive an
analytical formula which explains the emergence of these different spectral
scales. The behavior on the two coarser scales is determined by the lattice
geometry and the Polyakov loops, respectively. Furthermore, we analyze the
spectral statistics on all three scales, comparing to predictions from random
matrix theory. | hep-lat |
Uses of Effective Field Theory in Lattice QCD: Several physical problems in particle physics, nuclear physics, and
astrophysics require information from non-perturbative QCD to gain a full
understanding. In some cases the most reliable technique for quantitative
results is to carry out large-scale numerical calculations in lattice gauge
theory. As in any numerical technique, there are several sources of
uncertainty. This chapter explains how effective field theories are used to
keep them under control and, then, obtain a sensible error bar. After a short
survey of the numerical technique, we explain why effective field theories are
necessary and useful. Then four important cases are reviewed: Symanzik's
effective field theory of lattice spacing effects; heavy-quark effective theory
as a tool for controlling discretization effects of heavy quarks; chiral
perturbation theory as a tool for reaching the chiral limit; and a general
field theory of hadrons for deriving finite volume corrections. | hep-lat |
A microscopic semiclassical confining field equation for $U(1)$ lattice
gauge theory in 2+1 dimensions: We present a semiclassical nonlinear field equation for the confining field
in 2+1--dimensional $U(1)$ lattice gauge theory (compact QED). The equation is
derived directly from the underlying microscopic quantum Hamiltonian by means
of truncation. Its nonlinearities express the dynamic creation of magnetic
monopole currents leading to the confinement of the electric field between two
static electric charges. We solve the equation numerically and show that it can
be interpreted as a London relation in a dual superconductor. | hep-lat |
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