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The Standard Model and the Lattice: The $SU(3)\otimes SU(2) \otimes U(1)$ standard model maps smoothly onto a
conventional lattice gauge formulation, including the parity violation of the
weak interactions. The formulation makes use of the pseudo-reality of the weak
group and requires the inclusion a full generation of both leptons and quarks.
As in continuum discussions, chiral eigenstates of the Dirac operator generate
known anomalies, although with rough gauge configurations these are no longer
exact zero modes of the Dirac operator. | hep-lat |
Reducing cutoff effects in maximally twisted lattice QCD close to the
chiral limit: When analyzed in terms of the Symanzik expansion, lattice correlators of
multi-local (gauge-invariant) operators with non-trivial continuum limit
exhibit in maximally twisted lattice QCD ``infrared divergent'' cutoff effects
of the type a^{2k}/(m_\pi^2)^{h}, 2k\geq h\geq 1 (k,h integers), which tend to
become numerically large when the pion mass gets small. We prove that, if the
action is O(a) improved a` la Symanzik or, alternatively, the critical mass
counter-term is chosen in some ``optimal'' way, these lattice artifacts are
reduced to terms that are at worst of the order a^{2}(a^2/m_\pi^2)^{k-1}, k\geq
1. This implies that the continuum extrapolation of lattice results is smooth
at least down to values of the quark mass, m_q, satisfying the order of
magnitude inequality m_q >a^2\Lambda^3_{\rm QCD}. | hep-lat |
The Phase Diagram of 2 flavour QCD with improved Actions: It has been proposed, that the chiral continuum limit of 2-flavour QCD with
Wilson fermions is brought about by a phase in which flavour and parity
symmetry are broken spontaneously at finite lattice spacing. At finite
temperature this phase should retract from the weak coupling limit to form 5
cusps. This scenario is studied with tree level Symanzik improved actions for
both gauge and fermion fields on lattices of size $8^3\times 4$ and $12^2\times
24\times 4$. | hep-lat |
Renormalization of the effective theory for heavy quarks at small
velocity: The slope of the Isgur-Wise function at the normalization point,
$\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$
matrix element $V_{cb}$ from exclusive semileptonic decay data. A method for
measuring this parameter on the lattice is the effective theory for heavy
quarks at small velocity $v$. This theory is a variant of the heavy quark
effective theory in which the motion of the quark is treated as a perturbation.
In this work we study the lattice renormalization of the slow heavy quark
effective theory. We show that the renormalization of $\xi^{(1)}(1)$ is not
affected by ultraviolet power divergences, implying no need of difficult
non-perturbative subtractions. A lattice computation of $\xi^{(1)}(1)$ with
this method is therefore feasible in principle. The one-loop renormalization
constants of the effective theory for slow heavy quarks are computed to order
$v^2$ together with the lattice-continuum renormalization constant of
$\xi^{(1)}(1)$ . We demonstrate that the expansion in the heavy-quark velocity
reproduces correctly the infrared structure of the original (non-expanded)
theory to every order. We compute also the one-loop renormalization constants
of the slow heavy quark effective theory to higher orders in $v^2$ and the
lattice-continuum renormalization constants of the higher derivatives of the
$\xi$ function. Unfortunately, the renormalization constants of the higher
derivatives are affected by ultraviolet power divergences, implying the
necessity of numerical non-perturbative subtractions. The lattice computation
of higher derivatives of the Isgur-Wise function seems therefore problematic. | hep-lat |
A new framework to tune an improved relativistic heavy-quark action: We introduce a new non-perturbative method to tune the parameters of the
Columbia formulation of an anisotropic, clover-improved relativistic
heavy-quark (RHQ) action. By making use of suitable observables which can be
computed at a sequence of heavy-quark mass values, employing an $O(a)$-improved
discretized action with domain-wall chiral fermion, and safely interpolated
between the accessible heavy-quark mass region and the static point predicted
by heavy-quark effective theory, we are able to precisely determine the unknown
coefficients of the RHQ action. In this proof-of-principle study we benefit
from the RBC/UKQCD Iwasaki gauge configurations with $2+1$ flavors of dynamical
quarks, at three values of the lattice spacing varying from $0.11$ to $0.062$
fm. Preliminary results and applications to bottom spectroscopy are also
presented. | hep-lat |
Update on onium masses with three flavors of dynamical quarks: We update results presented at Lattice 2005 on charmonium masses. New
ensembles of gauge configurations with 2+1 flavors of improved staggered quarks
have been analyzed. Statistics have been increased for other ensembles. New
results are also available for P-wave mesons and for bottomonium on selected
ensembles. | hep-lat |
Chiral logs in twisted mass lattice QCD with large isospin breaking: The pion masses and the pion decay constant are calculated to 1-loop order in
twisted mass Wilson chiral perturbation theory, assuming a large pion mass
splitting and tuning to maximal twist. Taking the large mass splitting at
leading order in the chiral expansion leads to significant modifications in the
chiral logarithms. For example, the result for the charged pion mass contains a
chiral logarithm that involves the neutral pion mass instead of the charged
one. Similar modifications appear in the results for the neutral pion mass and
the decay constant. These new results are used in fits to lattice data obtained
recently by the European twisted mass collaboration. The data can be fitted
well, in general better than with the standard chiral perturbation theory
expressions that ignore the mass splitting. The impact on the extraction of
low-energy couplings is briefly discussed. | hep-lat |
Improving center vortex detection by usage of center regions as guidance
for the direct maximal center gauge: The center vortex model of quantum chromodynamic states that vortices, closed
color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant
excitations of the vacuum, causing confinement and dynamical chiral symmetry
breaking. In an appropriate gauge, as \textit{direct maximal center gauge},
vortices are detected by projecting onto the center degrees of freedom. Such
gauges suffer from Gribov copy problems: different local maxima of the
corresponding gauge functional can result in different predictions of the
string tension. By using non-trivial center regions, that is, regions whose
boundary evaluates to a non-trivial center element, a resolution of this issue
seems possible. We use such non-trivial center regions to guide simulated
annealing procedures, preventing an underestimation of the string tension in
order to resolve the Gribov copy problem. | hep-lat |
Quenched charmonium near the continuum limit: We study relativistic charmonium on very fine quenched lattices (beta=6.4 and
6.6). We concentrate on the calculation of the hyperfine splitting between
eta_c and J/psi, aiming for a controlled continuum extrapolation of this
quantity. Results for the eta_c and J/psi wave functions are also presented. | hep-lat |
Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge
theory on the lattice: The line of phase transitions, separating the confinement and the Coulomb
phases in the four-dimensional pure compact U(1) gauge theory with extended
Wilson action, is reconsidered. We present new numerical evidence that a part
of this line, including the original Wilson action, is of second order. By
means of a high precision simulation on homogeneous lattices on a sphere we
find that along this line the scaling behavior is determined by one fixed point
with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the
existence of a nontrivial and nonasymptotically free four-dimensional pure U(1)
gauge theory in the continuum very probable. The universality and duality
arguments suggest that this conclusion holds also for the monopole loop gas,
for the noncompact abelian Higgs model at large negative squared bare mass, and
for the corresponding effective string theory. | hep-lat |
Particle Projection Using a Complex Langevin Method: Using complex stochastic quantization, we implement a particle-number
projection technique on the partition function of spin-1/2 fermions at finite
temperature on the lattice. We discuss the method, its application towards
obtaining the thermal properties of finite Fermi systems in three spatial
dimensions, and results for the first five virial coefficients of
one-dimensional, attractively interacting fermions. | hep-lat |
Chiral phase transition in a random matrix model with three flavors: The chiral phase transition in the conventional random matrix model is the
second order in the chiral limit, irrespective of the number of flavors N_f,
because it lacks the U_A(1)-breaking determinant interaction term. Furthermore,
it predicts an unphysical value of zero for the topological susceptibility at
finite temperatures. We propose a new chiral random matrix model which resolves
these difficulties by incorporating the determinant interaction term within the
instanton gas picture. The model produces a second-order transition for N_f=2
and a first-order transition for N_f=3, and recovers a physical temperature
dependence of the topological susceptibility. | hep-lat |
$B_s$-$\bar{B_s}$ mixing from lattice QCD: We study the $B^0_s-\bar{B^0_s}$ mixing amplitude in Standard Model by
computing the relevant hadronic matrix element in the static limit of lattice
HQET with the Neuberger light quark action. In the quenched approximation, and
after matching to the $\bar{\rm MS}$ scheme in QCD, we obtain
$\hat{B}^{\bar{\rm MS},{\rm NLO}}_{B_s}(m_b)=0.940(16)(22)$. | hep-lat |
Domain wall fermion zero modes on classical topological backgrounds: The domain wall approach to lattice fermions employs an additional dimension,
in which gauge fields are merely replicated, to separate the chiral components
of a Dirac fermion. It is known that in the limit of infinite separation in
this new dimension, domain wall fermions have exact zero modes, even for gauge
fields which are not smooth. We explore the effects of finite extent in the
fifth dimension on the zero modes for both smooth and non-smooth topological
configurations and find that a fifth dimension of around ten sites is
sufficient to clearly show zero mode effects. This small value for the extent
of the fifth dimension indicates the practical utility of this technique for
numerical simulations of QCD. | hep-lat |
Exploring the Spectrum of QCD using the Lattice: The calculation of the spectrum of QCD is key to an understanding of the
strong interactions, and vital if we are to capitalize on the experimental
study of the spectrum. In this paper, we describe progress towards
understanding the spectrum of resonances of both mesons and baryons from
lattice QCD, focusing in particular on the resonances of the $I=1/2$ nucleon
states, and of charmonium mesons composed of the heavy charmed quarks. | hep-lat |
Locality of staggered overlap operators: We give an explicit proof for the locality of staggered overlap operators.
The proof covers the original two flavor construction by Adams as well as a
single flavor version. As in the case of Neuberger's operator, an admissibility
condition for the gauge fields is required. | hep-lat |
Gradient flow step-scaling function for SU(3) with ten fundamental
flavors: We calculate the step scaling function, the lattice analog of the
renormalization group $\beta$-function, for an SU(3) gauge theory with ten
fundamental flavors. We present a detailed analysis including the study of
systematic effects of our extensive data set generated with ten dynamical
flavors using the Symanzik gauge action and three times stout smeared M\"obius
domain wall fermions. Using up to $32^4$ volumes, we calculate renormalized
couplings for different gradient flow schemes and determine the step-scaling
$\beta$ function for a scale change $s=2$ on up to five different lattice
volume pairs. In an accompanying paper we discuss that gradient flow can
promote lattice dislocations to instanton-like objects, introducing
nonperturbative lattice artifacts to the step scaling function. Motivated by
the observation that Wilson flow sufficiently suppresses these artifacts, we
choose Wilson flow with the Symanzik operator as our preferred analysis. We
study systematic effects by calculating the step-scaling function based on
alternative flows (Zeuthen or Symanzik), alternative operators (Wilson
plaquette, clover), and also explore the effects of the perturbative tree-level
improvement. Further we investigate the effects due to the finite value of
$L_s$. | hep-lat |
High-degree Polynomial Noise Subtraction: In lattice QCD, the calculation of physical quantities from disconnected
quark loop calculations have large variance due to the use of Monte Carlo
methods for the estimation of the trace of the inverse lattice Dirac operator.
In this work, we build upon our POLY and HFPOLY variance reduction methods by
using high-degree polynomials. Previously, the GMRES polynomials used were only
stable for low-degree polynomials, but through application of a new, stable
form of the GMRES polynomial, we have achieved higher polynomial degrees than
previously used. While the variance is not dependent on the trace correction
term within the methods, the evaluation of this term will be necessary for
forming the vacuum expectation value estimates. This requires computing the
trace of high-degree polynomials, which can be evaluated stochastically through
our new Multipolynomial Monte Carlo method. With these new high-degree noise
subtraction polynomials, we obtained a variance reduction for the scalar
operator of nearly an order of magnitude over that of no subtraction on a $24^3
\times 32$ quenched lattice at $\beta = 6.0$ and $\kappa = 0.1570 \approx
\kappa_{crit}$. Additionally, we observe that for sufficiently high polynomial
degrees, POLY and HFPOLY approach the same level of effectiveness. We also
explore the viability of using double polynomials for variance reduction as a
means of reducing the required orthogonalization and memory costs associated
with forming high-degree GMRES polynomials. | hep-lat |
Critical Behaviour in the Single Flavor Thirring Model in 2+1d: Results of a lattice field theory simulation of the single-flavor Thirring
model in 2+1 spacetime dimensions are presented. The lattice model is
formulated using domain wall fermions as a means to recover the correct U(2)
symmetries of the continuum model in the limit where wall separation
$L_s\to\infty$. Simulations on $12^3, 16^3\times L_s$, varying self-interaction
strength $g^2$ and bare mass $m$ are performed with $L_s = 8, \ldots 48$, and
the results for the bilinear condensate $\langle\bar\psi\psi\rangle$ fitted to
a model equation of state assuming a U(2)$\to$U(1)$\otimes$U(1)
symmetry-breaking phase transition at a critical $g_c^2$. First estimates for
$g^{-2}a$ and critical exponents are presented, showing small but significant
departures from mean-field values. The results confirm that a symmetry-breaking
transition does exist and therefore the critical number of flavors for the
Thirring model $N_c > 1$. Results for both condensate and associated
susceptibility are also obtained in the broken phase on $16^3\times48$,
suggesting that here the $L_s\to\infty$ extrapolation is not yet under control.
We also present results obtained with the associated 2+1$d$ truncated overlap
operator DOL demonstrating exponential localisation, a necessary condition for
the recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilson
condition as $L_s\to\infty$ is extremely slow in the broken phase. | hep-lat |
SU(3) Deconfinement in (2+1)d from Twisted Boundary Conditions and
Self-Duality: We study the pure SU(3) gauge theory in 2+1 dimensions on the lattice using
't Hooft's twisted boundary conditions to force non-vanishing center flux
through the finite volume. In this way we measure the free energy of spacelike
center vortices as an order parameter for the deconfinement transition. The
transition is of 2nd order in the universality class of the 2d 3-state Potts
model, which is self-dual. This self-duality can be observed directly in the
SU(3) gauge theory, and it can be exploited to extract critical couplings with
high precision in rather small volumes. We furthermore obtain estimates for
critical exponents and the critical temperature in units of the dimensionful
continuum coupling. Finally, we also apply our methods to the (2+1)d SU(4)
gauge theory which was previously found to have a weak 1st order transition. We
nevertheless observe at least approximate q = 4 Potts scaling at length scales
corresponding to the lattice sizes used in our simulations. | hep-lat |
Delta expansion and Wilson fermion in the Gross-Neveu model:
Compatibility with linear divergence and continuum limit from inverse-mass
expansion: We apply the $\delta$-expansion to the Gross-Neveu model in the large $N$
limit with Wilson fermion and investigate dynamical mass generation from
inverse-mass expansion. The dimensionless mass $M$ defined via the effective
potential is employed as the expansion parameter of the bare coupling constant
$\beta$ which is partially renormalized by the subtraction of linear
divergence. We show that $\delta$-expansion of the $1/M$ series of $\beta$ is
compatible with the mass renormalization. After the confirmation of the
continuum scaling of the bare coupling without fermion doubling, we attempt to
estimate dynamical mass in the continuum limit and obtain the results
converging to the exact value for values of Wilson parameter $r\in (0.8,1.0)$. | hep-lat |
(2+1)-flavor QCD Thermodynamics from the Gradient Flow: Recently, we proposed a novel method to define and calculate the
energy-momentum tensor (EMT) in lattice gauge theory on the basis of the
Yang-Mills gradient flow [1]. In this proceedings, we summarize the basic idea
and technical steps to obtain the bulk thermodynamic quantities in lattice
gauge theory using this method for the quenched and $(2+1)$-flavor QCD. The
revised results of integration measure (trace anomaly) and entropy density of
the quenched QCD with corrected coefficients are shown. Furthermore, we also
show the flow time dependence of the parts of EMT including the dynamical
fermions. This work is based on a joint-collaboration between FlowQCD and WHOT
QCD. | hep-lat |
Twist-3 partonic distributions from lattice QCD: Twist-3 partonic distributions contain important information that
characterizes nucleon's structure. In this work, we show our lattice
exploration of the twist-3 PDFs $g_T(x)$, and $h_L(x)$. We also present our
preliminary results on the twist-3 GPD $\tilde{G}_2(x)$. We use the
quasi-distribution approach to connect the lattice-extracted matrix elements,
renormalized in the RI/MOM scheme, to light-cone distributions, applying the
matching procedure that we developed in parallel. We also calculate the twist-2
counterparts of $g_T(x)$ and $h_L(x)$, i.e. $g_1(x)$, and $h_1(x)$, and test
the Wandzura-Wilczek approximation. | hep-lat |
Light meson masses and decay constants in 2+1 flavour domain wall QCD: We present results for light meson masses and psedoscalar meson decay
constants in 2+1 flavour domain wall QCD with the DBW2 and Iwasaki gauge
actions, using lattices with linear sizes in the range 1.6 to 2.2fm and $u$ and
$d$ quark masses as low as one quarter of the strange quark mass. All data were
generated on the QCDOC machines at the University of Edinburgh and Brookhaven
National Laboratory. Despite large residual masses and a limited number of sea
quark mass values with which to perform chiral extrapolations, our results
agree with experiment and scale within errors. | hep-lat |
Hopping Parameter Expansion for Heavy-Light Systems: We present a technique which permits the calculation of two-point functions
of operators containing one heavy quark and an arbitrary number of light quarks
as analytic functions of the heavy-quark mass. It is based on the standard
Jacobi linear solver used for the calculation of quark propagators. Results for
the heavy-light pseudoscalar and vector meson masses are obtained on 16^3x48
lattices at beta = 6.2 using the Wilson fermion action, and agree with
published data. The incorporation of smeared operators and $O(a)$-improved
actions presents no problems. | hep-lat |
Can Sigma Models Describe Finite Temperature Chiral Transitions?: Large-N expansions and computer simulations indicate that the universality
class of the finite temperature chiral symmetry restoration transition in the
3D Gross-Neveu model is mean field theory. This is a counterexample to the
standard 'sigma model' scenario which predicts the 2D Ising model universality
class. We trace the breakdown of the standard scenario (dimensional reduction
and universality) to the absence of canonical scalar fields in the model. We
point out that our results could be generic for theories with dynamical
symmetry breaking, such as Quantum Chromodynamics. | hep-lat |
The non-perturbative part of the plaquette in quenched QCD: We define the non-perturbative part of a quantity as the difference between
its numerical value and the perturbative series truncated by dropping the order
of minimal contribution and the higher orders. For the anharmonic oscillator,
the double-well potential and the single plaquette gauge theory, the
non-perturbative part can be parametrized as A (lambda)^B exp{-C/lambda} and
the coefficients can be calculated analytically. For lattice QCD in the
quenched approximation, the perturbative series for the average plaquette is
dominated at low order by a singularity in the complex coupling plane and the
asymptotic behavior can only be reached by using extrapolations of the existing
series. We discuss two extrapolations that provide a consistent description of
the series up to order 20-25. These extrapolations favor the idea that the
non-perturbative part scales like (a/r_0)^4 with a/r_0 defined with the force
method. We discuss the large uncertainties associated with this statement. We
propose a parametrization of ln((a/r_0)) as the two-loop universal terms plus a
constant and exponential corrections. These corrections are consistent with
a_{1-loop}^2 and play an important role when beta<6. We briefly discuss the
possibility of calculating them semi-classically at large beta. | hep-lat |
Study of SU(2) gauge theories with multiple Higgs fields in different
representations: We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime
dimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple
Higgs fields in the adjoint representation, that can be mapped to cuprate
systems in condensed matter physics which host a rich phase diagram including
high-Tc superconductivity. It has been proposed that the theory with 4 adjoint
Higgs fields can be used to explain the physics of hole-doped cuprates for a
wide range of parameters. We show exploratory results on the phase diagram of
the theory.
On the other hand, we are interested in the 4 dimensional theory with 2 sets
of fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs Doublet
Model (2HDM), a proposed extension to the Standard Model of particle physics.
The goal is to understand the particle spectrum of the theory at zero
temperature and the electroweak phase transition at finite temperature. We
present exploratory results on scale setting and the multi-parameter phase
diagram of this theory. | hep-lat |
A strategy to study the role of the charm quark in explaining the
Delta{I}=1/2 rule: We present a strategy designed to separate several possible origins of the
well-known enhancement of the Delta{I}=1/2 amplitude in non-leptonic kaon
decays. In particular, we seek to disentangle the contribution of physics at
the typical QCD scale (soft-gluon exchange) from the effects at the scale of
the charm quark mass. This is achieved by considering QCD with an unphysically
light charm quark, so that the theory possesses an approximate SU(4)_L x
SU(4)_R chiral symmetry. By computing the relevant operator matrix elements and
monitoring their values as the charm quark mass departs from the
SU(4)-symmetric situation, the role of the charm quark can be assessed. We
study the influence of the charm quark mass in Chiral Perturbation Theory.
First results from lattice simulations in the SU(4)-symmetric limit are also
discussed. | hep-lat |
$ Δ$ baryon spectroscopy in lattice QCD: A variational analysis is performed within the framework of lattice QCD to
extract the masses of the spin-3/2 positive parity $ \Delta^+ $ baryons,
including radial excitations. $2+1$ flavour dynamical gauge-field
configurations provided by the PACS-CS collaboration via the ILDG are
considered. To improve our interpolator basis, we perform an iterative process
of source and sink smearing and solve a generalised eigenvalue problem using
the resulting fermion operators. We obtain a clear signal for the ground and
first excited states at a light quark mass corresponding to $ m_\pi = 413 $
MeV. Furthermore, we show that one can use the eigenvectors obtained in this
method to investigate the nature of these states, allowing us to classify our
results as $ 1s $ and $ 2s $ states for the ground and first excited states
respectively. Finally, we briefly highlight the method of Hamiltonian Effective
Field Theory which can be used to make comparison with quark model
expectations. | hep-lat |
Review on Composite Higgs Models: Composite Higgs Models explore the possibility that the Higgs boson is an
excitation of a new strongly interacting sector giving rise to electro-weak
symmetry breaking. After describing how this new sector can be embedded into
the Standard Model of elementary particle physics meeting experimental
constraints, I will review efforts by the community to explore the physics of
the new strong interaction using methods of lattice field theory. Challenges in
understanding the numerical results are discussed and an outlook is given on
possible future directions allowing to confirm or reject the composite Higgs
hypothesis. | hep-lat |
Neural multigrid for gauge theories and other disordered systems: We present evidence that multigrid works for wave equations in disordered
systems, e.g. in the presence of gauge fields, no matter how strong the
disorder, but one needs to introduce a "neural computations" point of view into
large scale simulations: First, the system must learn how to do the simulations
efficiently, then do the simulation (fast).
The method can also be used to provide smooth interpolation kernels which are
needed in multigrid Monte Carlo updates. | hep-lat |
New lattice approaches to the $ΔI=1/2$ rule: Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first
principles, but numerical calculations to date have been plagued by a variety
of problems. After a brief review of these problems, we present several new
methods for calculating $K\to\pi\pi$ amplitudes. These are designed for Wilson
fermions, though they can be used also with staggered fermions. They all
involve a non-perturbative determination of matching coefficients. We show how
problems of operator mixing can be greatly reduced by using point-split
hadronic currents, and how CP violating parts of the $K\to\pi\pi$ amplitudes
can be calculated by introducing a fake top quark. Many of the methods can also
be applied to the calculation of two body non-leptonic B-meson decays. | hep-lat |
Quark-gluon vertex with an off-shell O(a)-improved chiral fermion action: We perform a study the quark-gluon vertex function with a quenched Wilson
gauge action and a variety of fermion actions. These include the domain wall
fermion action (with exponentially accurate chiral symmetry) and the Wilson
clover action both with the non-perturbatively improved clover coefficient as
well as with a number of different values for this coefficient. We find that
the domain wall vertex function behaves very well in the large momentum
transfer region. The off-shell vertex function for the on-shell improved clover
class of actions does not behave as well as the domain wall case and,
surprisingly, shows only a weak dependence on the clover coefficient $c_{SW}$
for all components of its Dirac decomposition and across all momenta. Including
off-shell improvement rotations for the clover fields can make this action
yield results consistent with those from the domain wall approach, as well as
helping to determine the off-shell improved coefficient $c_q^\prime$. | hep-lat |
Frontiers of finite temperature lattice QCD: I review a selection of recent finite temperature lattice results of the past
years. First I discuss the extension of the equation of state towards high
temperatures and fi- nite densities, then I show recent results on the QCD
topological susceptibility at high temperatures and highlight its relevance for
dark matter search. | hep-lat |
Recent results in high temperature lattice gauge theories: We review some analytic results on the deconfinement transition in pure
lattice gauge theories. In particular we discuss the relationship between the
deconfinement transition in the $(d+1)$-dimensional $SU(2)$ model and the
magnetization transition in the $d$-dimensional Ising model. This analysis
leads to a precise estimate of the deconfinement temperature which agrees well
with that obtained with a Montecarlo simulation in the case in which the
lattice has only one link in the compactified time direction. | hep-lat |
Non-perturbative parton mass for the gluon: A gauge invariant, non-local observable is constructed in pure gauge theory,
which is identical to the gluon propagator in a particular gauge, permitting to
define a non-perturbative parton mass for the gluon. This mass can be shown to
be related to the 1P-1S mass splitting of heavy quarkonia. Preliminary
numerical results for 3d SU(2) yield m_A=0.37(6)g^2, while from the \bar{b}b
spectrum one infers m_A\approx 420 MeV for QCD. | hep-lat |
Subtleties and Fancies in Gauge Theory Non Trivial Vacuum: The one loop effective potential for a non-Abelian gauge configuration is
analyzed using the background field method. The Savvidy result and the
non-Abelian ansatz, the other alternative possible background that generates a
constant color magnetic field configuration, are compared. This second
possibility is very interesting because it avoids the possible coordinate
singularity, ${\rm Det}B_i^a=0$, and it is easy to implement in lattice
simulations. We emphasize the interesting dependence of the potential by the
gauge fixing parameter $\alpha$, when the loop expansion is performed around a
non trivial background configuration. Finally, we point out some crucial
differences in analyzing the vacuum structure between non-Abelian gauge
theories and the cases of scalar and Abelian gauge theories. | hep-lat |
The Weak-Coupling Limit of 3D Simplicial Quantum Gravity: We investigate the weak-coupling limit, kappa going to infinity, of 3D
simplicial gravity using Monte Carlo simulations and a Strong Coupling
Expansion. With a suitable modification of the measure we observe a transition
from a branched polymer to a crinkled phase. However, the intrinsic geometry of
the latter appears similar to that of non-generic branched polymer, probable
excluding the existence of a sensible continuum limit in this phase. | hep-lat |
The three-dimensional, three-state Potts Model in an External Field: We analyze the critical behaviour of the three-dimensional, three-state Potts
model in the presence of an external ordering field. From a finite size scaling
analysis on lattices of size up to 70**3 we determine the critical endpoint of
the line of first order phase transitions as (b_c, h_c) =(0.54938(2),
0.000775(10)). We determine the relevant temperature like and symmetry breaking
directions at this second order critical point and explicitly verify that it is
in the universality class of the three-dimensional Ising model. | hep-lat |
Color Structure of Gluon Field Magnetic Mass: The color structure of the gluon field magnetic mass is investigated in the
lattice SU(2) gluodynamics. To realize that, the interaction between a
monopole-antimonopole string and external neutral Abelian chromomagnetic field
flux is considered. The string is introduced in the way proposed by Srednicki
and Susskind. The neutral Abelian field flux is introduced through the twisted
boundary conditions. Monte Carlo simulations are performed on 4D lattices at
finite temperature. It is shown that the presence of the Abelian field flux
weakens the screening of the string field. That means decreasing the gluon
magnetic mass for this environment. The contribution of the neutral Abelian
field has the form of "enhancing" factor in the fitting functions. This
behavior independently confirms the long-range nature of the neutral Abelian
field reported already in the literature. The comparison with analytic
calculations is given. | hep-lat |
Polyakov loop fluctuations in SU(3) lattice gauge theory and an
effective gluon potential: We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge
theory using the Symanzik improved gauge action on different-sized lattices.
The longitudinal and transverse fluctu- ations of the Polyakov loop, as well
as, that of its absolute value are considered. We analyze their properties in
relation to the confinement-deconfinement phase transition. We also present
results based on simulations of (2+1)-flavor QCD on 32^3 x 8 lattice using
Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration. The
influences of fermions on the Polyakov loop fluctuations are discussed. We
show, that ratios of different susceptibilities of the Polyakov loop are
sensitive probes for critical behavior. We formulate an effective model for the
Polyakov loop potential and constrain its parameters from existing quenched
lattice data including fluctuations. We emphasize the role of fluctuations to
fully explore the thermodynamics of pure gauge theory within an effective
approach. | hep-lat |
Color screening potential at finite density in two-flavor lattice QCD
with Wilson fermions: We investigate chemical-potential (\mu) dependence of static-quark free
energies in both the real and imaginary \mu regions, performing lattice QCD
simulations at imaginary \mu and extrapolating the results to the real \mu
region with analytic continuation. Lattice QCD calculations are done on a
16^{3}\times 4 lattice with the clover-improved two-flavor Wilson fermion
action and the renormalization-group improved Iwasaki gauge action.
Static-quark potential is evaluated from the Polyakov-loop correlation
functions in the deconfinement phase. As the analytic continuation, the
potential calculated at imaginary \mu=i\mu_{\rm I} is expanded into a
Taylor-expansion series of i\mu_{\rm I}/T up to 4th order and the pure
imaginary variable i\mu_{\rm I}/T is replaced by the real one \mu_{\rm R}/T. At
real \mu, the 4th-order term weakens \mu dependence of the potential sizably.
At long distance, all of the color singlet and non-singlet potentials tend to
twice the single-quark free energy, indicating that the interactions between
heavy quarks are fully color-screened for finite \mu. For both real and
imaginary \mu, the color-singlet q{\bar q} and the color-antitriplet qq
interaction are attractive, whereas the color-octet q{\bar q} and the
color-sextet qq interaction are repulsive. The attractive interactions have
stronger \mu/T dependence than the repulsive interactions. The color-Debye
screening mass is extracted from the color-singlet potential at imaginary \mu,
and the mass is extrapolated to real \mu by analytic continuation. The
screening mass thus obtained has stronger \mu dependence than the prediction of
the leading-order thermal perturbation theory at both real and imaginary \mu. | hep-lat |
The chiral phase transition for QCD with sextet quarks: QCD with 2 massless colour-sextet quarks is studied as a model of Walking
Technicolor. We simulate lattice QCD with 2 light color-sextet staggered quarks
at finite temperature, and use the dependence of the coupling at the chiral
transition on the temporal extent, $N_t$, of the lattice in lattice units to
study the running of the bare lattice coupling with lattice spacing. Our goal
is to determine whether this theory is QCD-like and `walks', or if it is
conformal. If it is QCD-like, the coupling at the chiral transition should tend
to zero as $N_t \rightarrow \infty$ in a manner controlled by asymptotic
freedom, i.e. by the perturbative $\beta$-function. On the other hand, if this
theory is conformal, this coupling will approach a non-zero limit in the $N_t
\rightarrow \infty$ limit. We are extending our simulations on an $N_t=8$
lattice to determine the position of the chiral transition with greater
accuracy, and are performing simulations on an $N_t=12$ lattice. | hep-lat |
$B_s \to K \ell ν$ form factors from lattice QCD: We report the first lattice QCD calculation of the form factors for the
standard model tree-level decay $B_s\to K \ell\nu$. In combination with future
measurement, this calculation will provide an alternative exclusive
semileptonic determination of $|V_{ub}|$. We compare our results with previous
model calculations, make predictions for differential decay rates and branching
fractions, and predict the ratio of differential branching fractions between
$B_s\to K\tau\nu$ and $B_s\to K\mu\nu$. We also present standard model
predictions for differential decay rate forward-backward asymmetries,
polarization fractions, and calculate potentially useful ratios of $B_s\to K$
form factors with those of the fictitious $B_s\to\eta_s$ decay. Our lattice
simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC
Collaboration's $2+1$ asqtad gauge configurations, including two lattice
spacings and a range of light quark masses. | hep-lat |
Low-energy Scattering and Effective Interactions of Two Baryons at
$m_π\sim 450$ MeV from Lattice Quantum Chromodynamics: The interactions between two octet baryons are studied at low energies using
lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a
pion mass of $m_{\pi}\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The
two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and
include the spin-singlet and triplet $NN$, $\Sigma N$ ($I=3/2$), and $\Xi\Xi$
states, the spin-singlet $\Sigma\Sigma$ ($I=2$) and $\Xi\Sigma$ ($I=3/2$)
states, and the spin-triplet $\Xi N$ ($I=0$) state. The $s$-wave scattering
phase shifts, low-energy scattering parameters, and binding energies when
applicable, are extracted using L\"uscher's formalism. While the results are
consistent with most of the systems being bound at this pion mass, the
interactions in the spin-triplet $\Sigma N$ and $\Xi\Xi$ channels are found to
be repulsive and do not support bound states. Using results from previous
studies at a larger pion mass, an extrapolation of the binding energies to the
physical point is performed and is compared with experimental values and
phenomenological predictions. The low-energy coefficients in pionless EFT
relevant for two-baryon interactions, including those responsible for $SU(3)$
flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to
hold approximately at the chosen values of the quark masses, as well as the
$SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an
accidental $SU(16)$ symmetry found previously at a larger pion mass is further
observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is
used to make predictions for two-baryon systems for which the low-energy
scattering parameters could not be determined with LQCD directly in this study,
and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric
interactions, demonstrating the predictive power of two-baryon EFTs matched to
LQCD. | hep-lat |
Heavy quark free energies for three quark systems at finite temperature: We study the free energy of static three quark systems in singlet, octet,
decuplet and average color channels in the quenched approximation and in
2-flavor QCD at finite temperature. We show that in the high temperature phase
singlet and decuplet free energies of three quark systems are well described by
the sum of the free energies of three diquark systems plus self energy
contributions of the three quarks. In the confining low temperature phase we
find evidence for a Y-shaped flux tube in SU(3) pure gauge theory, which is
less evident in 2-flavor QCD due to the onset of string breaking. We also
compare the short distance behavior of octet and decuplet free energies to the
free energies of single static quarks in the corresponding color
representations. | hep-lat |
Axial Charges of Octet Baryons in Two-flavor Lattice QCD: We evaluate the strangeness-conserving $N N$, $\Sigma\Sigma$, $\Xi\Xi$,
$\Lambda\Sigma$ and the strangeness-changing $\Lambda N$, $\Sigma N$,
$\Lambda\Xi$, $\Sigma\Xi$ axial charges in lattice QCD with two flavors of
dynamical quarks and extend our previous work on
pseudoscalar-meson-octet-baryon coupling constants so as to include
$\pi\Xi\Xi$, $K\Lambda\Xi$ and $K\Sigma\Xi$ coupling constants. We find that
the axial charges have rather weak quark-mass dependence and the breaking in
SU(3)-flavor symmetry is small at each quark-mass point we consider. | hep-lat |
f_B and the Heavy-light Spectrum from NRQCD: The present status of lattice calculations of the B spectrum and f_B, using
NRQCD for the b quark, is discussed. | hep-lat |
CL2QCD - Lattice QCD based on OpenCL: We present the Lattice QCD application CL2QCD, which is based on OpenCL and
can be utilized to run on Graphic Processing Units as well as on common CPUs.
We focus on implementation details as well as performance results of selected
features. CL2QCD has been successfully applied in LQCD studies at finite
temperature and density and is available at
http://code.compeng.uni-frankfurt.de/projects/clhmc . | hep-lat |
The (LATTICE) QCD Potential and Running Coupling: How to Accurately
Interpolate between Multi-Loop QCD and the String Picture: We present a simple parameterization of a running coupling constant, defined
via the static potential, that interpolates between 2-loop QCD in the UV and
the string prediction in the IR. Besides the usual $\Lam$-parameter and the
string tension, the coupling depends on one dimensionless parameter,
determining how fast the crossover from UV to IR behavior occurs (in principle
we know how to take into account any number of loops by adding more
parameters). Using a new Ansatz for the LATTICE potential in terms of the
continuum coupling, we can fit quenched and unquenched Monte Carlo results for
the potential down to ONE lattice spacing, and at the same time extract the
running coupling to high precision. We compare our Ansatz with 1-loop results
for the lattice potential, and use the coupling from our fits to quantitatively
check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie
estimate of the coupling extracted from the plaquette, and determine Sommer's
scale $r_0$ much more accurately than previously possible. For pure SU(3) we
find that the coupling scales on the percent level for $\beta\geq 6$. | hep-lat |
The QCD Equation of State: Results for the equation of state in 2+1 flavor QCD at zero net baryon
density using the Highly Improved Staggered Quark (HISQ) action by the HotQCD
collaboration are presented. The strange quark mass was tuned to its physical
value and the light (up/down) quark masses fixed to $m_l = 0.05m_s$
corresponding to a pion mass of 160 MeV in the continuum limit. Lattices with
temporal extent $N_t=6$, 8, 10 and 12 were used. Since the cutoff effects for
$N_t>6$ were observed to be small, reliable continuum extrapolations of the
lattice data for the phenomenologically interesting temperatures range $130
\mathord{\rm MeV} < T < 400 \mathord{\rm MeV}$ could be performed. We discuss
statistical and systematic errors and compare our results with other published
works. | hep-lat |
Chiral gauge theories on the lattice without gauge fixing?: We discuss two proposals for a non-perturbative formulation of chiral gauge
theories on the lattice. In both cases gauge symmetry is broken by the
regularization. We aim at a dynamical restoration of symmetry. If the gauge
symmetry breaking is not too severe this procedure could lead in the continuum
limit to the desired chiral gauge theory. | hep-lat |
Higgs boson mass bounds in the presence of a very heavy fourth quark
generation: We study the effect of a potential fourth quark generation on the upper and
lower Higgs boson mass bounds. This investigation is based on the numerical
evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the
same Higgs-fermion coupling structure as in the Higgs sector of the electroweak
Standard Model. In particular, the considered model obeys a Ginsparg-Wilson
version of the underlying ${SU}(2)_L\times {U}(1)_Y$ symmetry, being a global
symmetry here due to the neglection of gauge fields in this model. We present
our results on the modification of the upper and lower Higgs boson mass bounds
induced by the presence of a hypothetical very heavy fourth quark doublet.
Finally, we compare these findings to the standard scenario of three fermion
generations. | hep-lat |
Pion Polarizabilities and Volume Effects in Lattice QCD: We use chiral perturbation theory to study the extraction of pion
electromagnetic polarizabilities from lattice QCD. Chiral extrapolation
formulae are derived for partially quenched QCD, and quenched QCD simulations.
On a torus, volume dependence of electromagnetic observables is complicated by
SO(4) breaking, as well as photon zero-mode interactions. We determine finite
volume corrections to the Compton scattering tensor of pions. We argue,
however, that such results cannot be used to ascertain volume corrections to
polarizabilities determined in lattice QCD with background field methods.
Connection is lacking because momentum expansions are not permitted in finite
volume. Our argument also applies to form factors. Volume effects for
electromagnetic moments cannot be deduced from finite volume form factors. | hep-lat |
Spectral functions at small energies and the electrical conductivity in
hot, quenched lattice QCD: In lattice QCD, the Maximum Entropy Method can be used to reconstruct
spectral functions from euclidean correlators obtained in numerical
simulations. We show that at finite temperature the most commonly used
algorithm, employing Bryan's method, is inherently unstable at small energies
and give a modification that avoids this. We demonstrate this approach using
the vector current-current correlator obtained in quenched QCD at finite
temperature. Our first results indicate a small electrical conductivity above
the deconfinement transition. | hep-lat |
Calculation of $ρ$ meson decay width from the PACS-CS configurations: We present preliminary results on the $\rho$ meson decay width from $N_f=2+1$
full QCD configurations generated by PACS-CS Collaboration. The decay width is
estimated from the $P$-wave scattering phase shift for the isospin $I=1$
two-pion system. The finite size formula presented by L\"uscher in the center
of mass frame and its extension to non-zero total momentum frame by Rummukainen
and Gottlieb are employed for the calculations of the phase shift. Our
calculations are carried out at $m_\pi=410\ {\rm MeV}$ ($m_\pi/m_\rho=0.46$)
and $a=0.091\ {\rm fm}$ on a $32^3\times 64$ ($La=2.9 {\rm fm}$) lattice. | hep-lat |
Testing universality and the fractional power prescription for the
staggered fermion determinant: In [Phys.Rev.Lett.92:162002 (2004), hep-lat/0312025] expressions for the
continuous Euclidean time limits of various lattice fermion determinants were
derived and compared in order to test universality expectations in Lattice QCD.
Here we review that work with emphasis on its relevance for assessing the
fractional power prescription for the determinant in dynamical staggered
fermion simulations. Some new supplementary material is presented; in
particular the status of the "universality anomaly" is clarified: it is shown
to be gauge field-independent and therefore physically inconsequential. | hep-lat |
Fast algorithms for simulating chiral fermions in U(1)lattice gauge
theory: In order to develop fast inversion algorithms we have used overlap solvers in
two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional
space-times dimensions has always been a testing ground for algorithms. By the
other side, motivated by our previews work that the two-grid algorithm converge
faster than the standard iterative methods for overlap inversion but not for
all quark masses, we thought to test this idea in less dimensions such as U(1)
gauge theory. Our main objective of this paper it is to implement and develop
the idea of a two level algorithm in a new algorithm coded in QCDLAB. This
implementation is presented in the preconditioned GMRESR algorithm, as our new
contribution in QCDLAB package. The preconditioned part of our algorithm,
different from the one of [18], is the approximation of the overlap operator
with the truncated overlap operator with finite N3 dimension. We have tested it
for 100 statistically independent configurations on 32 x 32 lattice background
U(1) field at coupling constant \b{eta}=1 and for different bare quark masses
mq = [0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1]. We have compared the
convergence history of the preconditioned GMRESR residual norm with another
overlap inverter of QCDLAB as an optimal one, such as SHUMR. We have shown that
our algorithm converges faster than SHUMR for different quark masses. Also, we
have demonstrated that it saves more time for light quarks compared to SHUMR
algorithm. Our algorithm is approximately independent from the quark mass. This
is a key result in simulations with chiral fermions in lattice theories. By the
other side, if we compare the results of [18] for quark mass 0.1 in SU(3),
results that our chosen preconditioned saves a factor of 2 but in U(1). Our
next step is to test this algorithm in SU(3) and to adopt it in parallel. | hep-lat |
Formulation of chiral gauge theories: We present a formulation of chiral gauge theories, which admits more general
spectra of Dirac operators and reveals considerably more possibilities for the
structure of the chiral projections. Our two forms of correlation functions
both also apply in the presence of zero modes and for any value of the index.
The decomposition of the total set of pairs of bases into equivalence classes
is carefully analyzed. Transformation properties are derived. | hep-lat |
Center-symmetric dimensional reduction of hot Yang-Mills theory: It is expected that incorporating the center symmetry in the conventional
dimensionally reduced effective theory for high-temperature SU(N) Yang-Mills
theory, EQCD, will considerably extend its applicability towards the
deconfinement transition. The construction of such a center-symmetric effective
theory for the case of two colors is reviewed and lattice simulation results
are presented. The simulations demonstrate that unlike EQCD, the new
center-symmetric theory undergoes a second order confining phase transition in
complete analogy with the full theory. | hep-lat |
Radially Excited States of 1P Charmonia and X(3872): The excited states of charmonia are numerically investigated in quenched
lattice QCD with improved gauge and Wilson fermion actions formulated on
anisotropic lattices. Through a constrained curve fitting algorithm, the masses
of the first excited states in $0^{++}$, $1^{++}$, and $1^{+-}$ channels are
determined to be 3.825(88), 3.853(57), and 3.858(70) GeV, respectively.
Furthormore, a node structure is also observed in the Bethe-Salpeter amplitude
of the $1^{++}$ first excited state. These observations indicate that X(3872)
could be the first radial excitation of $\chi_{c1}$. | hep-lat |
Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for
Meson Masses and Decay Constants: We discuss Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT) and
possible fitting strategies to Lattice QCD data at next-to-next-to-leading
order (NNLO) in the mesonic sector. We also present a complete calculation of
the masses of the charged pseudoscalar mesons, in the supersymmetric
formulation of PQ$\chi$PT. Explicit analytical results are given for up to
three nondegenerate sea quark flavors, along with the previously unpublished
expression for the pseudoscalar meson decay constant for three nondegenerate
sea quark flavors. The numerical analysis in this paper demonstrates that the
corrections at NNLO are sizable, as expected from earlier work. | hep-lat |
Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions: Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice
in arbitrary even dimensions is investigated by applying the method of exterior
differential calculus. The topological invariance, gauge invariance and
locality of the axial anomaly determine the explicit form of the topological
part. The anomaly is obtained up to a multiplicative constant for finite
lattice spacing and can be interpreted as the Chern character of the abelian
lattice gauge theory. | hep-lat |
The finite temperature transition for 3-flavour lattice QCD at finite
isospin density: We simulate 3-flavour lattice QCD with a small chemical potential $\mu_I$ for
isospin, at temperatures close to the finite temperature transition. Using
quark masses just above the critical mass for zero chemical potential, we
determine the position of the transition from hadronic matter to a quark-gluon
plasma as a function of $\mu_I$. We see evidence for a critical endpoint where
the transition changes from a crossover to a first-order transition as $\mu_I$
is increased. We argue that QCD at finite $\mu_I$ and QCD at finite
quark-numberchemical potential $\mu$ should behave similarly in this region. | hep-lat |
Physics From Breit-Frame Regularization Of a Lattice Hamiltonian: We suggest a Hamiltonian formulation on a momentum lattice using a physically
motivated regularization using the Breit-frame which links the maximal parton
number to the lattice size. This scheme restricts parton momenta to positive
values in each spatial direction. This leads to a drastic reduction of degrees
of freedom compared to a regularization in the rest frame (center at zero
momentum). We discuss the computation of physical observables like (i) mass
spectrum in the critical region, (ii) structure and distribution functions,
(iii) $S$-matrix, (iv) finite temperature and finite density thermodynamics in
the Breit-frame regularization. For the scalar $\phi^{4}_{3+1}$ theory we
present numerical results for the mass spectrum in the critical region. We
observe scaling behavior for the mass of the ground state and for some higher
lying states. We compare our results with renormalization group results by
L\"uscher and Weisz. Using the Breit-frame, we calculate for $QCD$ the relation
between the $W^{\mu \nu}$ tensor, structure functions (polarized and
unpolarized) and quark distribution functions. We use the improved parton-model
with a scale dependence and take into account a non-zero parton mass. In the
Bjorken limes we find the standard relations between $F_{1}$, $F_{2}$, $g_{1}$
and the quark distribution functions. We discuss the r\^ole of helicity. We
present numerical results for parton distribution functions in the scalar
model. For the $\phi^{4}$-model we find no bound state with internal parton
structure. For the $\phi^{3}$-model we find a distribution function with parton
structure similar to Altarelli-Parisi behavior of $QCD$. | hep-lat |
Stabilizing the electroweak vacuum by higher dimensional operators in a
Higgs-Yukawa model: The Higgs boson discovery at the LHC with a mass of approximately 126 GeV
suggests, that the electroweak vacuum of the standard model may be metastable
at very high energies. However, any new physics beyond the standard model can
change this picture. We want to address this important question within a
lattice Higgs-Yukawa model as the limit of the standard model (SM). In this
framework we will probe the effect of a higher dimensional operator for which
we take a $(\phi^{\dagger}\phi)^3$-term. Such a term could easily originate as
a remnant of physics beyond the SM at very large scales.
As a first step we investigate the phase diagram of the model including such
a $(\phi^{\dagger}\phi)^3$ operator. Exploratory results suggest the existence
of regions in parameter space where first order transitions turn to second
order ones, indicating the existence of a tri-critical line. We will explore
the phase structure and the consequences for the stability of the SM, both
analytically by investigating the constraint effective potential in lattice
perturbation theory, and by studying the system non-perturbatively using
lattice simulations. | hep-lat |
The chiral transition in two-flavor QCD: QCD with N_f=2 is a specially interesting system to investigate the chiral
transition. The order of the transition has still not been established. We
report the results of an in-depth numerical investigation performed with
staggered fermions on lattices with L_t=4 and L_s=12,16,20,24,32 and quark
masses am_q ranging from 0.01335 to 0.307036. Using finite-size techniques we
compare the scaling behavior of a number of thermodynamical susceptibilities
with the expectations of O(4) and O(2) universality classes. Clear disagreement
is observed. Indications of a first order transition are found. | hep-lat |
Nucleon form factors and structure functions with N_f=2+1 dynamical
domain wall fermions: We report isovector form factors and low moments of structure functions of
nucleon in numerical lattice quantum chromodynamics (QCD) from the on-going
calculations by the RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with
(2+1) dynamical flavors of domain-wall fermion (DWF) quarks. We calculate the
matrix elements with four light quark masses, corresponding to pion mass values
of m_\pi = 330-670 MeV, while the dynamical strange mass is fixed at a value
close to physical, on (2.7 fm)^3 spatial volume. We found that our axial
charge, g_A, at the lightest mass exhibits a large deviation from the heavier
mass results. This deviation seems to be a finite-size effect as the g_A value
scales with a single parameter, m_\pi L, the product of pion mass and linear
spatial lattice size. The scaling is also seen in earlier 2-flavor dynamical
DWF and Wilson quark calculations. Without this lightest point, the three
heavier mass results show only very mild mass dependence and linearly
extrapolate to g_A=1.16(6). We determined the four form factors, the vector
(Dirac), induced tensor (Pauli), axial vector and induced pseudoscalar, at a
few finite momentum transfer values as well. At the physical pion mass the
form-factors root mean square radii determined from the momentum-transfer
dependence %of the form factors are 20-30% smaller than the corresonding
experiments. The ratio of the isovector quark momentum to helicity fractions, <
x>_{u-d}/< x>_{\Delta u - \Delta d} is in agreement with experiment without
much mass dependence including the lightest point. We obtain an estimate,
0.81(2), by a constant fit. Although the individual momentum and helicity
fractions are yet to be renormalized, they show encouraging trend toward
experiment. | hep-lat |
Form factor for Dalitz decays from $J/ψ$ to light pseudoscalars: We calculate the form factor $M(q^2)$ for the Dalitz decay $J/\psi\to
\gamma^*(q^2)\eta_{(N_f=1)}$ with $\eta_{(N_f)}$ being the SU($N_f$) flavor
singlet pseudoscalar meson. The difference among the partial widths
$\Gamma(J/\psi\to \gamma \eta_{(N_f)})$ at different $N_f$ can be attributed in
part to the $\mathbf{U}_A(1)$ anomaly that induces a $N_f$ scaling. $M(q^2)$'s
in $N_f=1,2$ are both well described by the single pole model
$M(q^2)=M(0)/(1-q^2/\Lambda^2)$. Combined with the known experimental results
of the Dalitz decays $J/\psi\to Pe^+e^-$, the pseudoscalar mass $m_P$
dependence of the pole parameter $\Lambda$ is approximated by
$\Lambda(m_P^2)=\Lambda_1(1-m_P^2/\Lambda_2^2)$ with
$\Lambda_1=2.64(4)~\mathrm{GeV}$ and $\Lambda_2=2.97(33)~\mathrm{GeV}$. These
results provide inputs for future theoretical and experimental studies on the
Dalitz decays $J/\psi\to Pe^+e^-$. | hep-lat |
Noise, sign problems, and statistics: We show how sign problems in simulations of many-body systems can manifest
themselves in the form of heavy-tailed correlator distributions, similar to
what is seen in electron propagation through disordered media. We propose an
alternative statistical approach for extracting ground state energies in such
systems, illustrating the method with a toy model and with lattice data for
unitary fermions. | hep-lat |
The critical end point in QCD: In this talk I present the logic behind, and examine the reliability of,
estimates of the critical end point (CEP) of QCD using the Taylor expansion
method. | hep-lat |
The principle of indirect elimination: The principle of indirect elimination states that an algorithm for solving
discretized differential equations can be used to identify its own
bad-converging modes. When the number of bad-converging modes of the algorithm
is not too large, the modes thus identified can be used to strongly improve the
convergence. The method presented here is applicable to any standard algorithm
like Conjugate Gradient, relaxation or multigrid. An example from theoretical
physics, the Dirac equation in the presence of almost-zero modes arising from
instantons, is studied. Using the principle, bad-converging modes are removed
efficiently. Applied locally, the principle is one of the main ingredients of
the Iteratively Smooting Unigrid algorithm. | hep-lat |
Excited mesons from $N_f=2$ dynamical Clover Wilson lattices: We study mesons on the lattice with a special focus on excited states. For
that purpose we construct several quark sources with different spatial
smearings, including p-waves. These quark sources are then combined with the
appropiate Dirac structures to form meson interpolators of definite spin. We
use these operators to construct a cross correlation matrix from which we
extract ground and excited meson states using the variational method. For the
calculations we use gauge configurations with $N_f=2$ dynamical Clover Wilson
fermions provided by the CP-PACS collaboration. We show preliminary results for
pseudoscalar, scalar, vector and pseudovector mesons. | hep-lat |
$B_K$ with improved staggered fermions: analysis using SU(2) staggered
chiral perturbation theory: We report updated results for $B_K$ calculated using HYP-smeared staggered
fermions on the MILC asqtad 2+1 flavor lattices. We use four different lattice
spacings ($a \approx$ 0.12, 0.09, 0.06 and 0.045 fm) to control the continuum
extrapolation. We use SU(2) staggered chiral perturbation theory to do the data
analysis. We find that $B_K(\text{NDR}, \mu=2 \text{GeV}) = 0.526 \pm 0.007 \pm
0.024$ and $\hat{B}_K = B_K(\text{RGI}) = 0.720 \pm 0.010 \pm 0.033$. Here the
first error is statistical and the second systematic. The dominant source of
error is that due to our use of a truncated (one-loop) matching factor. | hep-lat |
Critical Exponents of the 3D Ising Universality Class From Finite Size
Scaling With Standard and Improved Actions: We propose a method to obtain an improved Hamiltonian (action) for the Ising
universality class in three dimensions. The improved Hamiltonian has suppressed
leading corrections to scaling. It is obtained by tuning models with two
coupling constants. We studied three different models: the +1,-1 Ising model
with nearest neighbour and body diagonal interaction, the spin-1 model with
states 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on the
lattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling
properties of the suitably tuned spin-1 model are compared in detail with those
of the standard Ising model. Great care is taken to estimate the systematic
errors from residual corrections to scaling. Our best estimates for the
critical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given error
estimates take into account the statistical and systematic uncertainties. | hep-lat |
The QCD phase diagram at nonzero quark density: We determine the phase diagram of QCD on the \mu-T plane for small to
moderate chemical potentials. Two transition lines are defined with two
quantities, the chiral condensate and the strange quark number susceptibility.
The calculations are carried out on N_t =6,8 and 10 lattices generated with a
Symanzik improved gauge and stout-link improved 2+1 flavor staggered fermion
action using physical quark masses. After carrying out the continuum
extrapolation we find that both quantities result in a similar curvature of the
transition line. Furthermore, our results indicate that in leading order the
width of the transition region remains essentially the same as the chemical
potential is increased. | hep-lat |
The $ρ$-resonance with physical pion mass from $N_f=2$ lattice QCD: We present the first-ever lattice computation of pi pi-scattering in the I=1
channel with Nf=2 dynamical quark flavours obtained including an ensemble with
physical value of the pion mass. Employing a global fit to data at three values
of the pion mass, we determine the universal parameters of the rho-resonance.
We carefully investigate systematic uncertainties by determining energy
eigenvalues using different methods and by comparing inverse amplitude method
and Breit-Wigner type parametrizations. Overall, we find mass 786(20) MeV and
width 180(6) MeV, including statistical and systematic uncertainties. In stark
disagreement with the previous Nf=2 extrapolations from higher than physical
pion mass results, our mass value is in good agreement with experiment, while
the width is slightly too high. | hep-lat |
The Charmonium Potential at Non-Zero Temperature: The potential between charm and anti-charm quarks is calculated
non-perturbatively using physical, rather than static quarks at temperatures on
both sides of the deconfinement transition $T_{\rm C}$, using a lattice
simulation with 2+1 dynamical quark flavours. We used the HAL QCD
time-dependent method, originally developed for inter-nucleon potentials. Our
lattices are anisotropic, with temporal lattice spacing less than the spatial
one which enhances the information content of our correlators at each
temperature. Local-extended charmonium correlators were calculated efficiently
by contracting propagators in momentum rather than coordinate space. We find no
significant variation in the central potential for temperatures in the confined
phase. As the temperature increases into the deconfinement phase, the potential
flattens, consistent with the expected weakening interaction. We fit the
potential to both the (a) Cornell and (b) Debye-screened potential forms, with
the latter better reproducing the data. The zero temperature string tension
obtained from (a) agrees with results obtained elsewhere, and it decreases with
temperature, but at a slower rate than from the static quark approximation. The
Debye mass from (b) is close to zero for small temperatures, but starts to
increase rapidly around $T_{\rm C}$. The spin-dependent potential is found to
have a repulsive core and a distinct temperature dependence above $T_{\rm C}$
at distances $\sim 1$ fm. | hep-lat |
A Study of the $N=2$ Kazakov-Migdal Model: We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In
contrast to our earlier work on the subject we have chosen here {\it not} to
integrate out the gauge fields but to keep them in the Monte Carlo simulation.
This allows us to measure observables associated with the gauge fields and
thereby address the problem of the local $Z_2$ symmetry present in the model.
We confirm our previous result that the model has a line of first order phase
transitions terminating in a critical point. The adjoint plaquette has a clear
discontinuity across the phase transition, whereas the plaquette in the
fundamental representation is always zero in accordance with Elitzur's theorem.
The density of small $Z_2$ monopoles shows very little variation and is always
large. We also find that the model has extra local U(1) symmetries which do not
exist in the case of the standard adjoint theory. As a result, we are able to
show that two of the angles parameterizing the gauge field completely decouple
from the theory and the continuum limit defined around the critical point can
therefore not be `QCD'. | hep-lat |
Lattice Artefacts In The Non-Abelian Debye Screening Mass In One Loop
Order: We compute the electric screening mass in lattice QCD with Wilson fermions at
finite temperature and chemical potential to one-loop order, and show that
lattice artefacts arising from a finite lattice spacing result in an
enhancement of the screening mass as compared to the continuum. We discuss the
magnitude of this enhancement as a function of the temperature and chemical
potential for lattices with different number of lattice sites in the temporal
direction that can be implemented in lattice simulations. Most of the
enhancement is found to be due to the fermion loop contribution. | hep-lat |
$O(a^2)$-improved actions for heavy quarks and scaling studies on
quenched lattices: We investigate a new class of improved relativistic fermion action on the
lattice with a criterion to give excellent energy-momentum dispersion relation
as well as to be consistent with tree-level $O\left(a^{2}\right)$-improvement.
Main application in mind is that for heavy quark for which $ma\simeq O(0.5)$.
We present tree-level results and a scaling study on quenched lattices. | hep-lat |
Excited States of U(1)$_{2+1}$ Lattice Gauge Theory from Monte Carlo
Hamiltonian: We address an old problem in lattice gauge theory - the computation of the
spectrum and wave functions of excited states. Our method is based on the
Hamiltonian formulation of lattice gauge theory. As strategy, we propose to
construct a stochastic basis of Bargmann link states, drawn from a physical
probability density distribution. Then we compute transition amplitudes between
stochastic basis states. From a matrix of transition elements we extract energy
spectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge
theory. We test the method by computing the energy spectrum, wave functions and
thermodynamical functions of the electric Hamiltonian of this theory and
compare them with analytical results. We observe a reasonable scaling of
energies and wave functions in the variable of time. We also present first
results on a small lattice for the full Hamiltonian including the magnetic
term. | hep-lat |
THE QCD ABACUS: A New Formulation for Lattice Gauge Theories: A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from
color triplet Fermions --- the standard quarks and a new Fermionic
``constituent'' of the gluon we call ``rishons''. The quarks are represented by
Dirac spinors on each site and the gauge fields by rishon-antirishon bilinears
on each link which together with the local gauge transforms are the generators
of an SU(6) algebra. The effective Lagrangian for the path integral lives in
$R^4 \times S^1$ Euclidean space with a compact ``fifth time'' of circumference
($\beta$) and non-Abelian charge ($e^2$) both of which carry dimensions of
length. For large $\beta$, it is conjectured that continuum QCD is reached and
that the dimensionless ratio $g^2 = e^2/\beta$ becomes the QCD gauge coupling.
The quarks are introduced as Kaplan chiral Fermions at either end of the finite
slab in fifth time. This talk will emphasize the gauge and algebraic structure
of the rishon or link Fermions and the special properties that may lead to fast
discrete dynamics for numerical simulations and new theoretical insight. | hep-lat |
Numerical tests of the electroweak phase transition and thermodynamics
of the electroweak plasma: The finite temperature phase transition in the SU(2) Higgs model at a Higgs
boson mass $M_H \simeq 34$ GeV is studied in numerical simulations on
four-dimensional lattices with time-like extensions up to $L_t=5$. The effects
of the finite volume and finite lattice spacing on masses and couplings are
studied in detail. The errors due to uncertainties in the critical hopping
parameter are estimated. The thermodynamics of the electroweak plasma near the
phase transition is investigated by determining the relation between energy
density and pressure. | hep-lat |
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 |
Massless Fermions on the Lattice: We consider a nonlocal lattice action for fermions fermion doubling in
lattice theories. It is shown, that it is possible to avoid the fermionic
doubling in the case of free fermions, but this approach does not reproduce
results for the effective action for gauge fields in the continuum theory,
because the high frequency fermion modes have a strong dependence on the gauge
field. | hep-lat |
The pion form factor on the lattice at zero and finite temperature: We calculate the electromagnetic form factor of the pion in quenched lattice
QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is
used together with the consistently O(a) improved current. We calculate the
pion form factor for masses down to m_pi = 360 MeV, extract the charge radius,
and extrapolate toward the physical pion mass. In the second part, we discuss
results for the pion form factor and charge radius at 0.93 T_c and compare with
zero temperature results. | hep-lat |
Disconnected contributions to D-meson semi-leptonic decay form factors: We calculate the disconnected contribution to the form factor for the
semileptonic decay of a D-meson into a final state, containing a flavor singlet
eta meson. We use QCDSF n_f=2+1 configurations at the flavor symmetric point
m_u=m_d=m_s and the partially quenched approximation for the relativistic charm
quark. Several acceleration and noise reduction techniques for the stochastic
estimation of the disconnected loop are tested. | hep-lat |
Finite Size Scaling and ``perfect'' actions: the three dimensional Ising
model: Using Finite-Size Scaling techniques, we numerically show that the first
irrelevant operator of the lattice $\lambda\phi^4$ theory in three dimensions
is (within errors) completely decoupled at $\lambda=1.0$. This interesting
result also holds in the Thermodynamical Limit, where the renormalized coupling
constant shows an extraordinary reduction of the scaling-corrections when
compared with the Ising model. It is argued that Finite-Size Scaling analysis
can be a competitive method for finding improved actions. | hep-lat |
K \to ππdecay amplitudes from the lattice: In order to directly compute physical two-pion K-decay amplitudes using
lattice methods we must prepare a two-pion state with non-zero relative
momentum. Building upon a proposal of Lellouch and L\"uscher, we describe a
finite-volume method to realize such a state as the lowest energy state of two
pions. | hep-lat |
Linear broadening of the confining string in Yang-Mills theory at low
temperature: The logarithmic broadening predicted by the systematic low-energy effective
field theory for the confining string has recently been verified in numerical
simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The
same effective theory predicts linear broadening of the string at low non-zero
temperature. In this paper, we verify this prediction by comparison with very
precise Monte Carlo data. The comparison involves no additional adjustable
parameters, because the low-energy constants of the effective theory have
already been fixed at zero temperature. It yields very good agreement between
the underlying Yang-Mills theory and the effective string theory. | hep-lat |
Accelerating lattice QCD simulations with 2 flavours of staggered
fermions on multiple GPUs using OpenACC - a first attempt: We present the results of an effort to accelerate a Rational Hybrid Monte
Carlo (RHMC) program for lattice quantum chromodynamics (QCD) simulation for 2
flavours of staggered fermions on multiple Kepler K20X GPUs distributed on
different nodes of a Cray XC30. We do not use CUDA but adopt a higher level
directive based programming approach using the OpenACC platform. The lattice
QCD algorithm is known to be bandwidth bound; our timing results illustrate
this clearly, and we discuss how this limits the parallelization gains. We
achieve more than a factor three speed-up compared to the CPU only MPI program. | hep-lat |
Phase diagram of QCD in strong background magnetic field: We discuss the phase diagram of QCD in the presence of a strong background
magnetic field, providing numerical evidence, based on lattice simulations of
QCD with $2+1$ flavours and physical quark masses, that the QCD crossover turns
into a first order phase transition for large enough magnetic field, with a
critical endpoint located between $eB=4$ GeV$^2$ (where we found an analytic
crossover at a pseudo-critical temperature $T_c=(98\pm3)$ MeV) and $eB=9$
GeV$^2$ (where the measured critical temperature is $T_c=(63\pm5)$ MeV). | hep-lat |
Gauge Invariance and Confinement in Noncompact Simulations of SU(2): Wilson loops have been measured at strong coupling, $\beta=0.5$, on a $12^4$
lattice in a noncompact simulation of pure SU(2) in which random compact gauge
transformations impose a kind of lattice gauge invariance. The Wilson loops
suggest a confining potential. | hep-lat |
The 't Hooft-Veneziano limit of the Polyakov loop models: The broad class of U(N) and SU(N) Polyakov loop models on the lattice are
solved exactly in the combined large N, Nf limit, where N is a number of colors
and Nf is a number of quark flavors, and in any dimension. In this 't
Hooft-Veneziano limit the ratio N/Nf is kept fixed. We calculate both the free
energy and various correlation functions. The critical behavior of the models
is described in details at finite temperatures and non-zero baryon chemical
potential. Furthermore, we prove that the calculation of the N-point (baryon)
correlation function reduces to the geometric median problem in the confinement
phase. In the deconfinement phase we establish an existence of the complex
masses and an oscillating decay of correlations in a certain region of
parameters. | 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 |
A Connection Between Complex-Temperature Properties of the 1D and 2D
Spin $s$ Ising Model: Although the physical properties of the 2D and 1D Ising models are quite
different, we point out an interesting connection between their
complex-temperature phase diagrams. We carry out an exact determination of the
complex-temperature phase diagram for the 1D Ising model for arbitrary spin $s$
and show that in the $u_s=e^{-K/s^2}$ plane (i) it consists of $N_{c,1D}=4s^2$
infinite regions separated by an equal number of boundary curves where the free
energy is non-analytic; (ii) these curves extend from the origin to complex
infinity, and in both limits are oriented along the angles $\theta_n =
(1+2n)\pi/(4s^2)$, for $n=0,..., 4s^2-1$; (iii) of these curves, there are
$N_{c,NE,1D}=N_{c,NW,1D}=[s^2]$ in the first and second (NE and NW) quadrants;
and (iv) there is a boundary curve (line) along the negative real $u_s$ axis if
and only if $s$ is half-integral. We note a close relation between these
results and the number of arcs of zeros protruding into the FM phase in our
recent calculation of partition function zeros for the 2D spin $s$ Ising model. | hep-lat |
Repairing Stevenson's step in the 4d Ising model: In a recent paper Stevenson claimed that analysis of the data on the wave
function renormalization constant near the critical point of the 4d Ising model
is not consistent with analytical expectations. Here we present data with
improved statistics and show that the results are indeed consistent with
conventional wisdom once one takes into account the uncertainty of lattice
artifacts in the analytical computations. | hep-lat |
High Spin Glueballs from the Lattice: We discuss the principles underlying higher spin glueball calculations on the
lattice. For that purpose, we develop numerical techniques to rotate Wilson
loops by arbitrary angles in lattice gauge theories close to the continuum. As
a first application, we compute the glueball spectrum of the SU(2) gauge theory
in 2+1 dimensions for both parities and for spins ranging from 0 up to 4
inclusive. We measure glueball angular wave functions directly, decomposing
them in Fourier modes and extrapolating the Fourier coefficients to the
continuum. This allows a reliable labelling of the continuum states and gives
insight into the way rotation symmetry is recovered. As one of our results, we
demonstrate that the D=2+1 SU(2) glueball conventionally labelled as J^P = 0^-
is in fact 4^- and that the lightest ``J=1'' state has, in fact, spin 3. | hep-lat |
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