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Overlap Fermion in External Gravity: On a lattice, we construct an overlap Dirac operator which describes the
propagation of a Dirac fermion in external gravity. The local Lorentz symmetry
is manifestly realized as a lattice gauge symmetry, while the general
coordinate invariance is expected to be restored only in the continuum limit.
The lattice index density in the presence of a gravitational field is
calculated. | hep-lat |
Energies and radial distributions of B_s mesons - the effect of
hypercubic blocking: This is a follow-up to our earlier work for the energies and the charge
(vector) and matter (scalar) distributions for S-wave states in a heavy-light
meson, where the heavy quark is static and the light quark has a mass about
that of the strange quark. We study the radial distributions of higher angular
momentum states, namely P- and D-wave states, using a "fuzzy" static quark. A
new improvement is the use of hypercubic blocking in the time direction, which
effectively constrains the heavy quark to move within a 2a hypercube (a is the
lattice spacing).
The calculation is carried out with dynamical fermions on a 16^3 times 32
lattice with a lattice spacing approximately 0.10 fm generated using the
non-perturbatively improved clover action. The configurations were generated by
the UKQCD Collaboration using lattice action parameters beta = 5.2, c_SW =
2.0171 and kappa = 0.1350.
In nature the closest equivalent of this heavy-light system is the B_s meson.
Attempts are now being made to understand these results in terms of the Dirac
equation. | hep-lat |
Lattice gauge theory and gluon color-confinement in curved spacetime: The lattice gauge theory for curved spacetime is formulated. A discretized
action is derived for both gluon and quark fields which reduces to the
generally covariant form in the continuum limit. Using the Wilson action, it is
shown analytically that for a general curved spacetime background, two
propagating gluons are always color-confined. The fermion-doubling problem is
discussed in the specific case of Friedman-Robertson-Walker metric. Lastly, we
discussed possible future numerical implementation of lattice QCD in curved
spacetime. | hep-lat |
$ππ$ scattering in partially-quenched twisted-mass chiral
perturbation theory: We study pion-pion scattering in partially-quenched twisted-mass lattice QCD
using chiral perturbation theory. The specific partially-quenched setup
corresponds to that used in numerical lattice QCD calculations of the $I=0$
scattering length. We study the discretization errors proportional to $a^2$,
with $a$ the lattice spacing, and the errors that arise due to the use of
L\"uscher's two-particle quantization condition in a theory that is not
unitary. We argue that the former can be as large as $\sim 100\%$, but explain
how they can be systematically subtracted using a calculation of the $I=2$
scattering amplitude in the same partially-quenched framework. We estimate the
error from the violation of unitarity to be $\sim 25\%$, and argue that this
error will be difficult to reduce in practice. | hep-lat |
Why the overlap formula does not lead to chiral fermions: We describe a conceptually simple, but important test for the overlap
approach to the construction of lattice chiral gauge theories. We explain the
equivalence of the overlap formula with a certain waveguide model for a simple
set of gauge configurations (the trivial orbit). This equivalence is helpful in
carrying out the test, and casts serious doubts on the viability of the overlap
approach. A recent note by Narayanan and Neuberger which points out a mistake
in our previous work is irrelevant in this context. | hep-lat |
Naive Lattice Fermion without Doublers: We discuss the naive lattice fermion without the issue of doublers. A local
lattice massless fermion action with chiral symmetry and hermiticity cannot
avoid the doubling problem from the Nielsen-Ninomiya theorem. Here we adopt the
forward finite-difference deforming the $\gamma_5$-hermiticity but preserving
the continuum chiral-symmetry. The lattice momentum is not hermitian without
the continuum limit now. We demonstrate that there is no doubling issue from an
exact solution. The propagator only has one pole in the first-order accuracy.
Therefore, it is hard to know the avoiding due to the non-hermiticity. For the
second-order, the lattice propagator has two poles as before. This case also
does not suffer from the doubling problem. Hence separating the forward
derivative from the backward one evades the doublers under the field theory
limit. Simultaneously, it is equivalent to breaking the hermiticity. In the
end, we discuss the topological charge and also demonstrate the numerical
implementation of the Hybrid Monte Carlo. | hep-lat |
Topological Susceptibility and Zero Mode Size in Lattice QCD: We use the overlap formalism to define a topological index on the lattice. We
study the spectral flow of the hermitian Wilson-Dirac operator and identify
zero crossings with topological objects. We determine the topological
susceptibility and zero mode size distribution, and we comment on the stability
of our results. | hep-lat |
Universality and Scaling at the chiral transition in two-flavor QCD at
finite temperature: The order of the phase transition in finite-temperature QCD with two
degenerate light quarks is still an open problem and corresponds to the last
question mark in the zero-density phase diagram of QCD. We argue that
establishing the nature of the transition in this case is also a crucial test
for numerical simulations of lattice QCD, allowing precise estimates of
possible systematic errors related e.g. to the choice of fermion-simulation
algorithm or of discretized formulation for fermions. | hep-lat |
The strong-coupling limit of minimal lattice Landau gauge: We study the gluon and ghost propagators of lattice Landau gauge in the
strong coupling limit $\beta = 0$ in pure SU(2) lattice gauge theory to find
evidence of the conformal infrared behaviour of these propagators as predicted
by a variety of functional continuum methods for asymptotically small momenta
$q^2 \ll \Lambda_\mathrm{QCD}^2$. In the strong-coupling limit, this same
behaviour is obtained for the larger values of $a^2q^2$ (in units of the
lattice spacing $a$), where it is otherwise swamped by the gauge field
dynamics. Deviations for $a^2 q^2 < 1 $ are well parametrized by a transverse
gluon mass $\propto 1/a$. Perhaps unexpectedly, these deviations are thus no
finite-volume effect but persist in the infinite-volume limit. They furthermore
depend on the definition of gauge fields on the lattice, while the asymptotic
conformal behaviour does not. | hep-lat |
Lattice investigation of the phase diagram of the 1+1 dimensional
Gross-Neveu model at finite number of fermion flavors: We explore the phase structure of the 1+1 dimensional Gross-Neveu model at
finite number of fermion flavors using lattice field theory. Besides a chirally
symmetric phase and a homogeneously broken phase we find evidence for the
existence of an inhomogeneous phase, where the condensate is a spatially
oscillating function. Our numerical results include a crude $\mu$-$T$ phase
diagram. | hep-lat |
Dynamics of Phase Transitions: The 3D 3-state Potts model: In studies of the QCD deconfining phase transition or cross-over by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. In this paper we extend our previous
study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model,
which serves as an effective model for some QCD properties. We investigate the
linear theory of spinodal decomposition in some detail. It describes the early
time evolution of the 3D model under a quench from the disordered into the
ordered phase well, but fails in 2D. Further, the quench leads to competing
vacuum domains, which are difficult to equilibrate, even in the presence of a
small external magnetic field. From our hysteresis study we find, as before, a
dynamics dominated by spinodal decomposition. There is evidence that some
effects survive in the case of a cross-over. But the infinite volume
extrapolation is difficult to control, even with lattices as large as $120^3$. | hep-lat |
A Study of Charmonium Systems across the Deconfinement Transition: We present results from lattice studies of charmonium systems near the
deconfinement transition temperature. On quenched isotropic lattices with
lattice spacings between 0.02 and 0.05 fm, bar{q} q systems with quark masses
close to the charm mass and with different spin-parity quantum numbers are
studied in the temperature range 0.9 Tc - 3 Tc. Results for temporal
correlators of local operators, and the spectral functions constructed from
them, are discussed. For the pseudoscalar and vector channels, the correlators
are observed to change very little across the deconfinement transition, unlike
in the case of the light quarks. | hep-lat |
Two-Dimensional Dynamical Triangulation using the Grand-canonical
Ensemble: The string susceptibility exponents of dynamically triangulated two
dimensional surfaces with sphere and torus topology were calculated using the
grand-canonical Monte Carlo method. We also simulated the model coupled to
d-Ising spins (d=1,2,3,5). | hep-lat |
Tests of the lattice index theorem: We investigate the lattice index theorem and the localization of the
zero-modes for thick classical center vortices. For non-orientable spherical
vortices, the index of the overlap Dirac operator differs from the topological
charge although the traces of the plaquettes deviate only by a maximum of 1.5%
from trivial plaquettes. This may be related to the fact that even in Landau
gauge some links of these configuration are close to the non-trivial center
elements. | hep-lat |
The Charm Quark on the Lattice: We formulate lattice fermions in a way that encompasses Wilson fermions as
well as the static and non-relativistic approximations. In particular, we treat
$m_qa$ systematically ($m_q$ is the fermion mass) showing how to understand the
Wilson action as an effective action for systems with $\vek{p}\ll m_q$. The
results show how to extract matrix elements and the spectrum from simulations
with $m_qa\approx1$, which is relevant for the charm quark. | hep-lat |
The finite temperature QCD using 2+1 flavors of domain wall fermions at
N_t = 8: We study the region of the QCD phase transition using 2+1 flavors of domain
wall fermions (DWF) and a $16^3 \times 8$ lattice volume with a fifth dimension
of $L_s = 32$. The disconnected light quark chiral susceptibility, quark number
susceptibility and the Polyakov loop suggest a chiral and deconfining crossover
transition lying between 155 and 185 MeV for our choice of quark mass and
lattice spacing. In this region the lattice scale deduced from the Sommer
parameter $r_0$ is $a^{-1} \approx 1.3$ GeV, the pion mass is $\approx 300$ MeV
and the kaon mass is approximately physical. The peak in the chiral
susceptibility implies a pseudo critical temperature $T_c = 171(10)(17)$ MeV
where the first error is associated with determining the peak location and the
second with our unphysical light quark mass and non-zero lattice spacing. The
effects of residual chiral symmetry breaking on the chiral condensate and
disconnected chiral susceptibility are studied using several values of the
valence $L_s$. | hep-lat |
Light meson decay constants beyond the quenched approximation: We calculate the effects of including dynamical fermion loops in the lattice
QCD estimates of meson decay constants, by extrapolating the results from
negative flavour numbers after a suitable matching of the pion and rho mass.
For moderately light quarks, the values of the decay constants not corrected
for the renormalization constants increase with respect to their quenched
values. | hep-lat |
Properties of U(1) lattice gauge theory with monopole term: In 4D compact U(1) lattice gauge theory with a monopole term added to the
Wilson action we first reveal some properties of a third phase region at
negative $\beta$. Then at some larger values of the monopole coupling $\lambda$
by a finite-size analysis we find values of the critical exponent $\nu$ close
to, however, different from the Gaussian value. | hep-lat |
Dirac Spectra of 2-dimensional QCD-like theories: We analyze Dirac spectra of two-dimensional QCD like theories both in the
continuum and on the lattice and classify them according to random matrix
theories sharing the same global symmetries. The classification is different
from QCD in four dimensions because the anti-unitary symmetries do not commute
with $\gamma_5$. Therefore in a chiral basis, the number of degrees of freedom
per matrix element are not given by the Dyson index. Our predictions are
confirmed by Dirac spectra from quenched lattice simulations for QCD with two
or three colors with quarks in the fundamental representation as well as in the
adjoint representation. The universality class of the spectra depends on the
parity of the number of lattice points in each direction. Our results show an
agreement with random matrix theory that is qualitatively similar to the
agreement found for QCD in four dimensions. We discuss the implications for the
Mermin-Wagner-Coleman theorem and put our results in the context of
two-dimensional disordered systems. | hep-lat |
Propagators in lattice Coulomb gauge and confinement mechanisms: We discuss the gluon propagator in 3- and 4-dimensional Yang-Mills theories
in Coulomb gauge and compare it with the corresponding Landau gauge propagator,
showing that for both the relevant IR mass scale coincides. We also report
preliminary results on Coulomb gauge ghost form factor and quark propagators
and give a comment on the gluon propagator's strong coupling limit. | hep-lat |
Simulations of Discrete Random Geometries: Simplicial Quantum Gravity
and Quantum String Theory: I investigate two discrete models of random geometries, namely simplicial
quantum gravity and quantum string theory. In four-dimensional simplicial
quantum gravity, I show that the addition of matter gauge fields to the model
is capable of changing its phase structure by replacing the branched polymers
of the pure gravity model with a new phase that has a negative string
susceptibility exponent and a fractal dimension of four. Some of the results
are derived from a strong coupling expansion of the model, a technique which is
used here for the first time in this context. In quantum string theory, I study
a discrete version of the IIB superstring. I show that the divergences
encountered in the discretization of the bosonic string are eliminated in the
supersymmetric case. I give theoretical arguments for the appearance of
one-dimensional structures in the region of large system extents that manifest
as a power-law tail in the link length distribution; this is confirmed by
numerical simulations of the model. I also examine a lower-dimensional version
of the IKKT matrix model, in which a similar effect can be observed. | hep-lat |
Employing the perturbative definition of the Higgs mass in a
non-perturbative calculation: In perturbative calculations the masses of the Higgs, the Ws and the Z are
usually determined from the pole position of the corresponding gauge-dependent
propagators. In full non-perturbative lattice calculations it is much more
direct to instead investigate the bound state spectrum with its
gauge-independent meaning, which then contains bound states of Higgses and/or
Ws and Zs. It is possible to extend the perturbative definition of the Higgs
mass also to such a full non-perturbative setting by determining the respective
full non-perturbative propagators of the Higgs, the Ws, and the Z, and analyze
their analytic structure. This helps connecting the Higgs properties indirectly
with gauge-invariant physics. This is here studied, using lattice gauge theory,
for the case of a W-Z-Higgs system. | hep-lat |
Strange quark contribution to nucleon form factors: We discuss methods for the calculation of disconnected diagrams and their
application to various form factors of the nucleon. In particular, we present
preliminary results for the strange contribution to the scalar and axial form
factors, calculated with N_f=2 dynamical flavors of Wilson fermions on an
anisotropic lattice. | hep-lat |
Moving NRQCD for B Form Factors at High Recoil: We derive the continuum and lattice tree-level moving NRQCD (mNRQCD) through
order 1/m^2. mNRQCD is a generalization of NRQCD for dealing with hadrons with
nonzero velocity u_mu. The quark's total momentum is written as P^mu=Mu^mu+k^mu
where k^mu << Mu^mu is discretized and Mu^mu is treated exactly. Radiative
corrections to couplings on the lattice are discussed. mNRQCD is particularly
useful for calculating B->pi and B->D form factors since errors are similar at
low and high recoil. | hep-lat |
Worm Algorithm for CP(N-1) Model: The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it
possesses confinement, asymptotic freedom and a non-trivial vacuum structure.
Due to the lower dimensionality and the absence of fermions, the computational
cost for simulating 2D CP(N-1) on the lattice is much lower than that for
simulating 4D QCD. However, to our knowledge, no efficient algorithm for
simulating the lattice CP(N-1) model has been tested so far, which also works
at finite density. To this end we propose a new type of worm algorithm which is
appropriate to simulate the lattice CP(N-1) model in a dual, flux-variables
based representation, in which the introduction of a chemical potential does
not give rise to any complications. In addition to the usual worm moves where a
defect is just moved from one lattice site to the next, our algorithm
additionally allows for worm-type moves in the internal variable space of
single links, which accelerates the Monte Carlo evolution. We use our algorithm
to compare the two popular CP(N-1) lattice actions and exhibit marked
differences in their approach to the continuum limit. | hep-lat |
Non-renormalization theorem in a lattice supersymmetric theory and the
cyclic Leibniz rule: N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two
supercharges, among four, are exactly conserved with the help of the cyclic
Leibniz rule without spoiling the locality. In use of the cohomological
argument, any possible local terms of the effective action are classified into
two categories which we call type-I and type-II, analogous to the D- and
F-terms in the supersymmetric field theories. We prove non-renormalization
theorem on the type-II terms which include mass and interaction terms with
keeping a lattice constant finite, while type-I terms such as the kinetic terms
have nontrivial quantum corrections. | hep-lat |
Symmetries of mesons after unbreaking of chiral symmetry and their
string interpretation: Using the chirally invariant overlap Dirac operator we remove its
lowest-lying quasizero modes from the valence quark propagators and study
evolution of isovector mesons with J=1. At the truncation level about 50 MeV
SU(2)_L \times SU(2)_R and U(1)_A symmetries get restored. However, we observe
a degeneracy not only within the chiral and U(1)_A multiplets, but also a
degeneracy of all possible chiral multiplets, i.e., the observed quantum levels
have a symmetry larger than U(2)_L \times U(2)_R and their energy does not
depend on the spin orientation of quarks and their parities. We offer a
possible interpretation of these energy levels as the quantum levels of the
dynamical QCD string. The structure of the radial J=1 spectrum is compatible
with E =(n_r +1)\hbar\omega with \hbar\omega = 900 \pm 70 MeV. | hep-lat |
Can lattice data for two heavy-light mesons be understood in terms of
simply two-quark potentials?: By comparing lattice data for the two heavy-light meson system (Q^2 qbar^2)
with a standard many-body approach employing only interquark potentials, it is
shown that the use of unmodified two-quark potentials leads to a gross
overestimate of the binding energy. | hep-lat |
Genetic Algorithm for SU(2) Gauge Theory on a 2-dimensional Lattice: An algorithm is proposed for the simulation of pure SU(N) lattice gauge
theories based on Genetic Algorithms(GAs). We apply GAs to SU(2) pure gauge
theory on a 2 dimensional lattice and show the results, the action per
plaquette and Wilson loops, are consistent with those by Metropolis method(MP)s
and Heatbath method(HB)s. Thermalization speed of GAs is especially faster than
the simple MPs. | hep-lat |
QCD-like technicolor on the lattice: This talk gives an overview, aimed at non-experts, of the recent progress on
the studies of technicolor models on the lattice. Phenomenologically successful
technicolor models require walking coupling; thus, an emphasis is put on the
determination of the beta-function of various models. As a case study we
consider SU(2) gauge field theory with two adjoint representation fermions,
so-called minimal walking technicolor theory. | hep-lat |
Screening masses in quenched (2+1)d Yang-Mills theory: universality from
dynamics?: We compute the spectrum of gluonic screening-masses in the $0^{++}$ channel
of quenched 3d Yang-Mills theory near the phase-transition. Our
finite-temperature lattice simulations are performed at scaling region, using
state-of-art techniques for thermalization and spectroscopy, which allows for
thorough data extrapolations to thermodynamic limit. Ratios among
mass-excitations with the same quantum numbers on the gauge theory, 2d Ising
and $\lambda\phi^{4}$ models are compared, resulting in a nice agreement with
predictions from universality. In addition, a gauge-to-scalar mapping,
previously employed to fit QCD Green's functions at deep IR, is verified to
dynamically describe these universal spectroscopic patterns | hep-lat |
The kaon B-parameter from unquenched mixed action lattice QCD: We present a preliminary calculation of B_K using domain-wall valence quarks
and 2+1 flavors of improved staggered sea quarks. Both the size of the residual
quark mass, which measures the amount of chiral symmetry breaking, and of the
mixed meson splitting Delta_mix, a measure of taste-symmetry breaking, show
that discretization effects are under control in our mixed action lattice
simulations. We show preliminary data for pseudoscalar meson masses, decay
constants and B_K. We discuss general issues associated with the chiral
extrapolation of lattice data, and, as an example, present a preliminary chiral
and continuum extrapolation of f_pi. The quality of our data shows that the
good chiral properties of domain-wall quarks, in combination with the light sea
quark masses and multiple lattice spacings available with the MILC staggered
configurations, will allow for a precise determination of B_K. | hep-lat |
Meson masses in electromagnetic fields with Wilson fermions: We determine the light meson spectrum in QCD in the presence of background
magnetic fields using quenched Wilson fermions. Our continuum extrapolated
results indicate a monotonous reduction of the connected neutral pion mass as
the magnetic field grows. The vector meson mass is found to remain nonzero, a
finding relevant for the conjectured $\rho$-meson condensation at strong
magnetic fields. The continuum extrapolation was facilitated by adding a novel
magnetic field-dependent improvement term to the additive quark mass
renormalization. Without this term, sizable lattice artifacts that would
deceptively indicate an unphysical rise of the connected neutral pion mass for
strong magnetic fields are present. We also investigate the impact of these
lattice artifacts on further observables like magnetic polarizabilities and
discuss the magnetic field-induced mixing between $\rho$-mesons and pions. We
also derive Ward-Takashi identities for QCD+QED both in the continuum
formulation and for (order $a$-improved) Wilson fermions. | hep-lat |
Continuum Limit of Scalar Masses and Mixing Energies: We evaluate the continuum limit of the valence approximation to the mass of
scalar quarkonium and to the scalar quarkonium-glueball mixing energy for a
range of different quark masses. Our results answer several questions raised by
the proposed identification of $f_0(1710)$ as composed primarily of the
lightest scalar glueball. | hep-lat |
Deflated GMRES with Multigrid for Lattice QCD: Lattice QCD solvers encounter critical slowing down for fine lattice spacings
and small quark mass. Traditional matrix eigenvalue deflation is one approach
to mitigating this problem. However, to improve scaling we study the effects of
deflating on the coarse grid in a hierarchy of three grids for adaptive
mutigrid applications of the two dimensional Schwinger model. We compare
deflation at the fine and coarse levels with other non deflated methods. We
find the inclusion of a partial solve on the intermediate grid allows for a low
tolerance deflated solve on the coarse grid. We find very good scaling in
lattice size near critical mass when we deflate at the coarse level using the
GMRES-DR and GMRES-Proj algorithms. | hep-lat |
Confinement in non-Abelian lattice gauge theory via persistent homology: We investigate the structure of confining and deconfining phases in SU(2)
lattice gauge theory via persistent homology, which gives us access to the
topology of a hierarchy of combinatorial objects constructed from given data.
Specifically, we use filtrations by traced Polyakov loops, topological
densities, holonomy Lie algebra fields, as well as electric and magnetic
fields. This allows for a comprehensive picture of confinement. In particular,
topological densities form spatial lumps which show signatures of the classical
probability distribution of instanton-dyons. Signatures of well-separated dyons
located at random positions are encoded in holonomy Lie algebra fields,
following the semi-classical temperature dependence of the instanton appearance
probability. Debye screening discriminating between electric and magnetic
fields is visible in persistent homology and pronounced at large gauge
coupling. All employed constructions are gauge-invariant without a priori
assumptions on the configurations under study. This work showcases the
versatility of persistent homology for statistical and quantum physics studies,
barely explored to date. | hep-lat |
Anisotropic Improved Gauge Actions; --Perturbative and Numerical Studies
--: The $\Lambda$ parameter on the anisotropic lattice, the spatial and
temperature coupling constant $g_{\sigma}$, $g_{\tau}$ and their derivative
with respaect to the the anisotropy parameter $\xi$ are studied perturbatively
for the class of improved actions, which cover tree level Symanzik's, Iwasaki's
and QCDTARO's improved actions. The $\eta(=g_{\tau}/g_{\sigma})$ becomes less
than 1 for Iwasaki's and QCDTARO's action, which is confirmed nonperturbatively
by numerical simulations. Derivatives of the coupling constants with respect to
the anisotropy parameter, $\partial g_{\tau}/\partial \xi$ and $\partial
g_{\sigma}/\partial \xi$, change sign for those improved actions. | hep-lat |
Flavour blindness and patterns of flavour symmetry breaking in lattice
simulations of up, down and strange quarks: QCD lattice simulations with 2+1 flavours (when two quark flavours are mass
degenerate) typically start at rather large up-down and strange quark masses
and extrapolate first the strange quark mass and then the up-down quark mass to
its respective physical value. Here we discuss an alternative method of tuning
the quark masses, in which the singlet quark mass is kept fixed. Using group
theory the possible quark mass polynomials for a Taylor expansion about the
flavour symmetric line are found, first for the general 1+1+1 flavour case and
then for the 2+1 flavour case. This ensures that the kaon always has mass less
than the physical kaon mass. This method of tuning quark masses then enables
highly constrained polynomial fits to be used in the extrapolation of hadron
masses to their physical values. Numerical results for the 2+1 flavour case
confirm the usefulness of this expansion and an extrapolation to the physical
pion mass gives hadron mass values to within a few percent of their
experimental values. Singlet quantities remain constant which allows the
lattice spacing to be determined from hadron masses (without necessarily being
at the physical point). Furthermore an extension of this programme to include
partially quenched results is given. | hep-lat |
Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with
Exact Supersymmetry: We construct two-dimensional N=(2,2) lattice super Yang-Mills theory, where
the gauge and Higgs fields are all represented by U(N) compact variables, with
keeping one exact supercharge along the line of the papers [1,2,3].
Interestingly, requirements of the exact supersymmetry as well as of the
compact gauge and Higgs fields lead to the gauge group U(N) rather than SU(N).
As a result of the perturbative renormalization argument, the model is shown to
flow to the target continuum theory without any fine-tuning. Different from the
case of noncompact Higgs fields, the path integral along the flat directions is
well-defined in this model. | hep-lat |
Lattice calculations of the spectroscopy of baryons with broken flavor
SU(3) symmetry and 3, 5, or 7 colors: Lattice Monte Carlo calculations of baryon spectroscopy in gauge groups
SU(N), N=3, 5, 7, are presented. The quenched valence fermions come in three
flavors, two degenerate mass ones and a third heavier flavor. The data shows
striking regularities reminiscent of the real-world case of N=3: higher angular
momentum states lie higher in mass, and Sigma-like states lie higher than
Lambda-like ones. These simple regularities are reasonably well described by
1/N expansions. | hep-lat |
Lattice Results for Heavy Light Matrix Elements: Lattice results for heavy light matrix elements are reviewed and some of
their implications are very briefly discussed. Despite the fact that in most
cases the lattice results for weak matrix elements at the moment have only a
modest accuracy of about 20--30\% they already have important phenomenological
repercussions; e.g.\ for $V_{td}/V_{ts}$, $x_s/x_d$ and $B\to K^\ast\gamma$.
Presented at the XXVII International Conference on High Energy Physics,
Glasgow, July 1994. | hep-lat |
Infrared Gluon and Ghost Propagators from Lattice QCD. Results from
large asymmetric lattices: We report on the infrared limit of the quenched lattice Landau gauge gluon
and ghost propagators as well as the strong coupling constant computed from
large asymmetric lattices. The infrared lattice propagators are compared with
the pure power law solutions from Dyson-Schwinger equations (DSE). For the
gluon propagator, the lattice data is compatible with the DSE solution. The
preferred measured gluon exponent being $\sim 0.52$, favouring a null zero
momentum propagator. The lattice ghost propagator shows finite volume effects
and, for the volumes considered, the propagator does not follow a pure power
law. Furthermore, the strong coupling constant is computed and its infrared
behaviour investigated. | hep-lat |
Two loop lattice expansion of the Schroedinger functional coupling in
improved QCD: The contributions of the improved fermion action of Sheikholeslami and
Wohlert to the two loop coefficient of the expansion of the Schroedinger
functional coupling in terms of the lattice coupling are calculated for the
gauge group SU(3). These coefficients are required for the second order
relation of lattice data to the MSbar-coupling. By taking into account all
improvement coefficients we are able to improve the Schroedinger functional to
two loop order. | hep-lat |
Meron-Cluster Simulation of a Chiral Phase Transition with Staggered
Fermions: We examine a (3+1)-dimensional model of staggered lattice fermions with a
four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian
formulation. This model cannot be simulated with standard fermion algorithms
because those suffer from a very severe sign problem. We use a new fermion
simulation technique - the meron-cluster algorithm - which solves the sign
problem and leads to high-precision numerical data. We investigate the finite
temperature chiral phase transition and verify that it is in the universality
class of the 3-d Ising model using finite-size scaling. | hep-lat |
An Experimenter's View of Lattice QCD: Lattice QCD has the potential this decade to maximize the sensitivity of the
entire flavor physics program to new physics and pave the way for understanding
physics beyond the Standard Model at the LHC in the coming decade. However, the
challenge for the Lattice is to demonstrate reliability at the level of a few
per cent given a past history of 10-20% errors. The CLEO-c program at the
Cornell Electron Storage Ring is providing the data that will make the
demonstration possible. | hep-lat |
Non-Perturbative Renormalization for Staggered Fermions (Self-energy
Analysis): We present preliminary results of data analysis for the non-perturbative
renormalization (NPR) on the self-energy of the quark propagators calculated
using HYP improved staggered fermions on the MILC asqtad lattices. We use the
momentum source to generate the quark propagators. In principle, using the
vector projection operator of $(\bar{\bar{\gamma_\mu \otimes 1}})$ and the
scalar projection operator $(\bar{\bar{1 \otimes 1}})$, we should be able to
obtain the wave function renormalization factor $Z_q'$ and the mass
renormalization factor $Z_q \cdot Z_m$. Using the MILC coarse lattice, we
obtain a preliminary but reasonable estimate of $Z_q'$ and $Z_q \cdot Z_m$ from
the data analysis on the self-energy. | hep-lat |
Screening at finite temperature and density: We present lattice QCD results on heavy quark free energies, extract from its
temperature dependence entropy and internal energy contributions, and discuss
the onset of medium effects that lead to screening of static quark-antiquark
sources in a thermal medium. Most results are obtained in (2+1)-flavour QCD on
a line of constant physics with almost realistic quark masses and compared to
previous results from 2-flavor QCD as well as pure gauge theory. Furthermore,
we discuss results on the density dependence of screening masses that have been
obtained using a leading order Taylor expansion in the baryon chemical
potential. | hep-lat |
Polymer-Chain Adsorption Transition at a Cylindrical Boundary: In a recent letter, a simple method was proposed to generate solvable models
that predict the critical properties of statistical systems in hyperspherical
geometries. To that end, it was shown how to reduce a random walk in $D$
dimensions to an anisotropic one-dimensional random walk on concentric
hyperspheres. Here, I construct such a random walk to model the
adsorption-desorption transition of polymer chains growing near an attractive
cylindrical boundary such as that of a cell membrane. I find that the fraction
of adsorbed monomers on the boundary vanishes exponentially when the adsorption
energy decreases towards its critical value. When the adsorption energy rises
beyond a certain value above the critical point whose scale is set by the
radius of the cell, the adsorption fraction exhibits a crossover to a linear
increase characteristic to polymers growing near planar boundaries. | hep-lat |
Hunting the static energy renormalon: We employ Numerical Stochastic Perturbation Theory (NSPT) together with
twisted boundary conditions (TBC) to search for the leading renormalon in the
perturbative expansion of the static energy. This renormalon is expected to
emerge four times faster than the one for the gluon conden- sate in the
plaquette. We extract the static energy from Polyakov loop calculations up to
12 loops and present preliminary results, indicating a significant step towards
confirming the theoretical expectation. | hep-lat |
Form factor ratios for $B_s \rightarrow K \, \ell \, ν$ and $B_s
\rightarrow D_s \, \ell \, ν$ semileptonic decays and $|V_{ub}/V_{cb}|$: We present a lattice quantum chromodynamics determination of the ratio of the
scalar and vector form factors for two semileptonic decays of the $B_s$ meson:
$B_s \rightarrow K \ell \nu$ and $B_s \rightarrow D_s \ell \nu$. In conjunction
with future experimental data, our results for these correlated form factors
will provide a new method to extract $|V_{ub}/V_{cb}|$, which may elucidate the
current tension between exclusive and inclusive determinations of these
Cabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form
factor results, we determine the ratio of the differential decay rates, and
forward-backward and polarization asymmetries, for the two decays. | hep-lat |
Behavior near $θ=π$ of the mass gap in the 2D O(3) non-linear
sigma model: The validity of the Haldane's conjecture entails that the mass gap of the
2-dimensional O(3) non-linear sigma model with a $\theta$-term must tend to
zero as $\theta$ approaches the value $\pi$ by following a precise law. In the
present paper we extract the related critical exponents by simulating the model
at imaginary $\theta$. | hep-lat |
Lattice QCD Determination of $g_A$: The nucleon axial coupling, $g_A$, is a fundamental property of protons and
neutrons, dictating the strength with which the weak axial current of the
Standard Model couples to nucleons, and hence, the lifetime of a free neutron.
The prominence of $g_A$ in nuclear physics has made it a benchmark quantity
with which to calibrate lattice QCD calculations of nucleon structure and more
complex calculations of electroweak matrix elements in one and few nucleon
systems. There were a number of significant challenges in determining $g_A$,
notably the notorious exponentially-bad signal-to-noise problem and the
requirement for hundreds of thousands of stochastic samples, that rendered this
goal more difficult to obtain than originally thought.
I will describe the use of an unconventional computation method, coupled with
"ludicrously'" fast GPU code, access to publicly available lattice QCD
configurations from MILC and access to leadership computing that have allowed
these challenges to be overcome resulting in a determination of $g_A$ with 1%
precision and all sources of systematic uncertainty controlled. I will discuss
the implications of these results for the convergence of $SU(2)$ Chiral
Perturbation theory for nucleons, as well as prospects for further improvements
to $g_A$ (sub-percent precision, for which we have preliminary results) which
is part of a more comprehensive application of lattice QCD to nuclear physics.
This is particularly exciting in light of the new CORAL supercomputers coming
online, Sierra and Summit, for which our lattice QCD codes achieve a
machine-to-machine speed up over Titan of an order of magnitude. | 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 |
The scalar, vector and tensor form factors for the pion and kaon from
lattice QCD: We present a calculation of the scalar, vector, and tensor form factors for
the pion and kaon in lattice QCD. We use an ensemble of two degenerate light, a
strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with
clover improvement. The corresponding pion and kaon masses are about 265 MeV
and 530 MeV, respectively. The calculation is done in both rest and boosted
frames obtaining data for four-vector momentum transfer squared up to
$-q^2=2.5$ GeV$^2$ for the pion and 3 GeV$^2$ for the kaon. The excited-states
effects are studied by analyzing six values of the source-sink time separation
for the rest frame ($1.12-2.23$ fm) and for four values for the boosted frame
($1.12-1.67$ fm). The lattice data are renormalized non-perturbatively and the
results for the scheme- and scale-dependent scalar and tensor form factors are
presented in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. We apply
different parametrizations to describe $q^2$-dependence of the form factors to
extract the scalar, vector, and tensor radii, as well as the tensor anomalous
magnetic moment. We compare the pion and kaon form factors to study SU(3)
flavor symmetry breaking effects. By combining the data for the vector and
tensor form factors we also obtain the lowest moment of the densities of
transversely polarized quarks in the impact parameter space. Finally, we give
an estimate for the average transverse shift in the $y$ direction for polarized
quarks in the $x$ direction. | hep-lat |
Signal/noise enhancement strategies for stochastically estimated
correlation functions: We develop strategies for enhancing the signal/noise ratio for stochastically
sampled correlation functions. The techniques are general and offer a wide
range of applicability. We demonstrate the potential of the approach with a
generic two-state system, and then explore the practical applicability of the
method for single hadron correlators in lattice quantum chromodynamics. In the
latter case, we determine the ground state energies of the pion, proton, and
delta baryon, as well as the ground and first excited state energy of the rho
meson using matrices of correlators computed on an exemplary ensemble of
anisotropic gauge configurations. In the majority of cases, we find a modest
reduction in the statistical uncertainties on extracted energies compared to
conventional variational techniques. However, in the case of the delta baryon,
we achieve a factor of three reduction in statistical uncertainties. The
variety of outcomes achieved for single hadron correlators illustrates an
inherent dependence of the method on the properties of the system under
consideration and the operator basis from which the correlators are
constructed. | hep-lat |
Infinite volume and continuum limits for gluon propagator in 3d SU(2)
lattice gauge theory: We study the Landau gauge gluon propagator D(p) in the 3d SU(2) lattice gauge
theory. We show that in the infinite-volume limit the expectation values over
the Gribov region \Omega, are different (in the infrared) from that calculated
in the fundamental modular region \Gamma. Also we show that this conclusion
does not change when spacing $a$ tends to zero. | hep-lat |
Measure dependence of 2D simplicial quantum gravity: We study pure 2D Euclidean quantum gravity with $R^2$ interaction on
spherical lattices, employing Regge's formulation. We attempt to measure the
string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size
scaling Ansatz in the expectation value of $R^2$. To check on effects of the
path integral measure we investigate two scale invariant measures, the
"computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$. | hep-lat |
Lattice Background Effective Action: a Proposal: We propose a method based on the Schr\"odinger functional for computing on
the lattice the gauge invariant effective action for external background
fields. We check this method by studying the U(1) lattice gauge theory in
presence of a constant magnetic background field. | hep-lat |
A precise determination of T_c in QCD from scaling: Existing lattice data on the QCD phase transition are analyzed in
renormalized perturbation theory. In quenched QCD it is found that T_c scales
for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05.
A preliminary estimate in QCD with two flavours of dynamical quarks shows that
this ratio depends on the quark mass. For realistic quark masses we estimate
T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in
quenched QCD at 1-loop order in renormalised perturbation theory. | hep-lat |
Strange quark momentum fraction from overlap fermion: We present a calculation of $< x >_s$ for the strange quark in the nucleon.
We also report the ratio of the strange $< x >$ to that of $u/d$ in the
disconnected insertion which will be useful in constraining the global fit of
parton distribution functions at small $x$. We adopt overlap fermion action on
$2 + 1$ flavor domain-wall fermion configurations on the $24^3 \times 64$
lattice with a light sea quark mass which corresponds to $m_{\pi}=330$ MeV.
Smeared grid $Z_3$ sources are deployed to calculate the nucleon propagator
with low-mode substitution. Even-odd grid sources and time-dilution technique
with stochastic noises are used to calculate the high mode contribution to the
quark loop. Low mode averaging (LMA) for the quark loop is applied to reduce
the statistical error of the disconnected insertion calculation. We find the
ratio $< x >_s/< x >_{u/d}^{\mathrm{DI}}= 0.78(3)$ in this study. | hep-lat |
A lattice potential investigation of quark mass and volume dependence of
the $Υ$ spectrum: We investigate bottomonia splittings by solving a Schrodinger-Pauli-type
equation with parametrisations of QCD potentials around those that have been
determined previously in lattice simulations. This is done both, in the
continuum and on finite lattices with resolutions ranging from a=0.2 fm down to
a=0.025 fm and extent of up to 12 fm or 144^3 lattice points. We find a strong
dependence of some splittings, in particular the 2S-1S and 1P-1S splittings, on
both the quark mass and the short range form of the static potential in the
neighbourhood of the bottom quark mass, while splittings such as 3S-2S and
2P-2S show reduced dependence on the short distance potential. We conclude that
the quenched quarkonium spectrum cannot be matched to experiment with a simple
redefinition of the lattice spacing. We investigate the size of relativistic
corrections as a function of the quark mass. Finite size effects are shown to
die out rather rapidly as the volume is increased, and we demonstrate the
restoration of rotational symmetry as the continuum limit is taken. | hep-lat |
Confinement and Topological Charge in the Abelian Gauge of QCD: We study the relation between instantons and monopoles in the abelian gauge.
First, we investigate the monopole in the multi-instanton solution in the
continuum Yang-Mills theory using the Polyakov gauge. At a large instanton
density, the monopole trajectory becomes highly complicated, which can be
regarded as a signal of monopole condensation. Second, we study instantons and
monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA)
gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find
monopole dominance for instantons in the confinement phase even at finite
temperatures. A linear-type correlation is found between the total
monopole-loop length and the integral of the absolute value of the topological
density (the total number of instantons and anti-instantons) in the MA gauge.
We conjecture that instantons enhance the monopole-loop length and promote
monopole condensation. | hep-lat |
$1^{-+}$ Hybrid in $J/ψ$ Radiative Decays from Lattice QCD: We present the first theoretical prediction of the production rate of
$1^{-+}$ light hybrid meson $\eta_1$ in $J/\psi$ radiative decays. In the
$N_f=2$ lattice QCD formalism with the pion mass $m_\pi\approx 350$ MeV, the
related electromagnetic multipole form factors are extracted from the
three-point functions that involve necessarily quark annihilation diagrams,
which are calculated through the distillation method. The partial width of
$J/\psi\to \gamma \eta_1$ is determined to be $2.29(77)~\mathrm{eV}$ at the
$\eta_1$ mass $m_{\eta_1}=2.23(4)$ GeV. If $\eta_1$ corresponds to the recently
observed $\eta_1(1855)$ in the process $J/\psi\to \gamma\eta_1(1855)\to \gamma
\eta\eta'$ by BESIII, then the branching fraction $\mathrm{Br}(J/\psi\to
\gamma\eta_1(1855))$ is estimated to be $6.2(2.2)\times 10^{-5}$, which implies
$\mathrm{Br}(\eta_1(1855)\to \eta\eta')\sim 4.3\%$. | hep-lat |
Improved Hamiltonians for Quantum Simulations: Quantum simulations of lattice gauge theories for the foreseeable future will
be hampered by limited resources. The historical success of improved lattice
actions in classical simulations strongly suggests that Hamiltonians with
improved discretization errors will reduce quantum resources, i.e. require
$\gtrsim 2^d$ fewer qubits in quantum simulations for lattices with $d$ spatial
dimensions. In this work, we consider $\mathcal{O}(a^2)$-improved Hamiltonians
for pure gauge theories and design the corresponding quantum circuits for its
real-time evolution in terms of primitive gates. An explicit demonstration for
$\mathbb{Z}_2$ gauge theory is presented including exploratory tests using the
ibm_perth device. | hep-lat |
Moving from continuous to discrete symmetry in the 2D XY model: We study the effects of discretization on the U(1) symmetric XY model in two
dimensions using the Higher Order Tensor Renormalization Group (HOTRG)
approach. Regarding the $Z_N$ symmetric clock models as specific
discretizations of the XY model, we compare those discretizations to ones from
truncations of the tensor network formulation of the XY model based on a
character expansion, and focus on the differences in their phase structure at
low temperatures. We also divide the tensor network formulations into core and
interaction tensors and show that the core tensor has the dominant influence on
the phase structure. Lastly, we examine a perturbed form of the XY model that
continuously interpolates between the XY and clock models. We examine the
behavior of the additional phase transition caused by the perturbation as the
magnitude of perturbation is taken to zero. We find that this additional
transition has a non-zero critical temperature as the perturbation vanishes,
suggesting that even small perturbations can have a significant effect on the
phase structure of the theory. | hep-lat |
The Quantized $O(1,2)/O(2)\times Z_2$ Sigma Model Has No Continuum Limit
in Four Dimensions. II. Lattice Simulation: A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is
developed, based on the continuum theory presented in the preceding paper.
Special attention is given to choosing a lattice action (the ``geodesic''
action) that is appropriate for fields having noncompact curved configuration
spaces. A consistent continuum limit of the model exists only if the
renormalized scale constant $\beta_R$ vanishes for some value of the bare scale
constant~$\beta$. The geodesic action has a special form that allows direct
access to the small-$\beta$ limit. In this limit half of the degrees of freedom
can be integrated out exactly. The remaining degrees of freedom are those of a
compact model having a $\beta$-independent action which is noteworthy in being
unbounded from below yet yielding integrable averages. Both the exact action
and the $\beta$-independent action are used to obtain $\beta_R$ from Monte
Carlo computations of field-field averages (2-point functions) and
current-current averages. Many consistency cross-checks are performed. It is
found that there is no value of $\beta$ for which $\beta_R$ vanishes. This
means that as the lattice cutoff is removed the theory becomes that of a pair
of massless free fields. Because these fields have neither the geometry nor the
symmetries of the original model we conclude that the $O(1,2)/O(2)\times Z_2$
model has no continuum limit. | hep-lat |
Curvature of the QCD critical line with 2+1 HISQ fermions: We present results on the curvature of the critical line of QCD with 2+1 HISQ
fermions at nonzero temperature and quark density obtained by analytic
continuation from imaginary chemical potentials. Monte Carlo simulations are
performed by means of the MILC code, suitably modified to include a nonzero
imaginary baryon chemical potential. We set the chemical potential at the same
value for the three quark species and work on the line of constant physics with
a light to strange mass ratio of 1/20 as determined in
Ref.~\cite{Bazavov:2011nk}. | hep-lat |
A class of chiral fermion models: We study the relation between the Roma and Zaragoza proposals for chiral
fermions on the lattice. The fermion action in the Roma approach is shown to be
equivalent to one of the Zaragoza type. This result is used to perform a
mean-field study of the phase diagram for chiral Yukawa models based on the
Roma action. The phase diagram is compared with the one based on the Zaragoza
model with the most local choice for the fermion interactions. | hep-lat |
Scaling in SU(3) Pure Gauge Theory with a Renormalization Group Improved
Action: We study the scaling properties of the static quark potential and the ratio
of the critical temperature $T_c$ to the square root of the string tension
$\sigma$ in the SU(3) pure gauge theory using a renormalization group improved
action. We first determine the critical coupling $\beta_c$ on lattices with
temporal extension $N_t=3$, 4, and 6, and then calculate the static quark
potential at the critical couplings on lattices at zero temperature. We note
that the static quark potentials obtained are rotationally invariant with
errors of at most 1 - 2 % in all the three cases, and that the potential $V(R)$
in physical units scales in the whole region of $R$ investigated. The values of
$T_{c}/\sqrt{\sigma}$ for the three cases in the infinite volume limit are
identical within errors. We estimate the value in the continuum limit to be
$T_{c}/\sqrt{\sigma} = 0.656(4)$, which is slightly larger than the value in
the continuum limit from the one-plaquette action, 0.629(3). | hep-lat |
Bound states for Overlap and Fixed Point Actions close to the chiral
limit: We study the overlap and the fixed point Dirac operators for massive fermions
in the two-flavor lattice Schwinger model. The masses of the triplet (pion) and
singlet (eta) bound states are determined down to small fermion masses and the
mass dependence is compared with various continuum model approximations. Near
the chiral limit, at very small fermion masses the fixed point operator has
stability problems, which in this study are dominated by finite size effects, | hep-lat |
The spin structure of the Lambda hyperon in quenched lattice QCD: It has been suggested to use the production of Lambda hyperons for
investigating the nucleon spin structure. The viability of this idea depends
crucially on the spin structure of the Lambda. Using nonperturbatively O(a)
improved Wilson fermions in the quenched approximation we have studied matrix
elements of two-quark operators in the Lambda. We present results for the axial
vector current, which give us the contributions of the u, d, and s quarks to
the Lambda spin. | hep-lat |
Polyakov loop in 2+1 flavor QCD: We study the temperature dependence of the renormalized Polyakov loop in 2+1
flavor QCD for temperatures T<210 MeV. We extend previous calculations by the
HotQCD collaboration using the highly improved staggered quark action and
perform a continuum extrapolation of the renormalized Polyakov loop. We compare
the lattice results with the prediction of non-interacting static-light hadron
resonance gas, which describes the temperature dependence of the renormalized
Polyakov loop up to T<140 MeV but fails above that temperature. Furthermore, we
discuss the temperature dependence of the light and strange quark condensates. | hep-lat |
Implicit schemes for real-time lattice gauge theory: We develop new gauge-covariant implicit numerical schemes for classical
real-time lattice gauge theory. A new semi-implicit scheme is used to cure a
numerical instability encountered in three-dimensional classical Yang-Mills
simulations of heavy-ion collisions by allowing for wave propagation along one
lattice direction free of numerical dispersion. We show that the scheme is
gauge covariant and that the Gauss constraint is conserved even for large time
steps. | hep-lat |
How far can you go ? Surprises and pitfalls in three-flavour chiral
extrapolations: The presence of strange sea quark pairs may have a significant impact of the
pattern of chiral symmetry breaking : in particular large differences can occur
between the chiral limits of two and three massless flavours (i.e., whether
$m_s$ is kept at its physical value or sent to zero). We recall some
indications of such a scenario in QCD, in relation with the peculiar dynamics
of the scalar sector. We explain how this could affect the convergence of
three-flavour chiral series, commonly used to extrapolate the results of
lattice simulations. Finally, we indicate how lattice simulations with three
dynamical flavours could unveil such an effect through the quark-mass
dependence of light meson masses and decay constants. | hep-lat |
The derivative expansion of the renormalization group: By writing the flow equations for the continuum Legendre effective action
(a.k.a. Helmholtz free energy) with respect to a particular form of smooth
cutoff, and performing a derivative expansion up to some maximum order, a set
of differential equations are obtained which at FPs (Fixed Points) reduce to
non-linear eigenvalue equations for the anomalous scaling dimension $\eta$.
Illustrating this by expanding (single component) scalar field theory, in two,
three and four dimensions, up to second order in derivatives, we show that the
method is a powerful and robust means of discovering and quantifying
non-perturbative continuum limits (continuous phase transitions). | hep-lat |
Electromagnetic Corrections in Staggered Chiral Perturbation Theory: To reduce errors in light-quark mass determinations, it is now necessary to
consider electromagnetic contributions to light-meson masses. Calculations
using staggered quarks and quenched photons are currently underway.
Suitably-extended chiral perturbation theory is necessary to extrapolate the
lattice data to the physical limit. Here we give (preliminary) results for
light-meson masses using staggered chiral perturbation theory including
electromagnetism, and discuss the extent to which quenched-photon simulations
can improve quark-mass calculations. | hep-lat |
Towards continuum limit of screening lengths with chiral Fermions: We investigate mesonic screening correlators at T=2T_c using the overlap
Fermions in the quenched approximation, where T_c is the QCD phase transition
temperature. Using lattices with temporal extent up to 8, we found that both
pseudoscalar and vector correlators exhibit a nice $cosh$ behaviour, leading to
a plateau behaviour in the local screening masses as a function of distance.
The rho and pi masses so determined show very little variation with the lattice
spacing a. This augurs well for the use of chiral Fermions, and further
suggests the small deviations of these masses from the ideal gas values are
genuine effects of interactions. | hep-lat |
The rate of photon production in the quark-gluon plasma from lattice QCD: We calculate the thermal rate of real-photon production in the quark-gluon
plasma at a temperature of $T=254$ MeV using lattice QCD. The calculation is
based on the difference between the spatially transverse and longitudinal parts
of the polarization tensor, which has the advantage of falling off rapidly at
large frequencies. We obtain this linear combination in the time-momentum
representation from lattice QCD with two flavors of quarks in the continuum
limit with a precision of about two parts per mille. Applying a theoretically
motivated fit ansatz for the associated spectral function, we obtain values for
the photon rate that are in line with QCD weak-coupling calculations; for
photon momenta $ 1.0\leq k[{\rm GeV}]\leq 1.4$, our non-perturbative results
constrain the rate to be no larger than twice the weak-coupling prediction. We
also provide a physics interpretation of the electromagnetic spectral functions
valid for all frequencies and momenta. | hep-lat |
Localised Dirac eigenmodes and Goldstone's theorem at finite temperature: I show that a finite density of near-zero localised Dirac modes can lead to
the disappearance of the massless excitations predicted by the
finite-temperature version of Goldstone's theorem in the chirally broken phase
of a gauge theory. | hep-lat |
Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory: We measure the vacuum energy of two-dimensional N=(2,2) super Yang-Mills
theory using lattice simulation. The obtained vacuum energy density is
E_0=0.09(9)(+10-8) g^2, where the first error is the systematic and the second
is the statistical one, measured in the dimensionful gauge coupling g which
governs the scale of the system. The result is consistent with unbroken
supersymmetry, although we cannot exclude a possible very small non-zero vacuum
energy. | hep-lat |
Machine-learning physics from unphysics: Finding deconfinement
temperature in lattice Yang-Mills theories from outside the scaling window: We study the machine learning techniques applied to the lattice gauge
theory's critical behavior, particularly to the confinement/deconfinement phase
transition in the SU(2) and SU(3) gauge theories. We find that the neural
network, trained on lattice configurations of gauge fields at an unphysical
value of the lattice parameters as an input, builds up a gauge-invariant
function, and finds correlations with the target observable that is valid in
the physical region of the parameter space. In particular, if the algorithm
aimed to predict the Polyakov loop as the deconfining order parameter, it
builds a trace of the gauge group matrices along a closed loop in the time
direction. As a result, the neural network, trained at one unphysical value of
the lattice coupling $\beta$ predicts the order parameter in the whole region
of the $\beta$ values with good precision. We thus demonstrate that the machine
learning techniques may be used as a numerical analog of the analytical
continuation from easily accessible but physically uninteresting regions of the
coupling space to the interesting but potentially not accessible regions. | hep-lat |
Energy--momentum tensor on the lattice: recent developments: It is conceivable that the construction of the energy--momentum tensor (EMT)
in lattice field theory enlarges our ability in lattice field theory and also
deepens our understanding on EMT at the non-pertubative level. In this talk, I
will review recent developments in this enterprise. | hep-lat |
A Critical Surface of Chiral-invariant System with Gauge Boson and
Fermions: In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and
four-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson
equation for the fermion self-energy function is studied on a lattice. We find
that a sensible infrared limit can be defined on a critical surface, which is
consistent with the critical line found in the continuum theory. | hep-lat |
End-to-end distribution function for dilute polymers: We study the end-to-end distribution function for dilute polymers. We present
a computation to order $O(\epsilon^2)$, $\epsilon = 4 - d$, and discuss in
detail its asymptotic behaviour for small and large distances. The theoretical
predictions are compared with Monte Carlo results, finding good agreement. | hep-lat |
Imaginary chemical potential and finite fermion density on the lattice: Standard lattice fermion algorithms run into the well-known sign problem at
real chemical potential. In this paper we investigate the possibility of using
imaginary chemical potential, and argue that it has advantages over other
methods, particularly for probing the physics at finite temperature as well as
density. As a feasibility study, we present numerical results for the partition
function of the two-dimensional Hubbard model with imaginary chemical
potential.
We also note that systems with a net imbalance of isospin may be simulated
using a real chemical potential that couples to I_3 without suffering from the
sign problem. | hep-lat |
Calculation of Moments of Structure Functions: The progress on the lattice computation of low moments of both the
unpolarised and polarised nucleon structure functions is reviewed with
particular emphasis on continuum and chiral extrapolations and comparison
between quenched and unquenched fermions. | hep-lat |
Near-Physical Point Lattice Calculation of Isospin-Breaking Corrections
to $K_{\ell2}/π_{\ell2}$: In recent years, lattice determinations of non-perturbative quantities such
as $f_K$ and $f_\pi$, which are relevant for $V_{us}$ and $V_{ud}$, have
reached an impressive precision of $\mathcal{O}(1\%)$ or better. To make
further progress, electromagnetic and strong isospin breaking effects must be
included in lattice QCD simulations.
We present the status of the RBC/UKQCD lattice calculation of
isospin-breaking corrections to light meson leptonic decays. This computation
is performed in a (2+1)-flavor QCD simulation using Domain Wall Fermions with
near-physical quark masses. The isospin-breaking effects are implemented via a
perturbative expansion of the action in $\alpha$ and $(m_u-m_d)$. In this
calculation, we work in the electro-quenched approximation and the photons are
implemented in the Feynman gauge and $\text{QED}_\text{L}$ formulation. | hep-lat |
Kaon decays and other hadronic processes in lattice QCD: This thesis deals with the study of properties and interactions of light
mesons. Specifically, we focus on hadronic decay and scattering processes,
which are dominated by effects of the strong interaction in the low-energy
regime. A peculiarity of the strong interaction is that perturbative expansions
fail at hadronic energy scales. Thus, genuine nonperturbative tools are
essential to obtain first-principles predictions. Here we use Lattice Field
Theory, and Effective Field Theories. The mathematical formulation of Quantum
Chromodynamics (QCD) and the methods to resolve its dynamics will be addressed
in Chapter 1. The research of this dissertation is divided in two parts.
Chapter 2 describes our study of the 't Hooft limit of QCD using lattice
simulations, while in Chapter 3 we consider processes that involve
multiparticle states. The 't Hooft limit provides a simplification of
nonabelian gauge theories that leads to nonperturbative predictions. We will
analyze the scaling with the number of colours of various observables, such as
meson masses, decay constants and weak matrix elements. A question we address
is the origin of the long-standing puzzle of the $\Delta I=1/2$ rule, that is,
the large hierarchy in the isospin amplitudes of the $K \to \pi\pi$ weak decay.
Regarding multiparticle processes, we will discuss generalizations of the
L\"uscher formalism to explore three-particle processes from lattice
simulations. The focus will be on our contributions, such as our implementation
of the finite-volume formalism that includes higher partial waves, and the
first application of the formalism to a full lattice QCD spectrum. We will also
comment on the extension of the approach to generic three-pion systems. A
summary in Spanish will be given in Chapter 4. The final part of the thesis
(Part II) includes the peer-reviewed publications in their original published
form. | hep-lat |
A non-perturbative mechanism for elementary particle mass generation: Taking inspiration from lattice QCD data, we argue that a finite
non-perturbative contribution to the quark mass is generated as a consequence
of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn
triggered by the explicitly breaking of chiral symmetry induced by the critical
Wilson term in the action. In pure lattice QCD this mass term cannot be
separated from the unavoidably associated linearly divergent contribution.
However, if QCD is enlarged to a theory where also a scalar field is present,
coupled to an SU(2) doublet of fermions via a Yukawa and a Wilson-like term,
then in the phase where the scalar field takes a non-vanishing expectation
value, a dynamically generated and "naturally" light fermion mass (numerically
unrelated to the expectation value of the scalar field) is conjectured to
emerge at a critical value of the Yukawa coupling where the symmetry of the
model is maximally enhanced. Masses dynamically generated in this way display a
natural hierarchy according to which the stronger is the strongest of the
interactions the fermion is subjected to the larger is its mass. | hep-lat |
Quark chiral condensate from the overlap quark propagator: From the overlap lattice quark propagator calculated in the Landau gauge, we
determine the quark chiral condensate by fitting operator product expansion
formulas to the lattice data. The quark propagators are computed on domain wall
fermion configurations generated by the RBC-UKQCD Collaborations with $N_f=2+1$
flavors. Three ensembles with different light sea quark masses are used at one
lattice spacing $1/a=1.75(4)$ GeV. We obtain
$\langle\bar\psi\psi\rangle^{\overline{\rm MS}}(2\mbox{
GeV})=(-305(15)(21)\mbox{ MeV})^3$ in the SU(2) chiral limit. | hep-lat |
The QCD phase diagram for small chemical potentials: We compute derivatives of thermodynamic quantities with respect to $\mu$, at
$\mu=0$ for 2 and 3 flavors of degenerate quark masses. This allows us to
estimate the phase transition line in the $T,\mu$ plane and quantify the
influence of a non vanishing chemical potential on the equation of state by
computing lines of constant energy, pressure and density. Moreover we evaluate
the order of the QCD phase transition by measuring the Binder Cumulant of the
chiral condensate. This gives access to the chiral critical point on the phase
transition line. | hep-lat |
Lattice QCD with Classical and Quantum Electrodynamics: We are doubtlessly familiar with some edition of Jackson's tome on
electrodynamics, and Schwinger's calculation of the anomalous magnetic moment
of the electron in QED. From the perspective of strong interactions, however,
electromagnetic effects usually amount to negligible contributions. Despite
this fact, electromagnetic probes have always been a fundamental source for our
knowledge of QCD experimentally. Elastic scattering of electrons off nucleons
provides us a window to their distributions of charge and magnetism. To account
for the spectrum of QCD at the percent level, moreover, we need isospin
breaking introduced from both quark masses and electric charges. This overview
concerns some of the prospects and progress of studying electromagnetic effects
in QCD. Our focus is divided between classical and quantum effects. In
classical electromagnetic fields, the dynamical response of QCD to external
conditions can be investigated. The vacuum and hadrons alike should be viewed
as media which respond to external fields: both magnetize and polarize in
magnetic fields, for example. At the quantum level, electromagnetism and QCD
renormalize each other. In the era of high precision lattice computations, both
strong and electromagnetic contributions must be accounted for to make
predictions at the percent level. | hep-lat |
Hadron Spectrum from Dynamical Lattice QCD Simulations: Recent progress in unquenched lattice QCD simulations is reviewed with
emphasis on understanding of chiral behavior for light quark masses. | hep-lat |
Higher representations on the lattice: perturbative studies: We present analytical results to guide numerical simulations with Wilson
fermions in higher representations of the colour group. The ratio of $\Lambda$
parameters, the additive renormalization of the fermion mass, and the
renormalization of fermion bilinears are computed in perturbation theory,
including cactus resummation. We recall the chiral Lagrangian for the different
patterns of symmetry breaking that can take place with fermions in higher
representations, and discuss the possibility of an Aoki phase as the fermion
mass is reduced at finite lattice spacing. | hep-lat |
A guide to light-cone PDFs from Lattice QCD: an overview of approaches,
techniques and results: Within the theory of Quantum Chromodynamics (QCD), the rich structure of
hadrons can be quantitatively characterized, among others, using a basis of
universal non-perturbative functions: parton distribution functions (PDFs),
generalized parton distributions (GPDs), transverse-momentum dependent
distributions (TMDs) and distribution amplitudes (DAs). For more than half a
century, there has been a joint experimental and theoretical effort to obtain
these partonic functions. However, the complexity of the strong interactions
has placed severe limitations, and first-principle results on the distributions
was extracted mostly from their moments computed in Lattice QCD. Recently,
breakthrough ideas changed the landscape and several approaches were proposed
to access the distributions themselves on the lattice.
In this paper, we review in considerable detail approaches directly related
to partonic distributions. We highlight a recent idea proposed by X. Ji on
extracting quasi-distributions that spawned renewed interest in the whole field
and sparked the largest amount of numerical studies of Lattice QCD. We discuss
theoretical and practical developments, including challenges that had to be
overcome, with some yet to be handled. We also review numerical results,
including a discussion based on evolving understanding of the underlying
concepts and theoretical and practical progress. Particular attention is given
to important aspects that validated the quasi-distribution approach, such as
renormalization, matching to light-cone distributions and lattice techniques.
In addition to a thorough discussion of quasi-distributions, we consider
other approaches: hadronic tensor, auxiliary quark methods, pseudo-PDFs, OPE
without OPE and good lattice cross sections. In closing, we provide prospects
of the field, with emphasis on the necessary conditions to obtain results with
controlled uncertainties. | hep-lat |
Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum: As a probe of the Yang-Mills vacuum, we study numerically the eigenmode
spectrum of the covariant lattice Laplacian operator. We find that the
eigenmodes at the low and high ends of the spectrum are localized in finite
regions whose volume is insensitive to the lattice volume. We also find that
the vacuum is seen very differently by localized modes of the covariant
Laplacian in different representations of the gauge group. In the fundamental
representation, the data suggests that the localization volume is finite in
physical units set by the string tension, and localization disappears when
center vortices are removed. In the adjoint and j=3/2 representations the low
and high-lying modes are far more localized, and the localization volume
appears to scale to zero, in physical units, in the continuum limit. The
adjoint Laplacian is insensitive to vortex removal, but we find that
exponential localization is absent for adjoint eigenmodes in the Higgs phase of
a gauge-Higgs theory. Localization is also absent in the spectrum of the
Coulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement
scenarios. | hep-lat |
Extraction of $|V_{cd}|$ and $|V_{cs}|$ from experimental decay rates
using lattice QCD $D \to π(K) \ell ν$ form factors: We present a determination of the Cabibbo-Kobayashi-Maskawa matrix elements
$|V_{cd}|$ and $|V_{cs}|$ obtained by combining the momentum dependence of the
semileptonic vector form factors $f_+^{D \to \pi}(q^2)$ and $f_+^{D \to
K}(q^2)$, recently determined from lattice QCD simulations, with the
differential rates measured for the semileptonic $D \to \pi \ell \nu$ and $D
\to K \ell \nu$ decays. Our analysis is based on the results for the
semileptonic form factors produced by the European Twisted Mass Collaboration
with $N_f = 2 + 1 + 1$ flavors of dynamical quarks in the whole range of values
of the squared 4-momentum transfer accessible in the experiments. The
statistical and systematic correlations between the lattice data as well as
those present in the experimental data are properly taken into account. With
respect to the standard procedure based on the use of only the vector form
factor at zero 4-momentum transfer, we obtain more precise and consistent
results: $|V_{cd} |= 0.2341 ~ (74)$ and $|V_{cs} |= 0.970 ~ (33)$. The
second-row CKM unitarity is fulfilled within the current uncertainties:
$|V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.996 ~ (64)$. Moreover, using for the
first time hadronic inputs determined from first principles, we have calculated
the ratio of the semileptonic $D \to \pi(K)$ decay rates into muons and
electrons, which represent a test of lepton universality within the SM,
obtaining in the isospin-symmetric limit of QCD: ${\cal{R}}_{LU}^{D\pi} =
0.985~(2)$ and ${\cal{R}}_{LU}^{DK} = 0.975~(1)$. | hep-lat |
Memory efficient finite volume schemes with twisted boundary conditions: In this paper we explore a finite volume renormalization scheme that combines
three main ingredients: a coupling based on the gradient flow, the use of
twisted boundary conditions and a particular asymmetric geometry, that for
$SU(N)$ gauge theories consists on a hypercubic box of size $l^2 \times
(Nl)^2$, a choice motivated by the study of volume independence in large $N$
gauge theories. We argue that this scheme has several advantages that make it
particularly suited for precision determinations of the strong coupling, among
them translational invariance, an analytic expansion in the coupling and a
reduced memory footprint with respect to standard simulations on symmetric
lattices, allowing for a more efficient use of current GPU clusters. We test
this scheme numerically with a determination of the $\Lambda$ parameter in the
$SU(3)$ pure gauge theory. We show that the use of an asymmetric geometry has
no significant impact in the size of scaling violations, obtaining a value
$\Lambda_{\overline{MS}} \sqrt{8 t_0} =0.603(17)$ in good agreement with the
existing literature. The role of topology freezing, that is relevant for the
determination of the coupling in this particular scheme and for large $N$
applications, is discussed in detail. | hep-lat |
Quenched hadron spectroscopy with improved staggered quark action: We investigate light hadron spectroscopy with an improved quenched staggered
quark action. We compare the results obtained with an improved gauge plus an
improved quark action, an improved gauge plus standard quark action, and the
standard gauge plus standard quark action. Most of the improvement in the
spectroscopy results is due to the improved gauge sector. However, the improved
quark action substantially reduces violations of Lorentz invariance, as
evidenced by the meson dispersion relations. | hep-lat |
Hadron Spectrum in QCD with Valence Wilson Fermions and Dynamical
Staggered Fermions at $6/g^2=5.6: We present an analysis of hadronic spectroscopy for Wilson valence quarks
with dynamical staggered fermions at lattice coupling $6/g^2 = \beta=5.6$ at
sea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched
approximation at $\beta=5.85$ and 5.95, both on $16^3 \times 32$ lattices. We
make comparisons with our previous results with dynamical staggered fermions at
the same parameter values but on $16^4$ lattices doubled in the temporal
direction. | hep-lat |
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