544 research outputs found
The QCD sign problem and dynamical simulations of random matrices
At nonzero quark chemical potential dynamical lattice simulations of QCD are
hindered by the sign problem caused by the complex fermion determinant. The
severity of the sign problem can be assessed by the average phase of the
fermion determinant. In an earlier paper we derived a formula for the
microscopic limit of the average phase for general topology using chiral random
matrix theory. In the current paper we present an alternative derivation of the
same quantity, leading to a simpler expression which is also calculable for
finite-sized matrices, away from the microscopic limit. We explicitly prove the
equivalence of the old and new results in the microscopic limit. The results
for finite-sized matrices illustrate the convergence towards the microscopic
limit. We compare the analytical results with dynamical random matrix
simulations, where various reweighting methods are used to circumvent the sign
problem. We discuss the pros and cons of these reweighting methods.Comment: 34 pages, 3 figures, references added, as published in JHE
Chiral Extrapolation of the Strangeness Changing K pi Form Factor
We perform a chiral extrapolation of lattice data on the scalar K pi form
factor and the ratio of the kaon and pion decay constants within Chiral
Perturbation Theory to two loops. We determine the value of the scalar form
factor at zero momentum transfer, at the Callan-Treiman point and at its soft
kaon analog as well as its slope. Results are in good agreement with their
determination from experiment using the standard couplings of quarks to the W
boson. The slope is however rather large. A study of the convergence of the
chiral expansion is also performed.Comment: few minor change
Lattice QCD at the physical point: Simulation and analysis details
We give details of our precise determination of the light quark masses
m_{ud}=(m_u+m_d)/2 and m_s in 2+1 flavor QCD, with simulated pion masses down
to 120 MeV, at five lattice spacings, and in large volumes. The details concern
the action and algorithm employed, the HMC force with HEX smeared clover
fermions, the choice of the scale setting procedure and of the input masses.
After an overview of the simulation parameters, extensive checks of algorithmic
stability, autocorrelation and (practical) ergodicity are reported. To
corroborate the good scaling properties of our action, explicit tests of the
scaling of hadron masses in N_f=3 QCD are carried out. Details of how we
control finite volume effects through dedicated finite volume scaling runs are
reported. To check consistency with SU(2) Chiral Perturbation Theory the
behavior of M_\pi^2/m_{ud} and F_\pi as a function of m_{ud} is investigated.
Details of how we use the RI/MOM procedure with a separate continuum limit of
the running of the scalar density R_S(\mu,\mu') are given. This procedure is
shown to reproduce the known value of r_0m_s in quenched QCD. Input from
dispersion theory is used to split our value of m_{ud} into separate values of
m_u and m_d. Finally, our procedure to quantify both systematic and statistical
uncertainties is discussed.Comment: 45 page
The scalar gluonium correlator: large-beta_0 and beyond
The investigation of the scalar gluonium correlator is interesting because it
carries the quantum numbers of the vacuum and the relevant hadronic current is
related to the anomalous trace of the QCD energy-momentum tensor in the chiral
limit. After reviewing the purely perturbative corrections known up to
next-next-to-leading order, the behaviour of the correlator is studied to all
orders by means of the large-beta_0 approximation. Similar to the QCD Adler
function, the large-order behaviour is governed by the leading ultraviolet
renormalon pole. The structure of infrared renormalon poles, being related to
the operator product expansion are also discussed, as well as a low-energy
theorem for the correlator that provides a relation to the renormalisation
group invariant gluon condensate, and the vacuum matrix element of the trace of
the QCD energy-momentum tensor.Comment: 14 pages, references added, discussion of IR renormalon pole at u=3
extended, similar version to appear in JHE
Singular values of the Dirac operator in dense QCD-like theories
We study the singular values of the Dirac operator in dense QCD-like theories
at zero temperature. The Dirac singular values are real and nonnegative at any
nonzero quark density. The scale of their spectrum is set by the diquark
condensate, in contrast to the complex Dirac eigenvalues whose scale is set by
the chiral condensate at low density and by the BCS gap at high density. We
identify three different low-energy effective theories with diquark sources
applicable at low, intermediate, and high density, together with their
overlapping domains of validity. We derive a number of exact formulas for the
Dirac singular values, including Banks-Casher-type relations for the diquark
condensate, Smilga-Stern-type relations for the slope of the singular value
density, and Leutwyler-Smilga-type sum rules for the inverse singular values.
We construct random matrix theories and determine the form of the microscopic
spectral correlation functions of the singular values for all nonzero quark
densities. We also derive a rigorous index theorem for non-Hermitian Dirac
operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE
Individual Eigenvalue Distributions for the Wilson Dirac Operator
We derive the distributions of individual eigenvalues for the Hermitian
Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac
Operator DW. The framework we provide is valid in the epsilon regime of chiral
perturbation theory for any number of flavours Nf and for non-zero low energy
constants W6, W7, W8. It is given as a perturbative expansion in terms of the
k-point spectral density correlation functions and integrals thereof, which in
some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at
fixed chirality nu this expansion truncates after at most nu terms for small
lattice spacing "a". Explicit examples for the distribution of the first and
second eigenvalue are given in the microscopic domain as a truncated expansion
of the Fredholm Pfaffian for quenched D5, where all k-point densities are
explicitly known from random matrix theory. For the real eigenvalues of
quenched DW at small "a" we illustrate our method by the finite expansion of
the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion
of W6 and W7 extende
Measuring every particle's size from three-dimensional imaging experiments
Often experimentalists study colloidal suspensions that are nominally
monodisperse. In reality these samples have a polydispersity of 4-10%. At the
level of an individual particle, the consequences of this polydispersity are
unknown as it is difficult to measure an individual particle size from
microscopy. We propose a general method to estimate individual particle radii
within a moderately concentrated colloidal suspension observed with confocal
microscopy. We confirm the validity of our method by numerical simulations of
four major systems: random close packing, colloidal gels, nominally
monodisperse dense samples, and nominally binary dense samples. We then apply
our method to experimental data, and demonstrate the utility of this method
with results from four case studies. In the first, we demonstrate that we can
recover the full particle size distribution {\it in situ}. In the second, we
show that accounting for particle size leads to more accurate structural
information in a random close packed sample. In the third, we show that crystal
nucleation occurs in locally monodisperse regions. In the fourth, we show that
particle mobility in a dense sample is correlated to the local volume fraction.Comment: 7 pages, 5 figure
The Mitochondrial Genome of Toxocara canis
Toxocara canis (Ascaridida: Nematoda), which parasitizes (at the adult stage) the small intestine of canids, can be transmitted to a range of other mammals, including humans, and can cause the disease toxocariasis. Despite its significance as a pathogen, the genetics, epidemiology and biology of this parasite remain poorly understood. In addition, the zoonotic potential of related species of Toxocara, such as T. cati and T. malaysiensis, is not well known. Mitochondrial DNA is known to provide genetic markers for investigations in these areas, but complete mitochondrial genomic data have been lacking for T. canis and its congeners. In the present study, the mitochondrial genome of T. canis was amplified by long-range polymerase chain reaction (long PCR) and sequenced using a primer-walking strategy. This circular mitochondrial genome was 14162 bp and contained 12 protein-coding, 22 transfer RNA, and 2 ribosomal RNA genes consistent for secernentean nematodes, including Ascaris suum and Anisakis simplex (Ascaridida). The mitochondrial genome of T. canis provides genetic markers for studies into the systematics, population genetics and epidemiology of this zoonotic parasite and its congeners. Such markers can now be used in prospecting for cryptic species and for exploring host specificity and zoonotic potential, thus underpinning the prevention and control of toxocariasis in humans and other hosts
- …