115 research outputs found
The scalar pion form factor in two-flavor lattice QCD
We calculate the scalar form factor of the pion using two dynamical flavors
of non-perturbatively -improved Wilson fermions, including both
the connected and the disconnected contribution to the relevant correlation
functions. We employ the calculation of all-to-all propagators using stochastic
sources and a generalized hopping parameter expansion. From the form factor
data at vanishing momentum transfer, , and two non-vanishing we
obtain an estimate for the scalar radius \left^\pi_{_{\rm S}} of
the pion at one value of the lattice spacing and for five different pion
masses. Using Chiral Perturbation Theory at next-to-leading order, we find
\left^\pi_{_{\rm S}}=0.635\pm0.016 fm at the physical pion
mass (statistical error only). This is in good agreement with the
phenomenological estimate from -scattering. The inclusion of the
disconnected contribution is essential for achieving this level of agreement.Comment: 15 pages, 10 pdf figures, uses revtex4-1; version to appear in PR
Towards non-linear quadrature formulae
Prompted by an observation about the integral of exponential functions of the
form , we investigate the possibility to
exactly integrate families of functions generated from a given function by
scaling or by affine transformations of the argument using nonlinear
generalizations of quadrature formulae. The main result of this paper is that
such formulae can be explicitly constructed for a wide class of functions, and
have the same accuracy as Newton-Cotes formulae based on the same nodes. We
also show how Newton-Cotes formulae emerge as the linear case of our general
formalism, and demonstrate the usefulness of the nonlinear formulae in the
context of the Pad\'e-Laplace method of exponential analysis.Comment: 14 pages, 3 figures (24 pdf files
Pad\'e and Pad\'e-Laplace Methods for masses and matrix elements
The problem of having to reconstruct the decay rates and corresponding
amplitudes of the single-exponential components of a noisy multi-exponential
signal is common in many other areas of physics and engineering besides lattice
field theory, and it can be helpful to study the methods devised and used for
that purpose in those contexts in order to get a better handle on the problem
of extracting masses and matrix elements from lattice correlators. Here we
consider the use of Pad\'e and Pad\'e-Laplace methods, which have found wide
use in laser fluorescence spectroscopy and beyond, emphasizing the importance
of using robust Pad\'e approximants to avoid spurious poles. To facilitate the
accurate evaluation of the Laplace transform required for the Pad\'e-Laplace
method, we also present a novel approach to the numerical quadrature of
multi-exponential functions.Comment: 6 pages, 4 PDF figures; poster presented at 39th International
Symposium on Lattice Field Theory (Lattice2022), 8-13 August, 2022, Bonn,
German
Open Source Software and the āPrivate-Collectiveā Innovation Model: Issues for Organization Science
Currently two models of innovation are prevalent in organization science. The "private investment"
model assumes returns to the innovator results from private goods and efficient regimes of
intellectual property protection. The "collective action" model assumes that under conditions of
market failure, innovators collaborate in order to produce a public good. The phenomenon of open
source software development shows that users program to solve their own as well as shared technical
problems, and freely reveal their innovations without appropriating private returns from selling the
software. In this paper we propose that open source software development is an exemplar of a
compound model of innovation that contains elements of both the private investment and the
collective action models. We describe a new set of research questions this model raises for scholars in
organization science. We offer some details regarding the types of data available for open source
projects in order to ease access for researchers who are unfamiliar with these, and als
CROSSROADSāIdentifying Viable āNeedāSolution Pairsā: Problem Solving Without Problem Formulation
Problem-solving research and formal problem-solving practice begin with the assumption that a problem has been identified or formulated for solving. The problem-solving process then involves a search for a satisfactory or optimal solution to that problem. In contrast, we propose that, in informal problem solving, a need and a solution are often discovered together and tested for viability as a āneedāsolution pair.ā For example, one may serendipitously discover a new solution and assess it to be worth adopting although the āproblemā it would address had not previously been in mind as an object of search or even awareness. In such a case, problem identification and formulation, if done at all, come only after the discovery of the needāsolution pair.
We propose the identification of needāsolution pairs as an approach to problem solving in which problem formulation is not required. We argue that discovery of viable needāsolution pairs without problem formulation may have advantages over problem-initiated problem-solving methods under some conditions. First, it removes the often considerable costs associated with problem formulation. Second, it eliminates the constraints on possible solutions that any problem formulation will inevitably apply
physics from fine lattices
We present a preliminary analysis of the charm quark mass and the mass and
decay constant of the meson obtained from dynamical simulations
of Wilson QCD on the large and fine lattices simulated by the CLS
effort.Comment: 6 pages, 2 figures; talk presented at Lattice 2008, XXVI
International Symposium on Lattice Field Theory, July 14-19, 2008,
Williamsburg, Virginia, US
The Shape of Covariantly Smeared Sources in Lattice QCD
Covariantly smeared sources are commonly used in lattice QCD to enhance the
projection onto the ground state. Here we investigate the dependence of their
shape on the gauge field background and find that the presence of localized
concentrations of magnetic field can lead to strong distortions which reduce
the smearing radii achievable by iterative smearing prescriptions. In
particular, as , iterative procedures like Jacobi smearing require
increasingly large iteration counts in order to reach physically-sized smearing
radii 0.5 fm, and the resulting sources are strongly distorted. To
bypass this issue, we propose a covariant smearing procedure (``free-form
smearing'') that allows us to create arbitrarily shaped sources, including in
particular Gaussians of arbitrary radius.Comment: 1+15 pages, 7 figures (24 pdf images
Lattice QCD calculation of hadronic light-by-light scattering
We perform a lattice QCD calculation of the hadronic light-by-light
scattering amplitude in a broad kinematical range. At forward kinematics, the
results are compared to a phenomenological analysis based on dispersive sum
rules for light-by-light scattering. The size of the pion pole contribution is
investigated for momenta of typical hadronic size. The presented numerical
methods can be used to compute the hadronic light-by-light contribution to the
anomalous magnetic moment of the muon. Our calculations are carried out in
two-flavor QCD with the pion mass in the range of 270 to 450MeV, and contain so
far only the diagrams with fully connected quark lines.Comment: 5 pages, 5 figure
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