31 research outputs found
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
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
HQET at order : II. Spectroscopy in the quenched approximation
Using Heavy Quark Effective Theory with non-perturbatively determined
parameters in a quenched lattice calculation, we evaluate the splittings
between the ground state and the first two radially excited states of the
system at static order. We also determine the splitting between first excited
and ground state, and between the and ground states to order
. The Generalized Eigenvalue Problem and the use of all-to-all
propagators are important ingredients of our approach.Comment: (1+18) pages, 3 figures (4 pdf files); pdflatex; v2: corrections to
table 1, results unaffecte
From Expert Discipline to Common Practice: A Vision and Research Agenda for Extending the Reach of Enterprise Modeling
The benefits of enterprise modeling (EM) and its contribution to organizational tasks are largely undisputed in business and information systems engineering. EM as a discipline has been around for several decades but is typically performed by a limited number of people in organizations with an affinity to modeling. What is captured in models is only a fragment of what ought to be captured. Thus, this research note argues that EM is far from its maximum potential. Many people develop some kind of model in their local practice without thinking about it consciously. Exploiting the potential of this âgrass roots modelingâ could lead to groundbreaking innovations. The aim is to investigate integration of the established practices of modeling with local practices of creating and using model-like artifacts of relevance for the overall organization. The paper develops a vision for extending the reach of EM, identifies research areas contributing to the vision and proposes elements of a future research Agenda
Charm quark mass and D-meson decay constants from two-flavour lattice QCD
We present a computation of the charm quark's mass and the leptonic D-meson decay constants f_D and f_{D_s} in two-flavour lattice QCD with non-perturbatively O(a) improved Wilson quarks. Our analysis is based on the CLS configurations at two lattice spacings (a=0.065 and 0.048 fm, where the lattice scale is set by f_K) and pion masses ranging down to ~ 190 MeV at L*m_pi > 4, in order to perform controlled continuum and chiral extrapolations with small systematic uncertainties
Charm quark mass and D-meson decay constants from two-flavour lattice QCD
We present a computation of the charm quark's mass and the leptonic D-meson decay constants f_D and f_{D_s} in two-flavour lattice QCD with non-perturbatively O(a) improved Wilson quarks. Our analysis is based on the CLS configurations at two lattice spacings (a=0.065 and 0.048 fm, where the lattice scale is set by f_K) and pion masses ranging down to ~ 190 MeV at L*m_pi > 4, in order to perform controlled continuum and chiral extrapolations with small systematic uncertainties
Electromagnetic form factors and axial charge of the nucleon from Nf = 2 + 1 Wilson fermions
We present an update on our determination of the electromagnetic form factors and axial charge of the nucleon from the Nf = 2 + 1 CLS ensembles with increased statistics and an additional finer lattice spacing. We also investigate the impact of O(a)-improvement of the currents