Towards non-linear quadrature formulae

Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda\mathrm{e}^{\alpha x}$, 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 $a\to 0$, iterative procedures like Jacobi smearing require increasingly large iteration counts in order to reach physically-sized smearing radii $r_{sm}\sim$ 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 1/m1/m: 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 $B_s$ system at static order. We also determine the splitting between first excited and ground state, and between the $B_s^*$ and $B_s$ ground states to order $1/m_b$. 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 “grass roots modeling” 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