64 research outputs found
Higher-Order Corrections to Instantons
The energy levels of the double-well potential receive, beyond perturbation
theory, contributions which are non-analytic in the coupling strength; these
are related to instanton effects. For example, the separation between the
energies of odd- and even-parity states is given at leading order by the
one-instanton contribution. However to determine the energies more accurately
multi-instanton configurations have also to be taken into account. We
investigate here the two-instanton contributions. First we calculate
analytically higher-order corrections to multi-instanton effects. We then
verify that the difference betweeen numerically determined energy eigenvalues,
and the generalized Borel sum of the perturbation series can be described to
very high accuracy by two-instanton contributions. We also calculate
higher-order corrections to the leading factorial growth of the perturbative
coefficients and show that these are consistent with analytic results for the
two-instanton effect and with exact data for the first 200 perturbative
coefficients.Comment: 7 pages, LaTe
Convergence Acceleration Techniques
This work describes numerical methods that are useful in many areas: examples
include statistical modelling (bioinformatics, computational biology),
theoretical physics, and even pure mathematics. The methods are primarily
useful for the acceleration of slowly convergent and the summation of divergent
series that are ubiquitous in relevant applications. The computing time is
reduced in many cases by orders of magnitude.Comment: 6 pages, LaTeX; provides an easy-to-understand introduction to the
field of convergence acceleratio
Resummed event shapes at hadron colliders
We present recently defined jet-observables for hadron-hadron dijet
production, which are designed to reconcile the seemingly conflicting
theoretical requirement of globalness, which makes it possible to resum them
(automatically) at NLL accuracy and the limited experimental reach of
detectors, so that they are measurable at the Tevatron and at the LHC.Comment: 7 pages, Talk given at the XXXIV International Symposium on
Multiparticle Dynamics, Sonoma, July 26 - August 1, 200
Microscopic universality with dynamical fermions
It has recently been demonstrated in quenched lattice simulations that the
distribution of the low-lying eigenvalues of the QCD Dirac operator is
universal and described by random-matrix theory. We present first evidence that
this universality continues to hold in the presence of dynamical quarks. Data
from a lattice simulation with gauge group SU(2) and dynamical staggered
fermions are compared to the predictions of the chiral symplectic ensemble of
random-matrix theory with massive dynamical quarks. Good agreement is found in
this exploratory study. We also discuss implications of our results.Comment: 5 pages, 3 figures, minor modifications, to appear in Phys. Rev. D
(Rapid Commun.
Testing and improving the numerical accuracy of the NLO predictions
I present a new and reliable method to test the numerical accuracy of NLO
calculations based on modern OPP/Generalized Unitarity techniques. A convenient
solution to rescue most of the detected numerically inaccurate points is also
proposed.Comment: References added. 1 Table added. Version accepted for publicatio
Generalized resummation of QCD final-state observables
The resummation of logarithmically-enhanced terms to all perturbative orders
is a prerequisite for many studies of QCD final-states. Until now such
resummations have always been performed by hand, for a single observable at a
time. In this letter we present a general `master' resummation formula (and
applicability conditions), suitable for a large class of observables. This
makes it possible for next-to-leading logarithmic resummations to be carried
out automatically given only a computer routine for the observable. To
illustrate the method we present the first next-to-leading logarithmic resummed
prediction for an event shape in hadronic dijet production.Comment: 9 pages, 1 figure; v2 includes substantial amplifications and
clarification
Calculating multivariate ruin probabilities via Gaver–Stehfest inversion technique.
Multivariate characteristics of risk processes are of high interest to academic actuaries. In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using the Gaver–Stehfest method of inverting Laplace transforms. This approach can be considered to be an alternative to recursive methods previously used in actuarial literatureMultivariate ultimate ruin probability; Laplace transform; Integral equations; Numerical methods;
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