Search results for "Padé approximant"
showing 10 items of 14 documents
Complex singularities in KdV solutions
2016
In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.
Strong-coupling expansion for the anharomonic oscillators −d2/dx 2+x 2+λx 2N
1992
A perturbation expansion based on a modified and scaled harmonic oscillator combined with Pade extrapolation techniques has been used to determine the expansion of the ground-state energy in fractional and negative powers of the coupling constant, valid for large values of λ.
Padé approximants and the prediction of non-perturbative parameters in particle physics
2010
Conference on Approximation and extrapolation of Convergent and Divergent Sequences and Series Luminy, FRANCE, SEP 28-OCT 02, 2009
Phenomenological applications of rational approximants
2016
We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function [Formula: see text] is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract [Formula: see text] from the semileptonic [Formula: see text] decays. Finally, the [Formula: see text] vector form factor in the TL region is explored using QAs.
Precise determination of resonance pole parameters through Pad\'e approximants
2014
In this work, we present a precise and model--independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Pad\'e approximants. Precise theoretical parameterizations of pion-pion scattering phase shifts based on once-- and twice-- subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrization the pole positions of the $f_0(500)$ at $\sqrt{s}=(453\pm 15) - i(297 \pm 15)$ MeV, the $\rho(770)$ at $\sq…
Riccati-Padé quantization and oscillatorsV(r)=grα
1993
We develop an alternative construction of bound states based on matching the Riccati threshold and asymptotic expansions via their two-point Pad\'e interpolation. As a form of quantization it gives highly accurate eigenvalues and eigenfunctions.
Pseudoscalar decays into lepton pairs from rational approximants
2016
The pseudoscalar decays into lepton pairs P! ‘‘ are analyzed with the machinery of Canterbury approximants, an extension of Pade approximants to bivariate functions. This framework provides an ideal model-independent approach to implement all our knowledge of the pseudoscalar transition form factors driving these decays, can be used for data analysis, and allows to include experimental data and theoretical constraints in an easy way, and determine a systematic error. We find that previous theoretical estimates for these branching ratios have underestimated their theoretical uncertainties. From our updated results, the existing experimental discrepancies for p 0 ! e + e and h! m + m channels…
High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices
1999
We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings \(\). In these star-graph expansions up to order 22 in the inverse temperature \(\), the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling Kc and the critical exponent \(\) of the spin-glass susceptibility in a large region of …
Updated pseudoscalar contributions to the hadronic light-by-light of the muon (g-2)
2016
In this work, we present our recent results on a new and alternative data-driven determination for the hadronic light-by-light pseudoscalar-pole contribution to the muon $(g-2)$. Our approach is based on Canterbury approximants, a rational approach to describe the required transition form factors, which provides a systematic and model-independent framework beyond traditional large-$N_c$ approaches. As a result, we obtain a competitive determination with errors according to future $(g-2)$ experiments including, for the first time, a well-defined systematic uncertainty.
η and η′ transition form factors from Padé approximants
2014
We employ a systematic and model-independent method to extract, from space- and time-like data, the η and η′ transition form factors (TFFs) obtaining the most precise determination for their low-energy parameters and discuss the Γη→γγ impact on them. Using TFF data alone, we also extract the η − η′ mixing parameters, which are compatible to those obtained from more sophisticated and input-demanding procedures.