Numerical Evaluation of Partial Wave Contributions to Pion–Nucleon Amplitudes

1974 ◽  
Vol 52 (8) ◽  
pp. 731-742 ◽  
Author(s):  
Robert C. Brunet
Keyword(s):  
Partial Wave ◽  
Fourth Order ◽  
Numerical Evaluation ◽  
Padé Approximants ◽  
Feynman Diagrams ◽  
Order Perturbation ◽  
Pade Approximants ◽  
Pion Nucleon ◽  
Low Order

We present detailed numerical evaluations of the partial wave projections of Feynman diagrams of second- and fourth-order in perturbation for the πN–πN scattering in the [Formula: see text] theory. Perturbative contributions to the S, P, and D waves of isospin 1/2 and 3/2 are given in tables of numerical values. Figures regrouping these results show surprising behavior for the ratios Re(4)/Re(2). These tables and figures allow easy calculations with models using low order perturbation terms such as Padé approximants.

scholarly journals An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
P. Hunana ◽  
A. Tenerani ◽  
G. P. Zank ◽  
M. L. Goldstein ◽  
G. M. Webb ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Fourth Order ◽  
Low Frequency ◽  
Padé Approximants ◽  
Landau Damping ◽  
Order Moment ◽  
Fluid Models ◽  
Frequency Limit ◽  
Long Wavelength ◽  
Pade Approximants

In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma response function $R(\unicode[STIX]{x1D701})=1+\unicode[STIX]{x1D701}Z(\unicode[STIX]{x1D701})=-Z^{\prime }(\unicode[STIX]{x1D701})/2$ . We then consider a one-dimensional (1-D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourth-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1-D closures at higher-order moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3-D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the fourth-order moment level. In appendix A, we provide comprehensive tables with Padé approximants of $R(\unicode[STIX]{x1D701})$ up to the eighth-pole order, with many given in an analytic form.

scholarly journals Low energy pion-nucleon phase shifts from a Padé approximants' approach

1968 ◽  
Vol 27 (1) ◽  
pp. 34-37
Author(s):  
E. Remiddi ◽  
M. Pusterla ◽  
J.A. Mignaco
Keyword(s):  
Padé Approximants ◽  
Phase Shifts ◽  
Low Energy ◽  
Pade Approximants ◽  
Pion Nucleon

scholarly journals Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams

1997 ◽  
Vol 56 (11) ◽  
pp. 6980-6992 ◽  
Author(s):  
Stanley J. Brodsky ◽  
John Ellis ◽  
Einan Gardi ◽  
Marek Karliner ◽  
Mark A. Samuel
Keyword(s):  
Padé Approximants ◽  
Feynman Diagrams ◽  
Pade Approximants

Pion-nucleon phase shifts and Padé approximants

1973 ◽  
Vol 53 (1) ◽  
pp. 191-196 ◽  
Author(s):  
M.C. Bergere ◽  
J.M. Drouffe
Keyword(s):  
Padé Approximants ◽  
Phase Shifts ◽  
Pade Approximants ◽  
Pion Nucleon

CALCULATION OF TWO-LOOP VERTEX FUNCTIONS FROM THEIR SMALL MOMENTUM EXPANSION

1995 ◽  
Vol 06 (04) ◽  
pp. 495-501 ◽  
Author(s):  
J. FLEISCHER
Keyword(s):  
Conformal Mapping ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Padé Approximants ◽  
Feynman Diagrams ◽  
Powerful Method ◽  
Small Momentum ◽  
Numerical Examples ◽  
Pade Approximants

In a recent paper1 a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared, a certain conformal mapping and subsequent resummation by means of Padé approximants. I present numerical examples.

Sign in / Sign up

Export Citation Format

Share Document