Non-degenerate perturbation theory. Test for a new perturbative expansion using some models of oscillator and rotator dynamics

1987 ◽  
Vol 20 (18) ◽  
pp. 4635-4647 ◽  
Author(s):  
A Grosjean ◽  
G Jolicard
Keyword(s):  
Perturbation Theory ◽  
Perturbative Expansion ◽  
Degenerate Perturbation Theory ◽  
Theory Test

The application of analytical methods in degenerate perturbation theory

1974 ◽  
Vol 21 (3) ◽  
pp. 1229-1233
Author(s):  
A. G. Makhanek ◽  
V. S. Korol'kov ◽  
A. F. Fedorov
Keyword(s):  
Perturbation Theory ◽  
Analytical Methods ◽  
Degenerate Perturbation Theory

scholarly journals PERTURBATIVE EXPANSION OF τ HADRONIC SPECTRAL FUNCTION MOMENTS

2014 ◽  
Vol 35 ◽  
pp. 1460442
Author(s):  
DIOGO BOITO
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Systematic Study ◽  
Higher Order ◽  
Perturbative Expansion ◽  
Main Stream ◽  
Spectral Functions ◽  
Perturbative Series ◽  
Fixed Order ◽  
Adler Function

In the extraction of αs from hadronic τ decay data several moments of the spectral functions have been employed. Furthermore, different renormalization group improvement (RGI) frameworks have been advocated, leading to conflicting values of αs. Recently, we performed a systematic study of the perturbative behavior of these moments in the context of the two main-stream RGI frameworks: Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT). The yet unknown higher order coefficients of the perturbative series were modelled using the available knowledge of the renormalon singularities of the QCD Adler function. We were able to show that within these RGI frameworks some of the commonly employed moments should be avoided due to their poor perturbative behavior. Furthermore, under reasonable assumptions about the higher order behavior of the perturbative series FOPT provides the preferred RGI framework.

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