Fisher's Zeros and Perturbative Series in Gluodynamics

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

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Stochastic computation of g − 2 in QED

Journal of High Energy Physics ◽

10.1007/jhep05(2021)119 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Ryuichiro Kitano ◽

Hiromasa Takaura ◽

Shoji Hashimoto

Keyword(s):

Perturbation Theory ◽

Numerical Computation ◽

Magnetic Moment ◽

Anomalous Magnetic Moment ◽

Stochastic Perturbation ◽

Higher Order ◽

Feynman Diagrams ◽

Perturbative Series ◽

Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

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Modified Padé approximants and perturbative series in quantum field theory

Il Nuovo Cimento A ◽

10.1007/bf02773547 ◽

1996 ◽

Vol 109 (12) ◽

pp. 1655-1667

Author(s):

G. Dattoli

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Padé Approximants ◽

Quantum Field ◽

Perturbative Series ◽

Pade Approximants

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Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory

10.7566/jpsht.1.063 ◽

2021 ◽

Vol 1 ◽

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Phase Transitions ◽

Series Expansion ◽

Quantum Electrodynamics ◽

Quantum Field ◽

Perturbative Series

Using resurgence theory to describe phase transitions in quantum field theory shows that information on non-perturbative effects like phase transitions can be obtained from a perturbative series expansion.

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PERTURBATIVE EXPANSION OF τ HADRONIC SPECTRAL FUNCTION MOMENTS

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194514604426 ◽

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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