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Resummation in QFT with Meijer G-functions

Antipin, Oleg; Maiezza, Alessio; Vasquez, Juan Carlos (2019) Resummation in QFT with Meijer G-functions. Nuclear physics. B, 941 . pp. 72-90. ISSN 0550-3213

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We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the model where we estimate the non-perturbative β-function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative β- function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety.

Item Type: Article
Uncontrolled Keywords: Resummation ; renormalisation
Subjects: NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Physics of Elementary Particles and Fields
Divisions: Theoretical Physics Division
Depositing User: Oleg Antipin
Date Deposited: 04 Dec 2020 08:09
DOI: 10.1016/j.nuclphysb.2019.02.014

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