Analytic coupling structure of large Nf (super) QED and QCD

Nicola Andrea Dondi*, Gerald V. Dunne, Manuel Reichert, Francesco Sannino

*Corresponding author for this work

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Abstract

We study the analytic properties of the 't Hooft coupling expansion of the beta function at the leading nontrivial large-Nf order for QED, QCD, super QED, and super QCD. For each theory, the 't Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order 1/Nf and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and nonsupersymmetric theories. We also discuss the expected structure at higher orders in the 1/Nf expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-Nf expansion is an essential step towards determining the ultraviolet fate of asymptotically nonfree gauge theories.

Original languageEnglish
Article number015013
JournalPhysical Review D
Volume100
Issue number1
ISSN2470-0010
DOIs
Publication statusPublished - 11. Jul 2019

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quantum chromodynamics
expansion
gauge theory
bubbles
diagrams
radii
coefficients

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@article{5782cc2d6ec84d78993e5c1402e6e288,
title = "Analytic coupling structure of large Nf (super) QED and QCD",
abstract = "We study the analytic properties of the 't Hooft coupling expansion of the beta function at the leading nontrivial large-Nf order for QED, QCD, super QED, and super QCD. For each theory, the 't Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order 1/Nf and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and nonsupersymmetric theories. We also discuss the expected structure at higher orders in the 1/Nf expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-Nf expansion is an essential step towards determining the ultraviolet fate of asymptotically nonfree gauge theories.",
author = "Dondi, {Nicola Andrea} and Dunne, {Gerald V.} and Manuel Reichert and Francesco Sannino",
year = "2019",
month = "7",
day = "11",
doi = "10.1103/PhysRevD.100.015013",
language = "English",
volume = "100",
journal = "Physical Review D",
issn = "2470-0010",
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Analytic coupling structure of large Nf (super) QED and QCD. / Dondi, Nicola Andrea; Dunne, Gerald V.; Reichert, Manuel; Sannino, Francesco.

In: Physical Review D, Vol. 100, No. 1, 015013, 11.07.2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Analytic coupling structure of large Nf (super) QED and QCD

AU - Dondi, Nicola Andrea

AU - Dunne, Gerald V.

AU - Reichert, Manuel

AU - Sannino, Francesco

PY - 2019/7/11

Y1 - 2019/7/11

N2 - We study the analytic properties of the 't Hooft coupling expansion of the beta function at the leading nontrivial large-Nf order for QED, QCD, super QED, and super QCD. For each theory, the 't Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order 1/Nf and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and nonsupersymmetric theories. We also discuss the expected structure at higher orders in the 1/Nf expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-Nf expansion is an essential step towards determining the ultraviolet fate of asymptotically nonfree gauge theories.

AB - We study the analytic properties of the 't Hooft coupling expansion of the beta function at the leading nontrivial large-Nf order for QED, QCD, super QED, and super QCD. For each theory, the 't Hooft coupling expansion is convergent. We discover that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order 1/Nf and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and nonsupersymmetric theories. We also discuss the expected structure at higher orders in the 1/Nf expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-Nf expansion is an essential step towards determining the ultraviolet fate of asymptotically nonfree gauge theories.

U2 - 10.1103/PhysRevD.100.015013

DO - 10.1103/PhysRevD.100.015013

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JO - Physical Review D

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SN - 2470-0010

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ER -