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

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

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Resumé

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.

OriginalsprogEngelsk
Artikelnummer015013
TidsskriftPhysical Review D
Vol/bind100
Udgave nummer1
ISSN2470-0010
DOI
StatusUdgivet - 11. jul. 2019

Fingeraftryk

quantum chromodynamics
expansion
gauge theory
bubbles
diagrams
radii
coefficients

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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",
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Analytic coupling structure of large Nf (super) QED and QCD. / Dondi, Nicola Andrea; Dunne, Gerald V.; Reichert, Manuel; Sannino, Francesco.

I: Physical Review D, Bind 100, Nr. 1, 015013, 11.07.2019.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer 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

M3 - Journal article

VL - 100

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 1

M1 - 015013

ER -