Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$

Abstract

We determine the $1/N_f^2$ and $1/N_f^3$ contributions to the QED beta function stemming from the closed set of nested diagrams. At order $1/N_f^2$ we discover a new logarithmic branch-cut closer to the origin when compared to the $1/N_f$ results. The same singularity location appears at $1/N_f^3$, and these correspond to a UV renormalon singularity in the finite part of the photon two-point function.

arXiv comment15 pages, 11 figures; v2: journal published version

References in corpus (30)

• New Developments in FeynCalc 9.0
• Renormalons
• The five-loop beta function of Yang-Mills theory with fermions
• Asymptotic safety guaranteed
• From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• The QCD beta-function at O(1/N_f)
• Vacuum stability of asymptotically safe gauge-Yukawa theories
• The massless two-loop two-point function
• Large N flavor beta-functions: a recap
• Asymptotically Safe Standard Model via Vector-Like Fermions
• Asymptotically Safe Standard Model Extensions?
• Conformal Window 2.0: The Large $N_f$ Safe Story
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Lectures on multiloop calculations
• Gauge-Yukawa theories: Beta functions at large $N_f$
• Large $N_f$ quantum field theory
• Safe Pati-Salam
• NumExp: Numerical epsilon expansion of hypergeometric functions
• Massless two-loop self-energy diagram: Historical review
• Gauge contribution to the $1/N_F$ expansion of the Yukawa coupling beta function
• Safety versus triviality on the lattice
• Safe Clockwork
• $\beta$-functions in large-$N_f$ supersymmetric gauge theories
• Analytic Coupling Structure of Large $N_f$ (Super) QED and QCD
• Safe Glueballs and Baryons
• A critical look at $\beta$-function singularities at large $N$
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$

Cited by in corpus (16)

• The nonperturbative functional renormalization group and its applications
• Physical Resurgent Extrapolation
• Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
• Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations
• Resonant resurgent asymptotics from quantum field theory
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Magnetic renormalons in a scalar self interacting $\lambda {\varphi }^4$ theory
• Renormalons beyond the Borel plane
• Thermomagnetic renormalons in a scalar self-interacting $\lambda {\varphi }^4$ theory
• The analytic structure of the fixed charge expansion
• Large $N_f$ for multiple representations
• Renormalization Flow of Nonlinear Electrodynamics
• Conformal Windows beyond Asymptotic Freedom