English

The four-loop beta-function in Quantum Chromodynamics

High Energy Physics - Phenomenology 2008-11-26 v1
Authors: T. van Ritbergen , J. A. M. Vermaseren , S. A. Larin
View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We present the analytical calculation of the four-loop QCD beta-function within the minimal subtraction scheme.

Keywords

QCD beta-function four-loop minimal subtraction scheme

Cite

@article{arxiv.hep-ph/9701390,
  title  = {The four-loop beta-function in Quantum Chromodynamics},
  author = {T. van Ritbergen and J. A. M. Vermaseren and S. A. Larin},
  journal= {arXiv preprint arXiv:hep-ph/9701390},
  year   = {2008}
}

Comments

9 pages, Latex, 1 figure, uses axodraw.sty

Related papers

View all related →
High Energy Physics - Phenomenology · Physics
Four-loop QCD MOM beta functions from the three-loop vertices at the symmetric point
Alexander Bednyakov, Andrey Pikelner
2020-04-15
High Energy Physics - Phenomenology · Physics
The three-loop QCD $\beta$-function and anomalous dimensions
S. A. Larin, J. A. M. Vermaseren
2011-05-05
High Energy Physics - Phenomenology · Physics
The Four-Loop QCD Beta-Function and Anomalous Dimensions
M. Czakon
2010-04-06
High Energy Physics - Phenomenology · Physics
Five-loop beta function for gauge theories: computations, results and consequences
F. Herzog, B. Ruijl, T. Ueda, J. Vermaseren +1
2025-10-31
High Energy Physics - Phenomenology · Physics
The five-loop beta function of Yang-Mills theory with fermions
F. Herzog, B. Ruijl, T. Ueda, J. A. M. Vermaseren +1
2017-03-08
High Energy Physics - Theory · Physics
Three-loop functions for a quartic model with a cutoff
A. V. Ivanov, V. A. Nikiforov
2026-03-24
High Energy Physics - Phenomenology · Physics
The 4-loop quark mass anomalous dimension and the invariant quark mass
J. A. M. Vermaseren, S. A. Larin, T. van Ritbergen
2009-10-30
High Energy Physics - Phenomenology · Physics
On the four-loop strong coupling beta-function in the SM
A. V. Bednyakov, A. F. Pikelner
2016-11-23
High Energy Physics - Phenomenology · Physics
Three-loop beta function and non-perturbative $\alpha_s$ in asymmetric momentum scheme
Ph. Boucaud, J. P. Leroy, J. Micheli, O. Pene +1
2010-03-19
High Energy Physics - Phenomenology · Physics
Gauge coupling beta functions to four-loop order in the Standard Model
Joshua Davies, Florian Herren, Colin Poole, Matthias Steinhauser +1
2020-02-26
High Energy Physics - Theory · Physics
Four loop renormalization of QCD in the Curci-Ferrari gauge
J. A. Gracey
2025-03-10
High Energy Physics - Phenomenology · Physics
Asymptotic Pad\'e Approximants and the SQCD $\beta$-function
I. Jack, D. R. T. Jones, M. A. Samuel
2009-10-30
High Energy Physics - Phenomenology · Physics
The four-loop renormalization group QCD and QED $\beta$-functions in the $V$-scheme and their analogy with the Gell-Mann--Low function in QED and QCD
A. L. Kataev, V. S. Molokoedov
2015-10-09
High Energy Physics - Phenomenology · Physics
Four-loop QCD $\beta$-function with different fermion representations of the gauge group
M. F. Zoller
2017-07-25
High Energy Physics - Phenomenology · Physics
Towards QCD running in 5 loops: quark mass anomalous dimension
P. A. Baikov, K. G. Chetyrkin, J. H. Kühn
2014-02-27
High Energy Physics - Phenomenology · Physics
Four-loop QCD propagators and vertices with one vanishing external momentum
B. Ruijl, T. Ueda, J. A. M. Vermaseren, A. Vogt
2017-06-28
High Energy Physics - Phenomenology · Physics
Three loop QCD MOM beta-functions
J. A. Gracey
2011-08-19
High Energy Physics - Phenomenology · Physics
A Prediction for the 4-Loop \beta Function
John Ellis, Marek Karliner, Mark. A. Samuel
2016-09-06
High Energy Physics - Phenomenology · Physics
Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD
K. G. Chetyrkin, A. Retey
2007-05-23
High Energy Physics - Phenomenology · Physics
Four-loop QCD cusp anomalous dimension at small angle
Andrey G. Grozin, Roman N. Lee, Andrey F. Pikelner
2022-11-18
High Energy Physics - Theory · Physics
One-loop $\mathbf{\beta}$ function of noncommutative scalar $QED_{4}$
M. Ghasemkhani, R. Bufalo, V. Rahmanpour, E. Nouri
2017-04-27
High Energy Physics - Lattice · Physics
The three-loop beta-fuction of QCD with the clover action
A. Bode, H. Panagopoulos
2009-11-07
High Energy Physics - Phenomenology · Physics
Four-loop wave function renormalization in QCD and QED
Peter Marquard, Alexander V. Smirnov, Vladimir A. Smirnov, Matthias Steinhauser
2018-04-04
High Energy Physics - Phenomenology · Physics
Di-photon amplitudes in three-loop Quantum Chromodynamics
Fabrizio Caola, Andreas von Manteuffel, Lorenzo Tancredi
2021-03-24
High Energy Physics - Phenomenology · Physics
Gluino Contribution to the 3-loop QCD beta function in the Minimal Supersymmetric Standard Model
L. Clavelli, P. W. Coulter, L. R. Surguladze
2009-10-30