A prediction for the 4-loop β function in QCD

John Ellis*, Marek Karliner, Mark A. Samuel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We predict that the four-loop contribution β3 to the QCD β function in the MS̄ prescription is given by β3 ≃ 23600(900) -6400(200) Nf + 350(70) N2f + 1.5N3f, where Nf is the number of flavours and the coefficient of N3f is an exact result from large-Nf expansion. In the phenomenologically-interesting case Nf = 3, we estimate β3 = (7.6 ± 0.1) × 103. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) Φ4 theory, and on variations in the details of our estimation method, which goes beyond conventional Padé approximants by estimating and correcting for subasymptotic deviations from exact results.

Original languageEnglish
Pages (from-to)176-181
Number of pages6
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number1-2
StatePublished - 8 May 1997


FundersFunder number
US Departmento f EnergyDE-AC03-76F00515
German-Israeli Foundation for Scientific Research and Development
Israel Academy of Sciences and Humanities
Israel Science Foundation


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