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

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arxiv 2003.08397 v2 pith:H4AFD7R2 submitted 2020-03-18 hep-th hep-lathep-ph

Nicola Andrea Dondi , Gerald V. Dunne , Manuel Reichert , Francesco Sannino This is my paper · ORCID
classification hep-thhep-lathep-ph
keywords functionbetasingularityappearsbranch-cutclosedclosercompared
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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  1. Probing Large $N_f$ Through Schemes

    hep-ph 2025-07 conditional novelty 5.0 of 10

    At most one renormalization scheme can keep the leading term of the large-Nf beta function dominant, so truncated large-Nf predictions of ultraviolet fixed points are not scheme-robust.

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