English

Seven loops $\phi^4$

High Energy Physics - Theory 2022-12-08 v1

Abstract

We give a detailed account of the theory of position space renormalization using graphical functions in the case of dimensionally regularized ϕ4\phi^4 theory in four dimensions. In this theory we calculate the beta function, the mass gamma function, and the self energy to seven loops in the minimal subtraction scheme. The anomalous dimension γ\gamma is calculated to loop order eight. When possible, we generalize to even dimensions 4\geq4 with particular focus on ϕ3\phi^3 theory in six dimensions. In this theory we calculate the anomalous dimension γ\gamma to loop order six.

Keywords

Cite

@article{arxiv.2212.03663,
  title  = {Seven loops $\phi^4$},
  author = {Oliver Schnetz},
  journal= {arXiv preprint arXiv:2212.03663},
  year   = {2022}
}

Comments

27 pages, 12 figures

R2 v1 2026-06-28T07:24:46.096Z