English

Resurgence of the Renormalization Group Equation

High Energy Physics - Theory 2020-03-17 v2 High Energy Physics - Phenomenology Mathematical Physics math.MP

Abstract

We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.

Keywords

Cite

@article{arxiv.1910.14507,
  title  = {Resurgence of the Renormalization Group Equation},
  author = {Jahmall Bersini and Alessio Maiezza and Juan Carlos Vasquez},
  journal= {arXiv preprint arXiv:1910.14507},
  year   = {2020}
}

Comments

20 pages, final journal version