2019/10/31 by Jahmall Bersini, Alessio Maiezza, Juan Carlos Vasquez · 2 citations
Physics and Astronomy · Mathematics · #hep-th #hep-ph #math-ph #math.MP
paper · pdf · doi:10.1016/j.aop.2020.168126
published as Annals Phys. 415 (2020) 168126 · 20 pages, final journal version
arxiv created 2020/03/03 · arxiv updated 2020/03/17
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.