A. S. Fedoruk | Searcharxiv

arXiv2026

New Solutions of RG Equations for α_s and y_{top}

We construct simple analytical solutions of the RG equations for the running couplings α_s and y_{top} in the asymptotic regime. These solutions have an explicit form, contain only logarithms and no special functions, and subsequently sum up the leading, subleading, etc logarithms in all orders of PT. While the effect of y_{top} on the running of α_s happens to be negligible, the role of α_s on the running of y_{top} is essential, the account of higher orders gives a noticeable contribution.

hep-th↗

arXiv2026

On the renormalization-group analysis of the SM: loops, uncertainties, and vacuum stability

Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art results. Our study focuses on the RGE solutions at different loop orders. We compare not only the standard (``diagonal'') loop counting when one considers gauge, Yukawa, and scalar self-coupling beta functions at the same order but also ``non-diagonal'' ones, inspired by the so-called Weyl consistency conditions. We discuss the initial conditions for RGE (``matching'') for different loop configurations and study the uncertainties of running couplings both related to the limited precision of the experimental input (``parametric'') and the missing high-order corrections (``theoretical''). As an application of our analysis we also estimate the electroweak vacuum decay probability and study how the uncertainties in the running parameters affect the latter. We argue that ``non-diagonal'' beta functions, if coupled with a more consistent ``non-diagonal'' matching, lead to larger theoretical uncertainty than ``diagonal'' ones.

hep-ph↗