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

Abstract: 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 alsonon-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 coupling both related to the limited precision of the experimental input (parametric'') and to 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 thenon-diagonal'' beta functions, if coupled with more consistent non-diagonal'' matching lead to larger theoretical uncertainty than thediagonal'' ones.