Updated Running Quark and Lepton Parameters at Various Scales

TL;DR

This work revisits the running of quark and lepton Yukawa couplings and CKM parameters in the Standard Model and MSSM using the latest PDG data, notably the reduced uncertainties in 2024. By propagating low-energy inputs through two-loop RGEs with Monte Carlo uncertainty assessment, the authors provide comprehensive SM running tables from $M_Z$ to $10^{16}$ GeV and MSSM results at the GUT scale for several $\tan\beta$ values and SUSY scales, along with an approximate method to include SUSY threshold corrections. The improved precision sharpens tests of flavour models and GUT relations, revealing tension with some simple CMD textures (e.g., GST and first-family double Yukawa ratios) when confronted with PDG 2024 results, while offering a practical framework for incorporating threshold effects into high-scale predictions. Overall, the paper delivers precise, model-building–oriented inputs that enhance the construction and testing of theories beyond the Standard Model, especially in the flavour sector and at the GUT scale.

Abstract

In the light of the recent Particle Data Group (PDG) release, we revisit the running quark and lepton Yukawa couplings, together with the quark mixing parameters, across a range of energy scales. The 2024 PDG determinations of low-energy fermion masses feature significantly smaller uncertainties, resulting from a reduced estimate of systematic errors compared to the more conservative treatment in the 2022 analysis. To assess the impact of these changes, we present running parameters obtained using both the 2022 and 2024 datasets, within the frameworks of the Standard Model (SM) and its minimal supersymmetric extension (MSSM). The evolved values, along with their associated $1σ$ uncertainties, are given within the SM framework at benchmark scales of $M_Z$ and $10^3$, $3\cdot 10^3$, $10^4$, $10^5$, $10^7$, $10^9$, $10^{12}$, and $10^{16}$ GeV. Within the MSSM, we additionally provide GUT-scale results for different choices of $\tanβ$, assuming supersymmetry breaking scales of 3 and 10 TeV, including an approximate way for taking supersymmetric loop threshold corrections into account. We furthermore discuss implications of the updated results for constructing and testing theories beyond the SM.