On the electroweak contribution to the matching of the strong coupling constant in the SM

Abstract

The effective renormalizable theory describing electromagnetic and strong interactions of quarks of five light flavors ($n_f=5$ QCD$\times$QED) is considered as a low-energy limit of the full Standard Model. Two-loop relation between the running strong coupling constants ${\alpha }_s$ defined in either theories is found by simultaneous decoupling of electroweak gauge and Higgs bosons in addition to the top quark. The relation potentially allows one to confront "low-energy determination of ${\alpha }_s$ with a high-energy one with increased accuracy. Numerical impact of new $\mathcal{O}({\alpha }_s\alpha )$ terms is studied at the $M_Z$ scale. It is shown that the corresponding contribution, although being suppressed with respect to $\mathcal{O}({\alpha }_s^2)$ terms, is an order of magnitude larger than the three-loop QCD corrections $\mathcal{O}({\alpha }_s^3)$ usually taken into account in four-loop renormalization group evolution of ${\alpha }_s$. The dependence on the matching scale is also analyzed numerically.

9 pages, 1 figure, a small typo in Eq. 18 is corrected (thanks to S. Martin), results are not affected and can be found as ancillary files

References in corpus (8)

• Big-Bang Nucleosynthesis
• Jets from Massive Unstable Particles: Top-Mass Determination
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops
• Three-loop SM beta-functions for matrix Yukawa couplings
• Three-loop Higgs self-coupling beta-function in the Standard Model with complex Yukawa matrices
• Running mass of the b-quark in QCD and SUSY QCD
• Decoupling in QED and QCD

Cited by in corpus (8)

• Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision
• Precise Values of Running Quark and Lepton Masses in the Standard Model
• Four-loop strong coupling beta-function in the Standard Model
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• The Standard Model at 200 GeV
• Matching relations for decoupling in the Standard Model at two loops and beyond
• Three-loop QCD corrections to the electroweak boson masses
• On the four-loop strong coupling beta-function in the SM