ABSTRACT
Chapter 19 describes the calculation of one-loop contributions of ElectroWeak Interactions to the muon anomaly, made possible by the advent of the renormalisable, electroweak Weinberg–Salam theory. The calculation of the weak anomaly in the Weinberg–Salam theory provided a first example of how a renormalisable, spontaneously broken, gauge theory works. Previous calculations of the weak anomaly were plagued by uncertainties related to the divergent structure of the Weak Interaction theory. The ElectroWeak correction integrates the calculation of pure electromagnetic corrections, initiated by the historical Schwinger paper (Chapter 12), and of the Hadron Vacuum Polarisation (HVP) corrections. The calculation is performed in the https://www.w3.org/1998/Math/MathML" display="inline"> ξ - gauge introduced by ‘t-Hooft, the bosons exchanged include https://www.w3.org/1998/Math/MathML" display="inline"> W , Z 0 and the Higgs boson H . The various steps of the calculation are extensively explained and commented in the Chapter. The size of the computed weak anomaly is about https://www.w3.org/1998/Math/MathML" display="inline"> 15 10 - 10 , smaller than the HVP effects, but anyway larger than the error of the present experimental determination. The last part of the Chapter presents a comparison of theoretical predictions of the muon anomaly with the latest experimental determination. Predictions include a most recent lattice QCD determination of HVP effects, which results to be in a quite remarkable agreement with the experiment, when added to the pure electromagnetic and electroweak contributions. Results including HVP determinations obtained from the experimental data on https://www.w3.org/1998/Math/MathML" display="inline"> e + e - → hadrons cross sections, on the other hand, display a discrepancy of about https://www.w3.org/1998/Math/MathML" display="inline"> 5 σ ≃ 20 10 - 10 error. The situation remains, at the moment, under close scrutiny.
