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The Standard Electroweak Theory and Beyond

Guido Altarelli

TL;DR

This collection of lectures systematically reviews the Standard Model's electroweak sector, detailing the gauge theory basis, the Higgs mechanism, and the CKM matrix, and then confronts the theory with precision data through renormalisation and higher-order corrections. It highlights how radiative corrections—especially those tied to the top quark mass and Higgs sector—shape predictions for observables such as $m_W$ and $ heta_W$, and introduces the epsilon formalism to separate weak-loop effects from other corrections. The text then argues for physics beyond the SM, focusing on naturalness and coupling unification, with supersymmetry (MSSM) as a leading candidate, and discusses dark matter, baryogenesis, and neutrino masses as phenomenological motivations. Finally, it surveys LEP2’s Higgs and new-physics program and outlines the implications of these data for the MSSM versus the SM, emphasizing a light Higgs preference and the potential for new physics to emerge at the TeV scale. The overarching message is that precision EW tests strongly support the Higgs mechanism and constrain extensions like SUSY, guiding future experimental searches at LEP2, Tevatron, and LHC.

Abstract

This set of lectures provides an elementary introduction to the standard electroweak theory, followed by a detailed discussion of its experimental tests. We then consider the conceptual limitations of the Standard Model and briefly review the existing phenomenological indications of new physics. We summarize the case for a supersymmetric extension of the Standard Model. Finally we describe the present and planned searches for the Higgs and for new physics.

The Standard Electroweak Theory and Beyond

TL;DR

This collection of lectures systematically reviews the Standard Model's electroweak sector, detailing the gauge theory basis, the Higgs mechanism, and the CKM matrix, and then confronts the theory with precision data through renormalisation and higher-order corrections. It highlights how radiative corrections—especially those tied to the top quark mass and Higgs sector—shape predictions for observables such as and , and introduces the epsilon formalism to separate weak-loop effects from other corrections. The text then argues for physics beyond the SM, focusing on naturalness and coupling unification, with supersymmetry (MSSM) as a leading candidate, and discusses dark matter, baryogenesis, and neutrino masses as phenomenological motivations. Finally, it surveys LEP2’s Higgs and new-physics program and outlines the implications of these data for the MSSM versus the SM, emphasizing a light Higgs preference and the potential for new physics to emerge at the TeV scale. The overarching message is that precision EW tests strongly support the Higgs mechanism and constrain extensions like SUSY, guiding future experimental searches at LEP2, Tevatron, and LHC.

Abstract

This set of lectures provides an elementary introduction to the standard electroweak theory, followed by a detailed discussion of its experimental tests. We then consider the conceptual limitations of the Standard Model and briefly review the existing phenomenological indications of new physics. We summarize the case for a supersymmetric extension of the Standard Model. Finally we describe the present and planned searches for the Higgs and for new physics.

Paper Structure

This paper contains 21 sections, 133 equations, 13 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Gauge Theories
  3. The Standard Model of Electroweak Interactions
  4. The Higgs Mechanism
  5. The CKM Matrix
  6. Renormalisation and Higher Order Corrections
  7. Status of the Data
  8. Precision Electroweak Data and the Standard Model
  9. A More General Analysis of Electroweak Data
  10. Basic Definitions and Results
  11. Experimental Determination of the Epsilon Variables
  12. Why Beyond the Standard Model?
  13. Conceptual Problems with the Standard Model
  14. Hints from Experiment
  15. Unification of Couplings
  16. ...and 6 more sections

Figures (13)

  • Figure 1: The three-gauge boson vertex: $V=\gamma,Z$
  • Figure 2: The Bjorken triangle corresponding to eq.(\ref{['km10']})
  • Figure 3: Triangle diagram that generates the ABJ anomaly
  • Figure 4: A summary of $\sin^2\theta_{eff}$ measurements)
  • Figure 5: Data vs theory in the $\epsilon_2$-$\epsilon_1$ plane. The origin point corresponds to the "Born" approximation obtained from the SM at tree level plus pure QED and pure QCD corrections. The predictions of the full SM (also including the improvements of ref.deg) are shown for $m_H$ = 70, 300 and 1000 GeV and $m_t=175.6\pm5.5~GeV$ (a segment for each $m_H$ with the arrow showing the direction of $m_t$ increasing from $-1\sigma$ to $+1\sigma$). The three $1-\sigma$ ellipses ($38\%$ probability contours) are obtained from a) "All Asymm." :$\Gamma_l$, $m_W$ and $\sin^2\theta_{eff}$ as obtained from the combined asymmetries (the value in eq. (\ref{['102']})); b) "All High En.": the same as in a) plus all the hadronic variables at the Z; c) "All Data": the same as in b) plus the low energy data.
  • ...and 8 more figures