Beyond the Standard Model

The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological implications for gauge coupling unification, proton decay, fermion masses, neutrino physics, collider signatures, dark matter, rare decays and anomalous magnetic moments. The forthcoming generation of experiments will certainly expose these ideas to several essential tests. 1. THE STANDARD MODEL The experimental success of the SU(3) × SU(2) × U(1) Standard Model (SM) of the strong and electroweak forces can be considered as the triumph of the gauge symmetry principle to describe particle interactions. As we now briefly summarize, there are many different facts which have to be taken into account when searching for a deeper underlying theory, and these are: 1.1 THE GOOD: The major success of the SM is that it accounts for essentially all present accelerator results. In particular: • The most accurately known quantity in particle physics is the magnetic moment of the electron, with its ‘anomalous’ part being ae ≡ (ge − 2)/2, i.e. the normalized difference in the gyromagnetic ratio ge with respect to the classical Dirac value ge = 2 (where the magnetic moment μ is related to the particle spin s through μ ≡ gs(e/2m)). The experimental and theoretical values are respectively [1] ae = { (115965218.7 ± 0.4) × 10−11 Exp. (115965214.0 ± 2.8)× 10−11 Th. . (1) The theoretical expression results from the computation of the loop corrections within the SM up to order O(α4), including diagrams such as those depicted in Figure 1. The one loop photon correction is the well known Schwinger term. Its prediction was actually one of the first major successes of QED, proving that radiative corrections could be made meaningful through renormalization and were indeed measurable. Higher order contributions include terms such as that involving the photon self energy in diagram (1.c) and the photon–photon scattering appearing in diagram (1.d). These two are actually the major sources of uncertainties for the magnetic moments of heavier leptons (μ or τ ), but for the electron the theoretical error is actually dominated by the uncertainty in the direct measurement of α using the Quantum Hall Effect. Indeed, one may use the theoretical expression for ae (as a fourth order polynomial in α) to infer a ‘theoretically based’ value for the electromagnetic coupling, which has a smaller error than the one obtained from direct measurements, and is α−1 = 137.03599993(52). This of course is the value at low energies, and running it to the scale of the Z boson, where for instance LEP measurements are done, one gets in the modified minimal subtraction (MS) scheme