Unification of Standard Model Gauge Couplings: Meaning, Status and Perspectives

Abstract

One of the most interesting conceptual developments of particle physics is the understanding that not only gauge couplings but also masses and other dynamical variables run with energy. The running of these quantities in itself has limited interest. The main goal is to find out how the unification of these quantities at high energy is linked with the solution of the many problems left open by the Standard Model in the energy range where our facilities operate. And this means if the new physics beyond the Standard Model can be seen now. This review lecture has the purpose of clarifying and indicating the correct way out. In fact what is needed are not qualitative arguments but a set of detailed calculations with definite prediction. The “geometrical” convergence of the three gauge couplings, α ₁, α ₂, α ₃, the origin of M _{SU SY} , and the reasons why this meaningless quantity, together with its “geometrical” consequences, should be abandoned, are discussed. The first step is to describe the convergence of the three gauge couplings with a set of seventeen differential non-linear equations, coupled by the radiative effects of the underlying physics: the inputs being the high precision LEP data, together with other experimental limits. The unification of the Standard Model gauge forces, SU(3) _c × SU(2) _L × U(1) _Y , is described by a set of Figures which allow a simple understanding of the various interconnections which exist between measured quantities and new Physics. These interconnections are often hidden in the complex mathematical formalism, but their knowledge is badly needed. Finally, the motivations why Supergravity is the right way out to overcome the limitations and problems of the Standard Model, are summarized. Understanding the Physics at the Planck scale tells us that the key for new Physics beyond the Standard Model could be at the Fermi scale and therefore the search for new Physics with existing facilities (Fermi-lab, LEP (I,II), HERA, Gran Sasso, SKK) should continue and be encouraged, as shown with detailed calculations.