ABSTRACT
This chapter is focused on the effective potential resulting from the inclusion of quantum corrections to the classical Higgs potential of Chapter 21. The expansion of the effective potential in powers of https://www.w3.org/1998/Math/MathML" display="inline"> ℏ , as well as its relation to the perturbative series in powers of the interaction Lagrangian is outlined. The results of this analysis show that the terms of order https://www.w3.org/1998/Math/MathML" display="inline"> ℏ L correspond to the sum of L-loop diagrams of perturbation theory. The calculation of the Higgs effective potential at one-loop level is described in detail, and the renormalisation group method is employed to describe its behaviour at large values of the field. The final section is devoted to the question of naturalness, or lack thereof, of the Standard Theory, which has been reopened by the recent discovery of the Higgs boson. The observation that the value of the Plank mass is exceptionally large compared to the mass scale of electroweak symmetry breaking—approximately given by the vacuum expectation value of the Higgs field https://www.w3.org/1998/Math/MathML" display="inline"> η —suggests that the Standard Theory should be regarded as the low-energy limit of a more fundamental theory, describing physics phenomena at energies https://www.w3.org/1998/Math/MathML" display="inline"> Λ > η . The extension of the Standard Theory based on supersymmetry, providing a connection between fermion and boson degrees of freedom, has been proposed as a possible solution to this problem. The future prospects and the need of new experimental facilities capable to explore the mass range relevant to supersymmetric particles are discussed.
