For Publisher's use THE HIGGS PUZZLE: EXPERIMENT AND THEORY

The present experimental and theoretical knowledge of the physics of electroweak symmetry breaking is reviewed. Data still favor a light Higgs boson, of a kind that can be comfortably accommodated in the Standard Model or in its Minimal Supersymmetric extension, but exhibit a non{trivial structure that leaves some open questions. The available experimental information may still be reconciled with the absence of a light Higgs boson, but the price to pay looks excessive. Recent theoretical ideas, linking the weak scale with the size of possible extra spatial dimensions, are brie°y mentioned. It is stressed once more that experiments at high{energy colliders, such as the Tevatron and the LHC, are the crucial tool for eventually solving the Higgs puzzle. Rome is a city so full of religious symbols that it provides some inspiration on how to organize a talk on the physics of electroweak symmetry breaking, where ¯rm experimental and theoretical results are mixed, so far, with a certain amount of beliefs. 1 The Standard Model (The Orthodoxy) The obvious starting point for any discussion of the Higgs puzzle ( ´ `what is the physics of electroweak symmetry breaking?') is the Standard Model (SM), by now ¯rmly estab-lished as the renormalizable quantum ¯eld theory of strong and electroweak interactions at presently accessible energies: in the spirit of the preface, it can be called `The Ortho-doxy'. The only SM ingredient still escaping experimental detection, in a theoretical con-struction that works incredibly well, is the Higgs 1 boson, H. Its properties are con-trolled by some well{known parameters of the fermion and gauge sectors (including the Fermi constant GF, which sets the value of the weak scale) plus an independent one, the Higgs mass mH. The elementary complex spin{0 ¯eld Á, an SU(2)L doublet of weak hypercharge Y = +1=2 (in the normalization where Q = T3L+ Y), is by now considered to be an essential part of what we call the SM. Indeed, it plays a fundamental role in the description of two symmetry{breaking phenomena. The ¯rst is the spontaneous breaking of the SU(2)L £ U(1)Y gauge symmetry down to the U(1)