. a Brief Introduction

I review the physics of the Higgs sector in the Standard Model and its minimal supersymmetric extension, the MSSM. I will discuss the prospects for discovering the Higgs particles at the upgraded Tevatron, at the Large Hadron Collider, and at a future high–energy e+e− linear collider with centre–of–mass energy in the 350–800 GeV range, as well as the possibilities for studying their fundamental properties. Some emphasis will be put on the theoretical developments which occurred in the last two years. 1. A brief introduction The search for Higgs bosons is the primary mission of present and future high–energy colliders. Detailed theoretical and experimental studies performed in the last few years, have shown that the single neutral Higgs boson that is predicted in the Standard Model (SM) [1] could be discovered at the upgraded Tevatron, if it is relatively light and if enough integrated luminosity is collected [2, 3] and can be detected at the LHC [3, 4] over its entire mass range 114.4 GeV < ∼ MH < ∼ 1 TeV in many redundant channels; see Fig. 1. In the context of the Minimal Supersymmetric Standard Model (MSSM), where the Higgs sector is extended to contain two CP–even neutral Higgs bosons h and H , a pseudoscalar A boson and a pair of charged scalar particles H [1], it has been shown that the lighter h boson cannot escape detection at the LHC and that in large areas of the parameter space, more than one Higgs particle can be found; see Fig. 1. ∗Plenary talk given at the Conference “Particles, Strings and Cosmology” (PASCOS), Bombay, India, 3–8 January 2003.