The Standard Model One of the most remarkable achievements of modern theoretical physics has been the construction of the Standard Model for weak, electromagnetic and strong interactions. It is a gauge theory based on the group U (1) ⊗ SU (2) ⊗ SU (3) which is spontaneously broken to U (1) ⊗ SU (3) . This relatively simple model epitomises our present knowledge of elementary particle interactions. It is analysed in detail in this School, so I present only a short summary. Given this result, let

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... us see what, if any, are the theoretical constraints. The Standard Model Higgs mass is given, at the classical level, by m 2 H = 2λv 2 , with v the vacuum expectation value of the Higgs field. The value of v is fixed by the value of the Fermi coupling constant G F / √ 2 = 1/(2v 2 ) which implies v ≈ 246 GeV. Therefore, any constraints will come from the allowed values of λ. A first set of such constraints is given by the classical requirement: 1 > λ > 0 ⇒ m H < 400-500 GeV .