A general account of the experimental results of the recently closed DESY-HERA accelerator and a presentation of the physics expected to be revealed by the LHC-CERN accelerator, beginning to deliver data in less than one year, is provided. An analysis of the impact of this information on the theoretical developments is included.Keywords: Standard Model; Supersymmetry; Lattice QCD We start by reproducing two recent press releases directly connected with the title of our lecture and that motivated it:On June 30, 2007, data taking at the electron-proton storage ring HERA at DESY will come to an end: For 15 years the particle physics experiments at HERA have provided a unique and detailed picture of the proton and the interacting forces said Prof. Rolf-Dieter Heuer, Research Director at DESY. Today it is certainly accepted that Fundamental Symmetry is a synonym of Particle Physics. This assertion has already its origin in the Relativity of Einstein. In fact, Wigner put it clearly in his phrase: "Einstein's work marks the inversion of a tendency, formerly the invariance principles were obtained from the laws of movement. Now it is natural for us to obtain the laws of Nature and prove their validity by means of the invariance laws.The present engine of development in Physics is Gauge Symmetry, that provides a unified treatment of the fundamental forces. The Standard Model of strong, weak and electromagnetic interactions, that we call (for obvious reasons) 3! is based on the symmetry SU(3) ⊗ SU(2) ⊗ U(1). In 't Hooft words it is the "Temporary solution to nearly a century of questions". 3! is one of the greatest success of physics. It comprises practically all that is known of the subatomic world in a concise set of principles and equations. Moreover, it exceeded experimental tests in energy ranges very distant from the ones included in its original design.The present knowledge of Quantum Field Theory based on gauge symmetry includes the important running behavior of coupling constants. Namely, the value of interaction couplings depends on the momentum scale that one is exploring. This is clearly seen in Fig. 1 for the case of Quantum Chromodynamics (QCD ≡ the 3 in 3!).There is a general consensus on the fact that 3! is not complete. It has aesthetical deficiencies and there are phenomena that are not included in it. Let us just mention some open questions: which is the cause of the symmetry breaking?; how do gauge interactions unify?; and Gravity?; what about dark matter and dark energy?; is there something else?; etc. FIG. 1: QCD running coupling constantIn order to answer these and other important questions, high energy collider accelerators have been and are the principal tools. In these machines, beams of e − , e + , p,p are accelerated in opposite directions and collide frontally. The next point is to decide in favor of electron or (and) protons and we are going to briefly discuss on it.Let us start by considering electron colliders. The paradigm of a recent collider of this type was LEP (Large Electron Positron)...
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