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1.2.1 The Standard Model

The goal of elementary particle physics is to identify the ultimate building blocks of Nature and the interactions among them, and find their simple description. Primary means of this endeavor is high energy accelerators. Advance of accelerator technology has been enabling us to probe ever-higher energy and thus ever-shorter distance, thereby leading us to deeper understanding of Nature. Over the past decades, we have learned that Nature consists of a small number of matter particles and among these matter particles lies a beautiful symmetry that is deeply connected with their interactions, and that the microscopic world of these elementary particles can be described by quantum field theory. The matter particles here are two kinds of spin 1/2 fermions, quarks and leptons, and the symmetry here is called gauge symmetry.

Conversely, we can start from the gauge symmetry and demand that any matter particle has to belong to some multiplet that is allowed by the gauge symmetry. A set of particles that comprise a multiplet mutually transform each other by gauge transformations and thus have to be regarded as different states of a single particle. Their distinction thus loses its absolute meanings, which naturally leads us to demand invariance of physics by any gauge transformations made independently at different points in space-time. The key point here is that this requirement of local gauge invariance forces us to introduce spin 1 gauge particles (gauge bosons) and, moreover, it dictates the form of the interaction mediated by them. This is called gauge principle.

The first and most important question in any model building guided by the gauge principle is the choice of the gauge symmetry (or corresponding gauge group). The gauge field theory that is based on the $SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$ is the Standard Model[4]. The standard model succeeded in describing all but one of the four known interactions--electromagnetic, weak, and strong--and has been tested to a great precision in particular in the last decade mainly through collider experiments. The test has reached a quantum level and firmly established the gauge principle. It is remarkable in this respect that the top quark, which was missing when the first JLC project design was drawn in 1992[3], was discovered[5] in the mass range that had been predicted[6] through the analysis of the quantum corrections. This filled the last empty slot of the matter multiplet of the Standard Model. Although the recent discovery of neutrino oscillation[7] requires extension of its particle contents[8], the other part of the Standard Model is still intact.

Nevertheless, there is a good reason for the Standard Model still being called a model. This is primarily because its core ingredient, the mechanism that is responsible for the spontaneous breaking of the gauge symmetry[9] hence for the generation of the masses of otherwise massless matter and force carrying particles, is left untested. In the Standard Model, a fundamental scalar (Higgs boson) field plays this role. Because of a new self-interaction (a four-point self-coupling hereafter called Higgs force), a Higgs field condenses in the vacuum and spontaneously breaks the $SU(2)_L \otimes U(1)_Y$gauge symmetry. The masses of the matter and force carrying particles are generated through their interactions with the Higgs field condensed in the vacuum, and are consequently proportional to their coupling strengths to and the density (the vacuum expectation value) of the condensed Higgs field. The masses of the gauge bosons, W and Z, could be predicted, since their interaction with the Higgs field that is responsible for the mass generation is the universal gauge interaction. The discovery of W and Z at the predicted masses[10] is a great triumph of the Standard Model. On the other hand, the masses of quarks and leptons are generated through yet another new interaction (hereafter called Yukawa force) that is arbitrarily put in by hand to parametrize the observed mass spectrum and mixing of the matter particles; more than half of the 18 parameters of the Standard Model are thus used for this parametrization.

We can summarize the current situation as follows. There is no doubt about the gauge principle on which the Standard Model is based and thus its breaking has to be spontaneous and caused by "something" that condenses in the vacuum. But the nature of this "something" still remains mysterious. Without revealing its nature, it will be difficult to understand real implications of the data on CP violation and flavor mixing to be accumulated at various laboratories in this decade. It should be stressed that, since the coupling of this "something" with a matter particle is proportional to the mass of the matter particle, the heaviest matter fermion found so far, the top quark, might hold the key to uncover the nature of this "something". In order to understand the Higgs and the Yukawa forces, therefore, we need not only to find the Higgs boson but also to study both the Higgs boson and the top quark in detail.

It is remarkable that just like the analysis of the quantum corrections enabled us to predict the mass range of the top quark before its discovery, the advance of the precision measurements in the last decade now allows us to indirectly measure the mass of the Higgs boson in the framework of the Standard Model. The data tell us that the mass of the Standard Model Higgs boson is less than 215 GeV at the 95% confidence level[11]. Recall that the mass of the Higgs boson is related to its four-point self-coupling, which becomes stronger at higher energies. This upper bound is surprisingly consistent with the picture that the Higgs self-coupling stays perturbative up to very high energy near the Planck scale and also with the recent indication of a possible Higgs signal at LEP[12]. Such a light Higgs boson lies well within the reach of the JLC in its startup phase and can be studied in great detail as we shall see in Chapter 2. We will be able to verify its quantum numbers and its couplings as well as to precisely determine its mass. If the Higgs boson mass is less than 150 GeV, we should be able to test the mechanism of the fermion mass generation. The top quark threshold region is sensitive to the Yukawa potential due to the Higgs boson exchange and at higher energies we will be able to measure the top Yukawa coupling directly as discussed in Chapter 4. The study of the Higgs boson branching ratios[13] can also tell us if the Yukawa coupling constants are proportional to the fermion masses. Such tests can be performed only at e+ e- colliders with a clean environment. In this way, the JLC is able to thoroughly establish the Standard Model.


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ACFA Linear Collider Working Group
E-Mail:acfareport@acfahep.kek.jp