I. INTRODUCTION During the course we will try to answer the question: What are the basic laws of physics? Namely, we will try to find out what the basic constituents of matter and what their funda- mental interactions are. While we cannot fully answer the question, it is amusing that we do have a good idea of what the answer is, at least when we talk about physics at energies below about 100 GeV. There exist a well established theory, called the Standard Model 1 (SM), that describe basically all what we probed in Nature. In this course we will understand the theory, its predictions, and how they were confirmed experimentally. In this first lecture I will describe the model and very roughly how it describes elementary particles and their interactions. For the moment you will have to trust me on most of the statements I will make. By the end of the course you will understand them. A. Theory We assume that our world can be described by a quantum field theory (QFT) in a 4d Minkowski space. Then, we need three ingredients to describe a theory 1. The gauge group. This determines the forces. 2. The representations of the spinors under the gauge group. These describe the matter. 3. The mechanism of Spontaneous Symmetry Breaking (SSB). This explains the origin of masses. The SM is defined as follows: 1. The gauge group is SU(3) C ⊗ SU(2) L ⊗ U(1) Y . (1.1) 2. There are three generations of fermions, 2 each transforms under the gauge group as Q (3 , 2) 1 / 6 ; U ( ¯ 3 , 1) 2 / 3 ; D ( ¯ 3 , 1) − 1 / 3 ; (1.2) L (1 , 2) − 1 / 2 ; E (1 , 1) − 1 , where the first [second] parameter in the parenthesis is the SU(3) [SU(2)] representa- tion, and the subindex is the U(1) Y charge. 1 The name “Standard Model” is misleading. We usually refer to a model as something that does not describe our problem but rather model it. The Standard Model is not a model, it is a theory. 2 Recall that the fundamental spinor representation is a Weyl spinor, not a Dirac spinor. Therefore, left handed and right handed spinors can carry different quantum numbers. 1
3. The scalar Higgs that transforms as H (1 , 2) 1 / 2 (1.3) is responsible to the SSB SU(2) L ⊗ U(1) Y → U(1) EM . (1.4) This SM has 18 free parameters 3 that we need to determine experimentally. We know 17 of them with a various degree of precision, ranging from 10 − 9 to 50%. The only unknown parameter is the mass of the Higgs boson where only a lower bound has been established. Three of the parameters (the coupling constants) describe the gauge sector, two (the Higgs and Z masses) the Higgs sector, and 13 (the fermion masses and mixing angles) the fermion– Higgs, or flavor, sector. How do we know that this is indeed the model of nature, and how do we measure its free parameters? For this we have to describe what we see in nature (actually, most of it is what we see in accelerators).
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