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2.1.2 The Standard Model of Electroweak Interactions

In analogy to the isospin of the strong interaction one classifies the known fundamental particles accordingly to their weak isospin TW. Since the weak interaction is maximum parity violating they form a left-handed doublet that carries weak charge and a right-handed singlet that does not. The latter therefore is identified with the projection .

Weak Isospin
1st Generation
2nd Generation
3rd Generation

Table 2-2 The generations of quarks and leptons in the standard model of electroweak interaction.

The logical consequence of the analogy of the weak interaction to electromagnetism is the advent of a particle[5] mediating the weak force like the photon mediates the electromagnetic interaction with the coupling constant a . The coupling constant of the weak interaction then is GV, furthermore the electric charge conservation law corresponds to the conservation of the vector current. Within the electroweak theory the beta transition is described using a virtual gauge vector boson (W-Boson) that couples the hadronic current to the leptonic current with equal strength. For a vanishing momentum transfer q2<< M2, where represents the mass of the W, the coupling constant gW of the W-Boson is directly related to GV via

The success of formulating local gauge invariance with non-Abelian symmetry groups, i.e. SU(2) - introduced by Yang and Mills - and the maximum chiral symmetry breaking of the weak interaction led to the electroweak interaction theory that was independently formulated by Weinberg and Salam based on previous work of Glashow [Gla61]. Herein the weak isospin group SU(2) was combined with the weak hypercharge group U(1) in order to account for charge conservation. Characteristic is the spontaneous symmetry breaking of the SU(2)xU(1) group by the Higgs field that explains the short reach of the weak interaction. This led to the prediction of the intermediate massive Vector-Bosons and their total chiral asymmetry. On top of that the U(1) symmetry remained unbroken and the (massless) intermediate Vector-Bosons was identified as the photon. This fundamental concept of gauge invariance and spontaneous symmetry breaking was verified later; at first, theoretically, when t'Hooft proved the renormalizability in 1971 before the predicted neutral currents were found (1973). Finally, the triumph for the Glashow-Weinberg-Salam theory of electroweak interaction was the discovery of the W±- and Z0-Bosons (1983). (Up to now only the Higgs-Boson remained undiscovered.)

The CVC Hypothesis in the framework of the SU(2)xU(1) electroweak group is a direct consequence of the Noether theorem that claims a conserved quantity for any continuous symmetry. Unlike axial transformations, vector rotations in hadronic flavour space leave the vacuum invariant and therefore a conserved vector current must exist.

[5] As seen before this necessarily has to be a boson obeying vector coupling.

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