Quark-lepton parallelism

There is, presently, evidence for a sequence of three generations of leptons, whose left-handed parts behave as doublets in the weak interactions 

To these, there seem to correspond a sequence of quark doublets 

The above picture is actually oversimplified and other diagrams are needed to account for the data (see Chapter 13). 

---

Here G"v and F v are elements of the field strength tensors for the two SU(2) principal bundles. So far the theory is entirely parallel to the basic standard model of electroweak intereactions. In further work the Dirac and Yukawa Lagrangians that couple the Higgs field to the leptons and quarks will be included. It will then be pointed out how this will modify the B field. The < )4 field may be written according to a small displacement in the vacuum energy ... 

In the current-current approach we have a parallelism between the leptonic doublets (e-)l (/u-)l quark doublet involving... 

L fj /L T /L In this way we have a complete parallelism between the three lepton doublets and the three quark doublets. The transformations under SU(2) are identical, but because of the fractional charges one needs... 

Perhaps the most remarkable development in particle pltysics in the 1970s was the discovery of several families of extremely narrow (i.e. long lived) vector mesons. We give here a brief survey of these particles, of their interpretation in terms of quark constituents and of the consequent implications for the parallelism between quarks and leptons. Some features of QCD needed in this analysis are explained. 

We have seen in earlier chapters that there seems to be a close parallelism between the sets of leptons and the sets of quarks, at least in so far as the unified weak and electromagnetic interaction is concerned. The leptons are essentially point-like in their behaviour, and it is not inconceivable that the quarks too enjoy this property. In that case we might expect the hadrons to behave, in certain situations, in a less complicated fashion than usual. If we think of the hadrons as complicated atoms or molecules of quarks, then at high energies and momentum transfers, where we are probing the inner structure, we may discover a relatively simple situation, with the behaviour controlled by almost free, point-like constituents. The idea that hadrons possess a granular structure and that the granules behave as hard point-like, almost free (but nevertheless confined) objects, is the basis of Feynman s (1969) parton model. 

---