Lepton couplings

At the present stage, we include only contributions of the first family of leptons in the thermodynamic potential. The conditions for the local extremum of ilq correspond to coupled gap equations for the two order parameters [Pg.387]

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 ... 

Positronium, being a readily available purely leptonic system and also a particle-antiparticle pair, has attracted considerable experimental interest over the years as a testing ground for the existence of exotic particles or couplings. The latter may perhaps manifest themselves in the decay properties of positronium, so that attempts have been made to observe forbidden modes. In particular, the longstanding discrepancy between the Michigan experimental value for oAo-ps and the results from QED calculations, described in subsection 7.1.1, has acted as a spur to such investigations. 

In the beta-decay allowed approximation, we neglect the variation of the lepton wave-functions over the nuclear volume and the nuclear momentum (this is equivalent to neglecting all total lepton orbital angular momenta L > 0). The total angular momentum carried off by the leptons is their total spin i.e. 5 = 1 or 0, since each lepton has When the lepton spins in the final state are antiparallel, se+s = stot = 0 the process is the Fermi transition with Vector coupling constant g = Cv (e.g. a pure Fermi decay 140(J r = 0+) —>14 N(JJ = 0+)). When the final state lepton spins are parallel, se + sv = stot = 1> the process is... 

It has been assumed so far that the leptons are massless. They can acquire masses in an analogous fashion to the masses of the bosons via coupling to the same Higgs field. Within the standard model the coupling proposed by Weinberg [14] is employed, which is of the Yukawa t3q)e... 

Y is again the weak hypercharge Y = 2 q — tz), which is 1/3 for u and d, 4/3 for Uij and —2/3 for dij. This ensures that the correct electric charges for the coupling of the up quark (+(2/3)e) and the down quark (—(l/3)e) to the field is obtained. The Yukawa term >CYuk.,g( ), which assigns masses to the quarks upon symmetry breaking, differs from that for the leptons, since both the up and the down quark carry masses ... 

The theories of electromagnetic and weak interactions have heen unified in 1967-1968 hy Glashow, Salam, and Weinberg. According to the electroweak theory, the coupling of intermediate W, Z° bosons to leptons and quarks is the same, as the coupling of photons to leptons and quarks. Thus, the W, particles hehave like heavy photons. 

The evidence that the r coupling is of the V-A type is by now fairly conclusive (see Chapter 14). The shape of the energy spectrmn of the emitted lepton in beta-decay contains a parameter known as the Michel parameter , which is sensitive to the spin structure of the coupling (see Chapter 3 of Bailin, 1982). For example one has ... 

Since we have already determined how and transform under these gauge transformations, the gauge invariant coupling to the left-handed leptons is now fixed. One must have... 

Note the important fact that Z couples to the electromagnetic current of the leptons. It will thus contribute to processes like e e — e e or... 

To obtain an estimate for the branching fraction we require the partial width r(W ud). As will be discussed in Chapter 9 quarks are assumed to couple to the W like the leptons (aside from the complication of Cabibbo mixing and its generalization, which we here ignore). To be precise we shall go through the calculation of r(W — in full detail... 

It is believed that all decay channels of the W are analogous to the pu one, and comprise three leptonic channels and ud, us, ub, cd, cs, c6 (each of the latter coming in three colours). As discussed in Chapter 9 the quark couplings are flavour dependent with, for example, the sum of tid+us+uB for each colour being equal in weight to one leptonic channel. Thus we expect, aside from small effects due to phase space... 

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