The Electroweak Interaction and Unification

We have seen that the electromagnetic and strong interactions are propagated between interacting particles by the exchange of gauge bosons-photons and gluons respectively between the particles. It is therefore natural to postulate that the weak interaction is propagated by additional gauge bosons. Since it is experienced by both hadrons and leptons it is to be expected that these gauge bosons will interact directly with the quark ingredients of hadrons and with leptons. Thus the beta-decay of a neutron into a proton (quark content uud), involving simply the transformation of a d-quark into a u-quark with the emission of an electron and an antineutrino, is now understood in terms of the process shown in figure 1.1(a). The interaction is propagated by a new gauge boson with negative charge known as the             W-boson. Similarly the leptonic decay of the muon can be understood in

Figure 1.1: (a) Beta decay of a d-quark; (b) muon decay.

terms of figure 1.1(b). The more complex decays inolving only hadrons can be similarly described in terms of the exchange of W-bosons between their component quarks. At this stage the existence of the W-bosons (they are required to exist with both positive and negative charge) is simply a postulate. However, a remarkable step forward in our understanding of the weak interaction was initiated in 1960 by Glashow, Weinberg and Salam (Nobel Laureates, 1979). It turns out that the weak interaction is not only similar to the electromagnetic interaction through their exchange of gauge bosons the W-boson and the photon but is intimately related to it, and that the coupling constant of the W-boson to quarks and leptons is the same as that of photons, namely e, the basic electric charge. The ‘weakness’ of the weak interaction is then accounted for if the W-boson is very heavy it needs to be about 85 times the mass of a proton. The weakness arises from the immense amount of energy needed to momentarily create the W-boson which, because of the limitations of the Heisenberg exclusion principle, can then only exist for a very short time. The full electroweak theory also required the existence of another gauge boson (the Z-boson) with zero electric charge, rather like the photon but very heavy. The existence of this new particle implied that hitherto unobserved weak interaction processes should take place and it was a great triumph for the theory when such processes were observed and when the W- and Z-bosons were actually detected (1983) at CERN in accelerator experiments and found to have the masses predicted by the theory. This combination of electromagnetic and weak interaction theory, known as electroweak theory, is beautiful and its predictions are fully confirmed by experiment. It is highly symmetrical in its formulation and the weak and electromagnetic interactions only exhibit their differences, for example the large difference in mass between the photon and the W- and Z-bosons, at low energies. This is referred to as spontaneous symmetry breaking. Spontaneous symmetry breaking occurs in other more familiar physical situations, for example in a bar magnet. At ordinary temperatures the magnetic iron atoms in a magnet line up pointing essentially in the same direction, yet the laws governing this behaviour are perfectly symmetrical and do not pick out any particular direction. The symmetry breaking in a magnet is easily explained in terms of the forces between the atoms which tend to line them up. The electroweak symmetry breaking is similarly attributed to the interaction of elementary particles with a new field pervading the whole of space and which is believed to be responsible for their masses. A theory of such a field was first put forward by Higgs in 1964 and just as the photon is a manifestation of the electromagnetic field so a manifestation of the Higgs field is expected the Higgs boson. It is predicted to be very heavy and so far has not been detected. One of the main incentives for building higher-energy accelerators such as the LHC is to produce and detect this particle. Of course it would be very satisfying if this ‘bringing together’ of the weak and electromagnetic interactions could be extended to include the strong interaction which has a similar mathematical structure and also involves six basic quarks analogous to the six basic leptons. Again, at the energies available in accelerators today, there are fundamental differences between the three types of interaction. Not least, the strong interaction is some 100 times stronger than the electromagnetic interaction. However we that the inter quark force becomes weaker when the quarks are very close together. This only happens at very high energies and to reach the situation when all three interactions have the same strength it is predicted that an energy the unification energy of the order of 10¹⁵-10¹⁶GeV is necessary. This is way beyond accelerator energies in the foreseeable future but such energies were around during the ‘big bang’ as the universe came into being. This retrieval of the overall symmetry at high energy is rather like the retrieval of full spatial symmetry with a magnet when its temperature is raised to around 1050K: at this temperature the magnetism, and of course its directionality, disappears. Below the unification energy spontaneous symmetry breaking ensues and the three interactions revert to the strengths we observe in the everyday world. During the last 20 years a major thrust of theoretical physics has been to try and develop complete and satisfactory unified theories of the weak, electromagnetic and strong interactions so called grand unification theories (GUTS). Such theories would mean that above the unification energy quarks and leptons would have essentially the same properties and could change one into the other. In turn, this would mean that even a low energy everyday proton, for example, would have a very small but finite probability of converting into a positron and a neutral pion. This process would violate the laws of lepton and baryon conservation  and its lifetime is estimated to be at least 10³⁰ years. So far it has not been observed. It is also predicted that magnetic monopoles loose north and south magnetic poles should exist. One very attractive and popular GUT is based on what is called super symmetry which proposes that basic spin-½ particles such as quarks and electrons have partners with integer spins and that, correspondingly, gauge bosons (photon, gluon, W, Z ) have partners with half integer spins. A further very promising development incorporating such ideas is to represent the basic particles, which one normally thinks of as ‘point like’ entities, by different vibrations of fundamental one dimensional strings (referred to as superstrings) which may have ends or be in loops superstring theory. Such a theory can only be formulated if space time has many more dimensions-possibly ten than the four (three space, one time) we have considered so far. The extra dimensions would be ‘curled up’ into a very small size and would, therefore be unobservable. Here it is interesting to note that superstring theories also naturally include gauge bosons having spin 2 and thus open the door to the possibility of a unified theory including the gravitational interaction. The possibility of finding such an all embracing unified theory will be discussed.