The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [93]
The Origin of Mass
By introducing the idea that particles can branch as well as hop we have entered into the domain of Quantum Field Theory, and hopping and branching is, to a large extent, all there is to it. We have, however, been rather negligent in our discussion of mass, for the good reason that we have been saving the best until last.
Modern-day particle physics aims to provide an answer to the question ‘what is the origin of mass?’ and it does so with the help of a beautiful and subtle piece of physics and a new particle – new in the sense that we have not yet really encountered it in this book, and new in the sense that nobody on Earth has ever encountered one ‘face to face’. The particle is named the Higgs boson, and the LHC has it firmly in its sights. At the time of writing this book in September 2011, there have been tantalizing glimpses, perhaps, of a Higgs-like object in the LHC data, but there are simply not enough events1 to decide one way or the other. It may well be that, as you read this book, the situation has changed and the Higgs is a reality. Or it may be that the interesting signals have vanished under further scrutiny. The particularly exciting thing about the question of the origin of mass is that the answer is extremely interesting beyond the obvious desire to know what mass is. Let us now explain that rather cryptic and offensively constructed sentence in more detail.
When we discussed photons and electrons in QED, we introduced the hopping rule for each and said that they are different – we used the symbol P(A,B) for the rule associated with an electron that hops from A to B and the symbol L(A,B) for the corresponding rule for a photon. It is time now to investigate why the rule is different in the two cases. There is a difference because electrons come in two different types (as we know, they ‘spin’ in one of two different ways), whilst photons come in three different types, but that particular difference will not concern us here. There is another difference, however, because the electron has mass while the photon does not – this is what we want to explore.
Figure 11.4 illustrates one way that we are allowed to think about the propagation of a massive particle. The figure shows a particle hopping from A to B in stages. It goes from A to point 1, from point 1 to point 2 and so on until it finally hops from point 6 to B. What is interesting is that, when written in this way, the rule for each hop is the rule for a particle with zero mass, but with one important caveat: every time the particle changes direction we are to apply a new shrinking rule, with the amount of shrinking inversely proportional to the mass of the particle we are describing. This means that, at each kink, the clocks of heavy particles receive less shrinking than the clocks of lighter particles. It is important to emphasize that this isn’t an ad hoc prescription. Both the zig-zag and the shrink emerge directly from the Feynman rules for the propagation of a massive particle, without any further assumptions.2 Figure 11.4 shows just one way that our heavy particle can get from A to B, i.e. via six kinks and six shrinkage factors. To get the final clock associated with a massive particle hopping from A to B we must, as always, add together the infinity of clocks associated with all of the possible ways that the particle can zig-zag its way from A to B. The simplest route is the direct one, with no kinks, but routes with huge numbers of kinks need to be considered too.
Figure 11.4. A massive particle travelling from A to B.
For particles with zero mass the shrinkage factor associated with each kink is a killer, because it is infinite. In other words, we are to shrink the clock to zero after the first kink. The only route that matters