What's the Matternotes session 5

by Steve Bryson

The Electroweak Theory

The electroweak theory is the theory that describes both theelectromagnetic and the weak nuclear force. Therefore electroweaktheory contains quantum electrodynamics (QED) as a subtheory. Infact, electroweak theory ways that the electromagnetic force isnot really a force by itself, but is rather a part a more generalforce, the other part of which is the weak nuclear force. In thisway, the electroweak theory is really a unified field theory,unifying the electromagnetic force with the weak nuclear force.This in itself is remarkable enough, but there is more. We must,of course, explain why the electromagnetic force looks sodifferent from the weak force, and in so doing we discover suchthings as why particles have mass, why the weak force appears asa short range, not a long range force, and we predict theexistence of previously unknown particles (three of which havesince been found!). We also find hints to the answers to suchquestions as why are there different flavors of quarks and whatis the difference between an electron and a neutrino.

The Weak Nuclear Force

We spent the last two classes talking about theelectromagnetic force and QED, the quantum theory that describesit. So let us introduce ourselves to the weak nuclear force.Unlike the other forces that we have discussed, the weak forceshows up in two ways. This force gives very small pushes toparticles (thus the name weak), and the weak force changes theidentity of particles. Thus the weak force is responsible for thedecay of, for example, a muon into an electron, an electronanti-neutrino, and a muon neutrino. Another example is the decayof a down quark into an up quark and an electron and an electronanti-neutrino. This last example is observed when a neutron (madeof an up and two downs) decays into a proton (made of two downsand an up) and an electron and an electron anti-neutrino. Thereare many more examples of such changes in identities.

These changes in identities are now understood (via the fullelectroweak theory) to be due to two particles called the W+and the W-. These W particles play the same role inthe weak interaction that the photon plays in QED. In other wordsthe W particles carry the weak 'force', and they do so bychanging the identity of particles (there is a third particlewhich also carries the weak force, the Z0, but moreabout that later). Basically, the W's will turn an electron intoan electron neutrino, or a muon into a muon neutrino, or a tauinto a tau neutrino. The W's will also turn a down (or strange ortop)quark into an up (or charm or bottom) quark. All of thesechanges can be reversed.

The other particle that carries the weak force is the Z0particle, which acts more like the photon in that it changes themotion of the particles that it interacts with. In this way,neutrinos (which have neither electromagnetic charge nor colorcharge, remember) can interact and 'push' on the other particles(though this push is very weak). The push due to the Z0particle is called 'the weak neutral current'.

This completes the summary of the effects of the weak nuclearforce. To understand just how and why this force acts the way itdoes, we must get into the full blown electroweak theory.

Back to the electroweak theory

As I said above, the W+, W-, and the Z0particles are analogous to the photon of QED in that they carrythe (in this case) weak force. These three particles are quitedifferent from the photon, however, in that they are massive(about 90 times heavier than the proton) and the W+and the W- carry an electromagnetic charge (positiveand negative, respectively). It is the massiveness of theseparticles that is responsible for the fact that the weak force isa short range force. Due to their large masses, these particlesare very short lived particles, living only on the order of 10-25seconds.

It turns out that what makes these force carrying particles somassive is the same thing that gives all the massive particlestheir masses! This is the structure of the electroweak force. Inthis way we understand the masses of all the particles to berelated and perhaps due to the electroweak interaction. In otherwords, if there were no electroweak force, it may be that none ofthe particles in nature would have any mass!

To get an account of what it is about the structure of theelectroweak theory that gives all of these remarkable features,you should now read over the Gauge Theories section of thehandout from session 3. Here you will find a description of theconcept of gauge symmetry which is the fundamental theoreticalunderpinning of all the theories that we have discussed. Thissymmetry is not as complete in the electroweak model as it is in,for example, QCD, and this lack of symmetry is directlyresponsible for all of the features of the electroweak theorydescribed above. The symmetry is said to be 'spontaneouslybroken', spontaneous because nobody knows why it happens in theelectroweak theory and not elsewhere.

In order to describe the spontaneous symmetry breaking of theelectroweak interactions, physicists had to introduce a newparticle called the Higgs boson. This particle has not beenobserved, and there are some theoretical reasons to doubt that itis fundamental -- it might be a bound state of as yet unknownfermions. There are no predictions as to what its mass is, norare there any specific predictions as to its properties asidefrom its being a boson. For this reason it is very difficult tosay that it does not exist (it may simply be too heavy to make incurrent accelerators), so finding it would settle a lot ofquestions.

Using spontaneous symmetry breaking and the Higgs boson wehave been able to predict such things as the existence and massesof the three particles that carry the weak force (W+,W-, and Z0) before they were discovered in1983. This is a spectacular confirmation of the electroweaktheory.

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