We have finally reached the stage where we can explain the Higgs mechanism.

In part 3 of this series, I said that the complete set of elementary particles consisted of six quarks, six leptons, six ‘gauge bosons’ (particles that are the agents of the four fundamental forces), and the Higgs particle. In part 7, I said that there were patterns among the 18 non-Higgs particles, apart from some anomalies. (For previous posts in this series, click on the Higgs folder just below the blog post title.)

It was noticed that the observed patterns among the quarks and leptons would be even more striking if they did not have mass. In order to explain those patterns (or ‘symmetries’), physicists invented a class of theories called ‘gauge theories’. These gauge theories predicted the existence of the force particles (which is why they are called ‘gauge bosons’) and that was satisfying. The catch was that if the symmetries were exact, then the quarks, leptons, and gauge bosons should all be massless, which they are clearly not, except for the graviton, gluon, and photon. So we say that these symmetries are ‘broken’ (i.e., not exact) and physicists looked for a way in which broken symmetries lead to masses.

When it comes to particles that are the source of forces, the rule of thumb is that the smaller the mass of the force particle, the longer the range of the force, with the forces mediated by massless particles being of infinite range. This is true for gravity and electromagnetism for which the corresponding graviton and photon are massless and the forces have infinite range. But while the gluons are also massless, the strong nuclear force acts only over a very short range. This can be explained by the fact that the strong nuclear forces are very strong and prevent the quarks and gluons from becoming free, resulting in them being permanently confined inside composite particles such as the proton and neutron.

The main anomaly was with the weak nuclear force. While the gravity, electromagnetic, and strong nuclear forces each had one force particle associated with them (graviton, photon, and gluon respectively), the remaining weak nuclear force had three particles W⁺, W^–, and Z. While the number of weak interaction particles was predicted by the gauge theories, the weak nuclear force is, as you might expect from the name, extremely weak so the particles associated with those forces cannot be confined within other particles. Hence if those force particles were also massless like the other gauge particles, the weak nuclear force would be of infinite range like gravity and electromagnetism. But we know that the weak nuclear force, like the strong nuclear force, is of extremely short range. The reason is that these particles have mass, and large ones at that. They have been measured to be W⁺= W^–=80.4 GeV; and Z=91.2 GeV, or roughly 100 times the mass of a proton.

How is it that just these three gauge force particles acquired masses? The answer lies with the Higgs mechanism.

In part 10, I described how the average value of the Higgs field was zero just after the Big Bang when the universe was in an extremely hot state but as it cooled slightly, we had the phenomenon of a ‘phase transition’ due to ‘spontaneous symmetry breaking’, in which the average value of the Higgs field in the vacuum abruptly acquired a non-zero value. This happened very quickly after the Big Bang, after about one-trillionth of a second (10^-12s).

So what was the state of play before that phase transition occurred? Before that, the 18 quarks, leptons, and gauge bosons were all massless. The bad news is that at that time, there were actually four Higgs fields present, with correspondingly four Higgs particles (and you thought one was bad enough!). All the Higgs fields had an average value of zero in the vacuum, just like the other fields.

But when the universe cooled past the phase transition point, the so-called Higgs mechanism kicked in, ‘mixing up’ (in a complicated mathematical way) the four original Higgs fields with the four fields that would later become the fields of the three weak interaction particles and the photon. The net result of this mixing process is that three of the four original Higgs fields got ‘absorbed’ (in some sense) by the other four fields, thus disappearing from the picture entirely for the rest of the universe’s life, leaving the one remaining Higgs field taking on the non-zero value it has now.

What happened to those three Higgs fields that lasted for such a short time? It turns out that the particles corresponding to those fields nobly sacrificed their lives in order to give masses to three particles, the W⁺, W^–, and Z, so that those particles got the masses that they have now. So in this process of mixing, the number of fields were reduced from eight (four Higgs, four electroweak) to five (one Higgs, three weak, one electromagnetic), with the particles corresponding to the three weak interaction fields acquiring masses in the process. It is this sequence of events that gave rise to the masses of the W⁺, W^–, and Z that is referred to as the Higgs mechanism.

So to summarize, as a result of spontaneous symmetry breaking via the Higgs mechanism, we end up after the electroweak phase transition with three massive particles that are excited states of the three weak interaction fields and that give rise to the short-range weak nuclear force, a massless photon that is an excited state of the long-range electromagnetic field that gives rise to the electromagnetic force, and the Higgs particle that does not give rise to any force but is an excited state of the Higgs field. Of all the fields, it is only the Higgs field that has a non-zero average value in the vacuum.

Next: How quarks and leptons acquire masses