Gimme An M! How the Higgs Gives you Mass.

> “I suppose I’ll open a bottle of something if they find it.” -Peter Higgs

Alright, all you quarks and leptons in the house. I’m looking at you in particular, up quark, down quark, and the electron. The up and down quarks combine to make up the proton and neutron, while the electron combines with nuclei to make up atoms.

We learned a little bit about how the Higgs will complete the standard model. And one of the things we mentioned is that the Higgs mechanism gives rest masses to all of the particles in the standard model.

This includes all the quarks (including the constituents of the proton and neutron) and leptons (including the electron). And one of the unavoidable questions I got was, “How?”

This is a good question, and a hard one to explain, but I think I have a good analogy, and it’s all about energy.

The initial liquid level represents the energy in your Universe. Imagine the Higgs field is like a molecule of oil that you drop into this 2-liter bottle. Where would you expect to find it? Well, if the bottle’s already this got a lot of liquid in it, your oil’s going to float on top.

So you know your oil drop’s going to be on the surface. But where is your drop going to wind up? Will it be towards the side of the bottle? In the middle? Somewhere in between?

The answer, of course, is that your drop can wind up anywhere. But if I take an average of all the possible outcomes, it would be in the center. That average value of the outcomes is what we call an expectation value, and in this case, the expectation value is zero. In other words, at high energies, the Higgs field is symmetric at this high energy, with an expectation value of zero.

But what if I drain the bottle?

This is what happens at lower energies. Well, now when I drop my oil droplet in, it will never land in the center. It will always roll down into one of the five wells at the bottom. The fact that all locations are now not equally likely makes us call this a broken symmetry, and the expectation value at these low energies is now not zero.

This whole process is called spontaneous symmetry breaking. And for the quarks and leptons in the standard model, when this Higgs symmetry is broken, every particle gets a mass due to two things:

1. The expectation value of the Higgs field, and 2. A coupling constant.

And this is kind of the problem. The expectation value of the Higgs field is the same for all of these particles, and not too difficult to determine. But that coupling constant? Not only is it different for every particle, but — in the standard model — it’s arbitrary.

In other words, we can determine what they are by measuring the masses of these particles, but the standard model gives us no way to predict them.

And part of the horror of the standard model is that it gives us the origin of the masses of the fundamental particles, and the interactions that give us protons, neutrons, electrons, atoms, planets, stars, and galaxies! But it doesn’t give us the fundamental masses without us measuring them.

This means when the Universe was at a higher energy, though, all the fundamental particles were massless. Could we re-create an environment like that at the LHC? Stay tuned…

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