# Particles, Field Theory, and the Higgs Boson

The buzz around the discovery of the Higgs boson last week induced Erin to challenge me to explain what it is! Well, I’m not a particle physicist, but I do like talking about science, so here goes.

It’s my opinion that the easiest way to understand the Higgs boson is by starting from forces and fields. In day to day life, there are two broad sorts of forces that we are used to encountering. There are forces that come from expending energy to create mechanical action, like pushing a door or throwing a ball. But there are also forces that arise due to intrinsic fields, such as gravitational force on an apple falling or magnetic force on a compass. These fields provide a way to quantify the fact that at every point in space, there are gravitational and electromagnetic and other forces coming from other near or not so near objects. If a new object is introduced to a point in space, it feels forces due to those fields. One way to think about it is that the fields transmit forces between objects, like the gravitational field which transmits forces between the Earth and the Sun. Thus, there is no true vacuum, in part because there is a measurable  gravitational field. Quantum field theory takes things a step further and describes everything in terms of fields. Then, what we have been calling ‘particles’ are special mathematical solutions to the field equations, like oscillations of the underlying field.

But when thinking about fields providing force, a very good question to ask is: what’s the physical mechanism for that? When I push on a door, I generate movement by activating muscles, which turns one chemical into another, turning energy that was stored in chemical bonds into a mechanical form of energy. My hand transfers that energy to the door, via the interface between door and hand at the spot where I’m pushing, and then the door moves. So if there is really a magnetic field pushing a compass needle, how is energy transferred to the needle in order for it to move?

The current thinking in particle physics is that each of these fields has a corresponding particle that transfers the forces from that field. So for an electromagnetic interaction between two particles, there is actually a third particle type that is being exchanged, which is what conveys energy from the field. Usually these mediating particles are ‘virtual’, meaning they exist over very short distances but can have high energies (the requirement of short lifetime for high energy comes from the uncertainty principle between energy and time). In the Standard Model of particle physics, these mediators are called gauge bosons. For example, the electromagnetic field is mediated by the photon, which you may know as the quantum of light. There are special forces that are only noticeable on very short length scales, such as those in the nucleus of atoms. These are the nuclear strong and weak forces, mediated by gluons and W and Z bosons. An additional gauge boson for the force of gravity, called the graviton, has been theorized but not yet detected.

The Standard Model of particle interactions was intended as a framework for unifying the electromagnetic, strong, and weak forces, meaning that it had to account for the properties of gauge bosons. Accounting for the mass of these gauge bosons has been complex: the photon is massless, but the W and Z bosons have a significant mass. But in early formulations of the Standard Model, all particles were treated as massless, and it was a big issue to find a way to fit non-zero particle mass into the picture. The Higgs field is a means to that end, dreamt up by the theoretical physicist Peter Higgs in 1964. It is another field which interacts with particles and contributes to the forces that they experience, this time by giving them mass. The Higgs field is often described as a field which slows some particles down as if they were moving through treacle, but Higgs himself has mentioned his dislike of the idea that the particles experience drag or turbulence due to the Higgs field. The analogy with drag and turbulence implies that energy is being dissipated, but the Higgs field affects particles without reducing their energy. Higgs proposes thinking of it as similar to the refraction of light as it enters a medium like water. As the properties of light are changed by moving through water, so the properties of the particle are being changed by interaction with the Higgs field. How particles interact with the Higgs field determines their mass.

If the Higgs field is real, the corresponding gauge boson must exist. And, a new boson with many of the expected properties of the Higgs boson has now been found in two corroborating experiments at CERN, a particle physics laboratory in Geneva.

There are many different theoretical ways to add the Higgs field into the Standard Model. But most of them predict a fairly high energy for the Higgs boson, and so as accelerator energies rose progressively over the decades and the Higgs boson was not found, Higgs bosons of low mass were eliminated as possibilities. The Large Hadron Collider, which went online in 2008, was expected to have an energy range capable of either finding a Higgs boson that fit with one version of the Standard Model, or proving that the Standard Model contained a serious error. The newly discovered Higgs boson seems to fit the Standard Model, though more work is needed to figure out which version of the Standard Model was correct.

There are still lots of questions to be answered regarding the Standard Model, though. The Standard Model does not incorporate gravity or relativity. It doesn’t explain why the range of mass values for other fundamental particles is huge and kind of arbitrary, as opposed to the few fixed values for charge that fundamental particles can have. It also doesn’t explain why there is more matter than anti-matter (sometimes called CP-violation), or what dark matter or dark energy (both of which have been observed by astronomers) might be. So the discovery of the Higgs boson is definitely a triumph for the particle physics community, but there are still plenty of discoveries to be made!

### 8 responses to “Particles, Field Theory, and the Higgs Boson”

1. Your explanation was very clear. Unfortunately for me, I am now more confused than when I started to read it. I now think of a particle as a localized excitation of a field. If this is the right way to think about things, then a proton, ignoring quarks for the moment, is a localized excitation of the electromagnetic field, the strong field, the weak field, the gravitational field, and, possibly, the Higgs field. The movement of the proton through space time would be controlled by the motion of excitations of each of these fields through space time. Why or how do all of these fields get excited at the same point in space time? Why do we have particles and not just an endless sea of uncorrelated bosons? I know that physicists have told me that particles are condensed bosons and that condensation occurred as the temperature of the universe dropped and the fog of photons disappeared to become the particles that we see. But this explanation is always presented just in terms of the bosons of the electromagnetic field, photons. Why did the other bosons join the party to produce particles? Why did this joining of bosons produce only the particles that we see and not some other particles? I think that the Standard Model is a formal way of organizing experimental results so that the Standard Model yields only the particles that we see, but I no longer understand the colocalization of the different kinds of bosons to yield what we call particles. Can you help me understand why we have particles and not just a bunch of bosons?

• Jessamyn Fairfield

So, it was very clear, but you’re more confused than before? Hmm, that doesn’t sound right…

Your questions are missing one really big piece, which is fermions. A universe composed of gauge bosons would indeed be confusing, but we also have fermions, which behave fundamentally differently from bosons. For the most part, all those bosons are mediating interactions between fermions, and the fermions interact with the underlying fields in such a way that they have various intrinsic properties, such as mass, spin, and charge.

Keep in mind also that matter as we know it did not condense only from bosons, but from the quark-gluon plasma shortly after the big bang. It’s important that the progenitor to our universe contained both bosons and fermions , because it is impossible to build either from the other due to their different spins and different fundamental properties. Each symmetry-breaking epoch after the Big Bang yielded both bosons and fermions as the fundamental forces were decoupled.

2. You got me thinking while I was reading Natalie Angier’s “Canon” and Iain Bank’s “Consider Phlebas.” If I put a boat in a bucket of water and spin around in a circle, then the water, the bucket, and the boat move away from me. If I spin fast enough, the boat floats on the water but the surface of the water is now perpendicular to the ground. I can write equations for the forces on the water and the boat that show that the acceleration of the bucket and its contents as I swing it should result in what I see. Where I am lost is in knowing how to translate these effects into components of the strong, weak, electromagnetic and gravitational forces. Is a Higgs field floating my boat or is something else going on?

• Jessamyn Fairfield

I think your question could be rephrased more generally as, ‘When I solve a mechanics problem, how should I relate the things I am thinking about to fundamental fields and forces?’ And in general, above a very small length scale, you will mostly be talking about electromagnetic and gravitational effects, due to charge and mass, which means talking about forces occurring via the electromagnetic and Higgs fields.

3. I was talking more generally. I think that I understand a single particle moving in a Higgs field. I don’t think that I understand a bucket and boat moving in a Higgs field on the surface of the Earth. I don’t understand how centripetal forces relate to Higgs fields. By swinging the bucket am I altering the local Higgs field or am I doing something else?

4. Eugene Bersing

Question: I have heard that the rest mass of the Higgs Boson is 125Bev at a relativistic mass of 7Tev. This is something like the rest mass of 133 protons. Now if the Boson is necessary to create the field, and only the field can give mass to particles, then how could the hydrogen atom exist unless it was about 133 times heavier than it is?

• Jessamyn Fairfield

For particles that mediate fundamental forces, the mass of the particle determines the range of the force. It doesn’t have anything to do with the properties of other particles that interact with the force, the same way that charge of a photon doesn’t affect the charge of an electron.

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