PMU199S notes

The Standard Model of particle physics

Subatomic particles as probes of the structure of matter

Ernest Rutherford (a.k.a. Lord Rutherford of Nelson) was a New Zealander, and is honoured today by having his image on the back of the NZD$100 bill. He is the only really famous alum of my undergraduate alma mater, the University of Canterbury. He is famous for work he did in Canada and Britain, including splitting the atom in 1911. His brilliant idea was to fire little missiles called $\alpha$-particles at Gold atoms in a thin foil, to figure out what they were made of. $\alpha$-particles are helium nuclei and are produced in one type of nuclear fission reactions. Here is a schematic diagram of Rutherford's apparatus; the actual experiments were carried out by Hans Geiger and Ernest Marsden.

Rutherford's apparatus for figuring out atomic structure.

This experiment is famous because the experimenters got an almighty surprise. Physicists of the day expected his alpha particles to get deflected either not at all or only a little bit as they went through the atom, which was thought to be constituted much like a plum pudding. Their conception was that positively and negatively charged particles within the atom would be roughly evenly distributed throughout, so the $\alpha$-particles would not get a particularly bumpy ride through the atom. Rutherford expected his fluorescent screen to show flashes indicating either no deflection or minor deflections of alpha-particles, with a soft-looking distribution.

The results were so unexpected that the experimenters said it was like artillery shells bouncing back off tissue paper! Yes, there were a lot of undeflected particles, but there were also a few very large deflections along with the smaller ones. The results gave the Rutherford team a harder distribution than expected. They realized that the large deflections imply that there is an extra-hard little nuggetty structure deep inside the atom that bounces the impinging $\alpha$-particles off at cock-eyed angles. Based on Rutherford's team's work, we now know that the positive charge of the atom is concentrated in a very dense, hard, small region about 100,000 times smaller than the width of the atom, known as the nucleus, while the negative charge of the atom is carried by a fluffy cloud of electrons surrounding the nucleus. The radius of an atomic electron cloud is of the order of $10^{-10}$m, also known as an Angstrom, while the nuclear radius is about $10^{-15}$m in size.

The Geiger-Marsden experiments are famous because they got famous results, but the process they used was also interesting. Physicists love to probe things, by tickling a system of interest with whatever probes are available.

Particle physicists did not stop at Rutherford's experiment: they kept developing techniques, building better accelerators, and making new discoveries. One of the Nobel Prize worthy discoveries happened at SLAC, a big particle accelerator lab near Stanford University in California, back in the hippy era. Physicists there had the bright idea of firing electrons into protons and neutrons -- and they discovered substructure! Each proton and neutron has three little nuggetty bits inside called quarks, bound together strongly by gluons. The biggest recent Nobel worthy discovery in particle physics was the discovery of the Higgs boson. This was announced in July 2012 by the ATLAS and CMS collaborations at the Large Hadron Collider at CERN.

Physicist Periodic Table

Chemistry has a Periodic Table of the elements. Physics has its own version of a chart of subatomic structure, called the Standard Model of Particle Physics. This is our topic for this week.

Zoo of subatomic particles

Particle ID

How do particle physicists know which particle is which? This question is important in the same way that being able to tell your kids apart is important. A clever idea is to pick invariants -- properties of the subatomic particle that remain unchanged regardless of changes in perspective, like displacement, rotation, or relative motion. We want to be able to recognize an electron just as well if it is stopped in a car in Montreal or in a robot flying by Mars or rotating around somewhere in the Andromeda galaxy.

Physicists rely on the symmetries of spacetime to classify the invariants that are available. There are only three for elementary particles: mass $m$, spin $s$, and force charges $q$. Since all three are the same regardless of perspective changes, they make perfect particle labels. An electron has the same mass, spin, and force charges everywhere, in all situations. The electrons that help make up the atoms of your wallet are identical in every way to those that help make up the molecules of poo that your neighbour's dog deposits on your lawn.

Note: some physics for poets classes confuse the issue by saying that mass changes with motion. This is a misconception. Only the energy of a particle changes with its motion; the mass remains invariant. Also, we do not allow mass to become imaginary because that gives rise to dangerous (free) tachyons, which wreck causality and spoil our ability to predict anything at all using physics.

Mass of a subatomic particle can be anything from zero to very large. Spin is different: it is quantized, meaning that it can only take on some very specific values. Spin can be zero or integer or half-integer, measured in units of a fundamental physical constant named $\hbar$ (whose value in SI units is approximately $6.63 \times 10^{-34}$Js). The values force charges can take depend on the force, and we will not delve into detail here except to mention that electric charge is measured in units of the charge on the electron, which in SI units is approximately $1.6 \times 10^{-19}$As. This means that if you have a 10 Amp current flowing in your hairdryer circuit for a second that is made up of approximately sixty billion billion moving electrons.

Bosons and fermions

Nature makes a crucial distinction between bosons, which have spin $0, \hbar, 2\hbar, 3\hbar,\ldots$, and fermions, which have spin $(1/2)\hbar,(3/2)\hbar,(5/2)\hbar,(7/2)\hbar,\ldots$. Up at high temperatures when particles race around with a lot of average energy of motion (kinetic energy), bosons and fermions behave pretty much the same. But when you cool a system down to extremely low temperature, it matters hugely whether you are a boson or a fermion.

The Pauli Exclusion Principle (PEP) is a really important property of fermions: it says that no two fermions can be in the same quantum state at the same time. In plain language, this means that fermions have elbows. You simply cannot crowd them on top of one another: if you try, it never works. This fact helps explain (among other things) why atoms with more protons in their nucleus are physically larger: each allowed orbit for electrons can only hold a few electrons. The PEP is also responsible for holding up white dwarf stars and neutron stars, i.e., those elbows can be pretty strong!

Bosons have no problem with being crowded right on top of each other. Sometimes, if you try really hard and use extremely low temperature, you can get bosons to go into a state like a group hug called Bose-Einstein Condensation (BEC). In BEC, systems show off quantum effects that are really noticeable compared to what you get for a single boson. We will not say any more about BEC here for lack of time; suffice it to say that it is an awesome topic. BEC was first discovered experimentally only in 1995.

Matter (a.k.a. stuff) in particle physics is composed of fermions, while bosons play the role of force messenger particles.

Ice skater analogy

Imagine that you are standing on a freshly Zamboni'd ice hockey rink in your ice skates. Imagine that your friend Ben is there with you, holding a basketball. Now imagine what happens if Ben throws the ball towards you. In which direction does he move? Backwards. The reason is called recoil and originates in a physics principle called conservation of momentum. A familiar example might be the kick you feel when you fire a gun. The bullet escapes out the barrel at high speed, but it is not very massive. The gun is much more massive, so it moves backwards in response much more slowly. That is known as recoil. Recoil is why Ben is moving away from you since he threw you the basketball.

Now imagine what happens when you catch the basketball. You move in the same direction as the basketball was moving, except slower because you weigh more. That's also how recoil works. OK. Now throw the basketball to Ben. What happens? You recoil from him in response, which makes you move a bit faster overall away from Ben. So now, after one complete exchange of the basketball, you are moving away from each other. Now repeat the whole cycle several times. What's the result? You and Ben are moving away from each other more strongly.

The analogy is that the basketball is like the photon, while you and Ben are like electrons. The exchange of the basketball (photon) between the two humans (electrons) is just like transmission of a (repulsive electric) force. Except for one thing: you did not actually touch each other directly. You had an effect on each other by both interacting with the basketball individually.

The ice skater analogy is not perfect, in that it is harder to explain attractive forces. But it is a very helpful analogy for getting your head around explaining forces acting at a distance in terms of subatomic particle interactions.

Force messengers

There are four different forces known in Nature -- gravity, electromagnetic, strong nuclear and weak nuclear. Gravity holds you on Earth and Earth in orbit around the Sun. The electromagnetic force describes electricity and magnetism -- which you can see are connected if you watch a compass needle move around during an electrical storm! As we discussed in Week 1, the strong nuclear force holds the atomic nucleus together. You can see the power of the strong force when you set off a nuclear bomb. The weak nuclear force is responsible for some kinds of radioactivity and for the fusion reaction that powers our Sun. So even though the weak force is weaker between two subatomic particles than the strong force, it is still mighty.

The messenger for electromagnetism is known as the photon, which has zero mass and spin one. The messenger for gravity, the hypothesized graviton, has zero mass and spin two. The messenger for the colour (strong nuclear) force is known as the gluon, which has zero mass and spin one. For the weak nuclear force, the messengers are known as the W+, W-, and Z bosons, which have spin one and are all quite heavy. The Higgs boson (responsible for mass of quarks, leptons and the weak bosons) has spin zero and is the most massive boson discovered so far by humans.

All of these particles have been seen and studied in particle accelerator laboratories. I think the single important fact about the Large Hadron Collider (LHC) is that 8000+ human beings from over 70 different countries around the world are working together on science, cooperating madly across borders and beliefs. You will be writing your second Essay about the LHC and the discovery of the Higgs boson; the online sources I have provided you for the essay on the course web site should provide you everything you need to know, vital statistics and otherwise.

Antiparticles

Before 1928 nobody had even proposed the idea of an antiparticle. Paul Dirac proposed the existence of the positron, a particle with the same mass and spin as the electron but with the opposite charge. The most important property of the positron is that, if it meets an electron, they annihilate each other into a blaze of pure energy (photons). The positron was discovered in 1932.

Physicists later realized that every subatomic particle has an antiparticle. The antiparticle has the same mass as the particle, and the same spin, but the opposite force charges. Particle-antiparticle collisions result in annihilation into energy. The interesting thing is that you can do the reverse too: if you have enough energy, under the right conditions, you can create particle-antiparticle pairs. This is called pair creation. A few particles are their own antiparticles. This can only happen if the particle has zero charge to start with, like the photon.

We can see evidence of antiparticles in the sky, from energetic blazes of light called gamma rays that they emit when they find their corresponding particles and annihilate. One of the great puzzles of modern astroparticle physics is to explain why particles are much more common in the universe than antiparticles.

Antiparticles also occur in cosmic ray showers, which are brief events that happen when a cosmic ray hits the atmosphere and slams into an atom of gas way up there, banging it up and creating a shower of subatomic particles from the collision. Cosmic rays are energetic particles originating in outer space. About 89% of cosmic rays are protons; about 10% are photons, and most of the rest are alpha particles, nuclei of heavier elements, and electrons.

Antiparticles are found all the time inside modern particle accelerators. They are extremely relevant to LHC physics.

Force charges

Groups of subatomic particles with similar properties have traditional names associated with them. Here are some of the important ones.

The electron (e) has two heavier cousins: the mu (μ) and the tau (τ). All three of them have spin (1/2)ℏ and negative electric charge. Each of these three subatomic particles has an associated neutrino, called the electron neutrino (νe), the muon neutrino (νμ), and the tau neutrino (ντ). Neutrinos have spin (1/2)ℏ and zero electric charge. The group of all six together is called the leptons.

How about the group known as the quarks? The up (u) and down (d) quarks making up the proton and neutron have heavier cousins known as the charm (c) and strange (s) quarks, and the top (t) and bottom (b) quarks. All of them have spin (1/2)ℏ and electric charge. Subatomic particles composed of quarks and gluons are known as mesons (quark-antiquark) and baryons (quark-quark-quark). Two examples of baryons are the proton and the neutron. The group of mesons and baryons together is known as the hadrons.

Particles with electric charge feel the electromagnetic force. Particles with weak nuclear (also called flavour) charge feel the weak force. Particles with strong nuclear (also called colour) charge feel the strong force. Finally, everything with energy feels the gravitational force. It is the most democratic force in the universe. This is one of the reasons why gravity is my favourite.

Here is a table describing who feels which force.

ParticleElectromagnetism?Strong nuclear?Weak nuclear?Gravity?
e, νe, μ, νμ, τ, ντyes and no*noyesyes
u, d, c, s, t, byesyesyesyes
photon [1]nononoyes
gluon [2]noyesnoyes
W+, W-, Z [3]yes and no*noyesyes
graviton [4]nononoyes
Higgsnonoyesyes

* The e, μ, and τ have electric charge, but the neutrinos do not. The W+ and W- have electric charge, but the Z does not.
[1] The photon is the messenger of the electromagnetic force.
[2] The gluon is the messenger of the strong nuclear force.
[3] The W+, W-, Z are the messengers of the weak nuclear force.
[4] The graviton is the messenger of the gravitational force.

Colour force

Anyway, back to the colour-force. It turns out that there are precisely three types of possible colour charges associated to the colour-force (a.k.a. the strong nuclear force). Physicists figured this out by doing a bucketload of painstaking experiments and lots of abstract thinking. Quite arbitrarily, physicists of the day decided to call the three possibilities for colour-charge Red, Green and Blue. These are not actual, real-life colours like the colours of light -- the word colour is only meant as an analogy. Physicists could just as well have decided to call the three options Raspberry, Chocolate and Vanilla, and dubbed it the Gelato-Force. But they went with Red, Green, and Blue, and dubbed it the Colour-Force. Once the name caught on, we were stuck with it. When particle theorists figured out all the moving parts properly, they called their final version Quantum ChromoDynamics, or QCD. (Chromo- comes from the Greek word for colour.) If you use this phrase you will sound like Sheldon on the Big Bang Theory.

The one useful aspect about using colour words (rather than, say, ice cream words) to describe the strong nuclear force is that making colourless objects is easier to understand because the rules work just like they do for light. If you want to make something colourless with light, you use equal quantities of Red, Green, and Blue. If you do this with quarks, using one Red quark, one Green quark, and one Blue quark, you get a baryon. Baryons are colourless three-quark combos. Or to make something colourless you could instead add together a colour and its complementary (opposite) colour. Doing this with quark ingredients, if you take a quark, say, a Red one, and add an antiquark that's anti-Red, you would get a meson. Mesons are colourless two-quark combos. Mesons and most baryons are unstable: they do not live for longer than a tiny fraction of a second.

A small aside about colours of light. The opposite of Red is Green+Blue, which is known as Cyan. The opposite of Blue is Green+Red, which is known as Yellow. The opposite of Green is Red+Blue, which is known as Magenta. You can make any colour of light by starting with a palette of (Red,Green,Blue) or (Cyan,Magenta,Yellow).

Colour confinement

The colour-force (a.k.a. strong nuclear force) is different than the electromagnetic, gravitational, and weak-nuclear forces in one very big way. Colour confines at low energies, which means that colour-force dynamics gets tightly confined to distance scales smaller than the size of an atomic nucleus. Colour does not leak out: you cannot see it at longer length scales at all. This is totally unlike your two most familiar forces -- gravity and electromagnetism -- which have infinite range. Even the weak nuclear force, which is also short-range, is not as strict as the strong force; it does not confine at low energy. Instead, it is Higgsed.

What does confinement mean in plainer language? Well, the quarks and gluons which participate in colour-force dynamics do some very pretty dances together within the proton and neutron. They have strong attractive forces happening inside, with colours flying everywhere. It is pretty fascinating and pretty intricate. And pretty messy. But the idea is that we never see those dance moves with human eyes. It is all going on under the hood as far as we are concerned. We just see the colourless proton or neutron.

When colour is confined, like in our universe today, quarks, which carry colour charge, are not allowed to run around naked. Naked gluons are not allowed either. Quarks are only allowed to live within colourless composite particles -- baryons and mesons -- made up of coloured quarks bound together by coloured gluons. For example, an up quark inside the proton that makes up a nucleus of hydrogen in your body.

Particle physicists are like mechanics who insist on opening up the hood and tinkering with the engine. We insist on understanding the colour force even when it is not easy to experiment on it. Physicists currently have a partial understanding of how colour confinement works. What we do not yet understand is why colour confines. If you become a researcher and can explain why, to the satisfaction of academic physicist and mathematician researchers, then you can claim a USD$1,000,000 prize from the Clay Mathematics Institute. Let no-one ever say that there is no money to be made in mathematics!

Let us end with two brief examples of building baryons. If we want to make a proton, we have to use two up quarks (u) and one down quark (d). More briefly, we say that a proton is uud. A neutron, by contrast, is udd: it is composed of one up quark and two down quarks. But for our protons and neutrons to be properly colourless, we have to add one more little detail to our description. The u, u, and d in the proton must be three different colours, in equal proportions. This ensures that the proton is colourless overall, even though it is built out of coloured ingredients. Similarly for the neutron.

Essay sources