Well, this series keeps getting longer and longer. I initially intended it to be just one part, then I decided it really needed an introductory article to set things up; that introductory article soon became two parts, and then the second of those ran long and got split into two. And now, I’ve found myself going into much greater depth in this fourth part than I had expected. So, I’m just going to stop trying to predict how many more parts there will be; we’ll work our way through the particle zoo and finish whenever we finish. Incidentally, if you found yourself getting lost with the previous parts, or if you haven’t read them at all, I’d still encourage you to give this one a try; I’m hoping it’s written in such a way that you’ll still get something out of it.
We’ll mainly be talking about the Standard Model of particle physics, currently our best understanding of how the universe works1, though we’ll also get into some hypothetical particles that go beyond the Standard Model. The Standard Model is a Quantum Field Theory containing seventeen2 types of particles.
We’re going to take a tour through all of these particles, and beyond. But rather than going through that chart systematically, I’m going to jump around so as to, I hope, introduce new concepts in a more sensible way. Today we’re going to cover pretty much everything that’s required to build an atom, the unit out of which most of the world as we experience it is made.
Electrons and Photons
Let’s start our tour with an old friend: the electron. We talked about electrons in the context of Quantum Electrodynamics last time, and of course you’re all familiar with them as constituents of the atom. The electron, when you come down to it, is easily the particle most relevant to our everyday experience; it’s the foundation of all chemistry, not to mention electricity.
The electron has spin 1/2, making it a fermion. Its mass is about 511 keV (remember, since mass is a form of energy, we typically talk about it in units of energy), which is about 9.1×10^-31 kilograms. The electron’s negative electric charge is defined as the “elementary charge”, which we denote with e. The electron’s antiparticle is called a positron; it has the same mass, and spin, but its electric charge is +e rather than -e.
The electron is about as nice and uncomplicated a particle as you could want. It primarily interacts via electromagnetism, which is described by Quantum Electrodynamics, the cleanest and most well-behaved realistic quantum field theory.
One important thing to note about the electron is that it’s stable. In the previous article, I talked about particle decays (for instance, a neutron spontaneously decaying and producing a proton, an electron, and an anti-neutrino). I noted there that in order to maintain the conservation of energy, a particle can only decay into some set of particles whose total mass is less than that of the initial particle. You also may recall that the more “options” a particle has in terms of how it decays – what set of particles it decays into, and how the excess energy is split up between them – the more likely it is to decay. (The range of these “options” that are available is called the phase space for the decay.) The result is that heavy particles tend to have shorter lifetimes than light particles, because they have more available phase space for decay. The 511 keV electron is pretty light – the proton and neutron, for instance, have masses in excess of 900 MeV.
And in fact it turns out that there is no available combination of particles an electron can decay into. The only particles we know of with masses smaller than the electron are neutrinos and massless bosons (we’ll talk about both of these later), all of which are electrically neutral. Since the electron has an electric charge of -e, if it were to decay, the set of resulting particles would have to have charges adding up to a total of -e; the initial charge has to equal the final charge. But the only particles lighter than the electron all have charge 0, and there’s no way to add up a bunch of 0s into anything but 0. Therefore, in the Standard Model, the electron cannot decay.
But as I mentioned last time, physicists spend a lot of time looking for supposedly forbidden events. If we ever did see an electron decay, that would be evidence for physics beyond the Standard Model. It would mean that either there were some very light particles that we’ve never observed before or (more likely) that there was some rare process in which charge was not perfectly conserved. I bring this up because it illustrates a point about how physics is done. No number of experiments can ever definitively verify that the electron does not decay; but what we can do is search for electron decays and, when we fail to find them, put some limits on the probability for such a decay. Currently, that lower bound is that the electron lifetime is greater than about 6.6×10^28 years. This quoting of upper or lower bounds on the properties of a particle is something one sees all the time in particle physics.
It’s hard to talk about the electron without introducing the photon. The photon has spin 1, making it a boson. It’s one of the Standard Model bosons that are often referred to as “gauge bosons”, which are the messenger particles that carry the fundamental forces3. In particular, the photon is the carrier of the electromagnetic force. What does this mean? It means that what we see on a macroscopic level as, for instance, a repulsion between two like charges is really the sum of a lot of processes like this:
Here one electron emits a photon, and another absorbs it. And if we calculate, from QED, the rate at which this happens for each possible combination of momentum, we find that the net effect of all these interactions is to push the particles apart. Similarly, if we do the calculation for a pair of particles with opposite charges, the net effect is to pull them together. And ultimately all of the phenomena of electric and magnetic forces comes down to interactions mediated by these photons.
Since light is an electromagnetic phenomenon, photons are also the particles that “make up” light. All of our experience of light comes down to QED interactions between photons and charged particles – when our eyes detect light, that’s because a photon has been absorbed by an electron in an atom in a rod or cone cell; when you turn on a light bulb, you’re causing electrons in the bulb to emit photons; when light appears to bend in a glass of water, that’s because the photons passing through are interacting with protons and electrons in the water.
The photon is believed to be massless, and experiments have put an upper bound of something around 10^-17 eV on its mass. In any Quantum Field Theory, any particle with a mass of zero, like the photon, will always be moving at the universal maximum speed of c, which is why this speed is called the speed of light. Because it has no mass, all of a photon’s energy is in the form of kinetic energy.
Electrons in Atoms
Now that we’ve introduced the electron and the photon, I want to take a quick detour to talk about atoms. You know that an atom consists of a nucleus, containing protons and neutrons, surrounded by electrons. We’ll get to the nucleus in due course, but for now, think of the whole nucleus as just a big positive charge at the center of the atom. Because the nucleus is charged, it couples to the electromagnetic force; it can emit and absorb photons just like a positron or electron. And as with a positron and electron, the net effect of all that exchange of photons between the positively charged nucleus and a negatively charged electron is one of attraction – that’s why electrons end up in what we call a “bound state” in an atom, tethered by the exchange of those photons.
The picture that you may have in your head, though, of electrons orbiting the nucleus like planets around a star, is a bit misleading. For a freely moving particle, kinetic energy is not quantized; it doesn’t come in discrete units like angular momentum. But a bound particle typically does have only discrete energy states available to it. Mathematically, this is because saying that a particle is bound amounts to putting certain “boundary conditions” on the state of that particle, conditions which can only be satisfied if the particle has certain energy values. As an analogy, you can think of it as if the electron’s state is a wave that goes up and down in a ring around the nucleus, with the boundary condition being that once it has gone all the way around, it needs to end up back where it started. So this wave could complete one oscillation as it goes around, or it could complete two, or three, but it has to be some integer; it can’t go through one and half oscillations, because then the wave wouldn’t match up when it returned to the starting point.
This is called a “standing wave”. The more oscillations the wave goes through (i.e. the higher the frequency), the higher the energy of the electron. Since only discrete numbers of oscillations are permitted, only discrete energy levels are allowed.
An electron in one of these energy levels, or “orbitals” as they’re often called, has a definite kinetic energy, but not a definite position. So instead of thinking of an electron as being like a little planet going around the nucleus, a somewhat better picture is to think of it as a cloud of probability surrounding the nucleus – those probabilities corresponding to how likely you’d be to find the electron in any given place if you did make a measurement of its position.
Since photons have kinetic energy, when an electron emits a photon, it has to give up some of its own kinetic energy. But if an electron is in an atom, it has to exist in one of the allowed energy levels – so it can only ever emit a photon if it gives up exactly the right amount of energy such that it ends up in an allowed energy level. If it’s already in the lowest available energy level, it can’t emit a photon. And since it’s a fermion, the Pauli exclusion principle applies, meaning only one electron can occupy any given state – so if all the lower energy levels are already filled, it also can’t emit a photon. Similarly, if an electron absorbs energy from a photon, it will always absorb exactly enough to jump up to an available energy level. This is called an “excited state”. Of course, if a photon gives the electron enough energy to break it free of the electrical attraction of the nucleus, then the electron will leave the atom, becoming a free particle that can have whatever energy it likes. We’ve talked about how in particle physics, if a process is allowed, then it will happen. This means that if an electron is bound in an atom in some energy level, then if there is a lower energy level available, it’s only a matter of time before the electron emits a photon and thereby jumps down from this “excited state” to the lower energy level, the “ground state”.
There’s a lot more that could be said about this, which would take us even farther away from the topic of elementary particles, but I wanted to talk about atoms mainly as a way of showing how this picture of the atom that you may have learned about in high school is related to the fundamental particle physics we’ve been talking about.
Quarks and Gluons
You might expect that having dealt with the electron, we’d move on to the other constituents of an atom, the proton and neutron. But in the Standard Model, the proton and neutron are not elementary particles; they’re composite particles made of things called quarks. So let’s talk about quarks.
Whereas the electron and photon were identified as particles in 1897 and 1905, by J. J. Thomson and Albert Einstein, respectively, quarks were completely unknown before the 1960s. It was thought that protons and neutrons were elementary particles, and early Quantum Field Theory treated them as excitations of fundamental fields, just like the electron. Starting in the ’40s, several other particles, similar to the proton and neutron but short-lived, were discovered; this larger class of particles is what we now call “hadrons”, and we’ll get to them in due course. As physicists studied the properties (charge, spin, mass, etc.) of these hadrons, though, they began to notice certain patterns. In the early 1960s, Muray Gell-Mann realized that one could arrange these hadrons in something analogous to the periodic table for the elements, systematically predicting what hadrons should exist and what their properties should be. And soon Gell-Mann and, independently, George Zweig realized that these patterns could be neatly explained if one posited that they represented different combinations of a small number of basic building blocks. Gell-Mann called these building blocks “quarks”4.
Quarks come in six flavors (yes, “flavor” is a technical term in particle physics), but let’s start with just two of them, called the up quark and the down quark. The up quark has a mass of 2.2 MeV (so, about four times as much as an electron) and an electric charge of +2/3e. The down quark has a mass of about 4.7 MeV and a charge of -1/3e. Both are spin 1/2 fermions.
Since they have electric charge, quarks interact via electromagnetism – in other words, they couple to photons; a photon can be absorbed or emitted by a quark, just like by an electron. Unlike electrons, though, quarks also interact via something called the strong nuclear force, or just the “strong force”. Just as electromagnetism is described by the theory of Quantum Electrodynamics (QED), the strong force is described by something called Quantum Chromodynamics (QCD).
In electromagnetism, we have the electric charge, a conserved quantity and a property of particles that dictates how strongly they couple to the photon, and thus how strongly they “feel” the electromagnetic force. With the strong force, we have something analogous called “color charge”. But whereas there is only one kind of electric charge, there are three varieties of color charge, called red, blue, and green. (These names, incidentally, have nothing to do with actual colors; the terminology came about just through analogy to the three primary colors of human vision.) Quarks come in any of these three colors, so a particular quark might be, say, a red up quark or a green down quark. There are also, of course, antiquarks; these have opposite electric and color charges. So, an up antiquark (or just “anti-up”) has an electric charge of -2/3e, and a color charge of either “anti-red”, “anti-blue”, or “anti-green”. These color charges have a peculiar way of adding together – any color cancels out with its anti-color, just like positive and negative electric charges, but the combination of all three colors, red + blue + green, also cancels out to zero total color.
Just as the photon serves as the “messenger” particle for electromagnetism, the gluon is the messenger of the strong force. Like the photon, it is a spin-1 boson, and also like the photon it is massless. But unlike the photon, the gluon does carry a charge – not an electric charge, but a color charge. In fact, each gluon carries one unit of positive color charge and another unit of negative, or anti-, color charge. You can have, say, a red anti-blue gluon, or a green anti-red gluon, and so on5. It’s worth pausing a moment to take note of this. The photon couples to particles with electric charge, but the photon itself doesn’t have an electric charge. The gluon, on the other hand, couples to particles with color charge, and it also has color charge itself. That means that gluons also couple to themselves; a vertex like this is allowed in QCD, whereas the corresponding diagram for a photon is not allowed (note that the curly line is traditionally used for gluons in Feynman diagrams):
This self-interaction of the gluon is one of the things that makes QCD more difficult to work with than QED. The other is that the strong force is, well, strong. In the last part, I talked about how when we calculate the probability for a process, each vertex in the diagram multiplies the probability by a fraction called the “coupling constant”. Coupling constants are actually not exactly constant – they can vary with the energy of the particles involved. The electromagnetic coupling constant is about 1/137 at low energies, and it increases slowly as energy goes up. The strong coupling constant, on the other hand, is close to 1 at low energies and decreases as energy goes up. In QED, because the coupling constant is small, the contribution from diagrams containing many vertices is negligible. In QCD, on the other hand, each additional vertex doesn’t really reduce the probability all that much, at least at low energies. This means that the perturbation theory, technique of calculating the probability of a given process as an infinite sum of increasingly complex diagrams, doesn’t work in low-energy QCD, and a variety of other more sophisticated techniques are used – which I, alas, am not really competent to talk about in any detail.
As a result of the large coupling constant and the self-interaction of gluons, the strength of the strong force acting between quarks also does not decrease with distance the way that of electromagnetism does. This leads to something called color confinement, which means that quarks are never found “free”; they are always bound together by the strong force in groups that are color-neutral. Any process that would pull one quark out of this group would require so much energy that it would spontaneously create additional quark/antiquark pairs, and these would then pair up with the existing quarks to create new color-neutral combinations.
OK, I feel like I just blew through a lot of stuff pretty quickly, so let’s review a bit. Like electrons, quarks have electric charge and interact via electromagnetism. But unlike electrons, they also have color charge and interact via the strong force. This means that, in addition to coupling to the photon, they also couple to the gluon. The gluon itself also carries color charge, which means that the gluon couples to itself. The strong force is, as the name suggests, intrinsically stronger than electromagnetism, which makes the theory that describes it, QCD, more difficult to work with than QED. And finally, the strength of the strong force does not decrease with distance the way the electromagnetic force does, and as a result, particles carrying color charge cannot exist in a “free” state; they are only found as constituents of color-neutral composite particles. So let’s talk a a little bit about those composite particles.
Protons and Neutrons
Any composite particle made up of quarks bound together by gluons is called a hadron. Color confinement dictates that hadrons must be color-neutral, and there are two pretty simple ways of combining quarks to make a color-neutral composite. You could have a particle made up of a quark of some color and an antiquark of the same (negative) color (e.g. a green quark and an anti-green antiquark), or you could a have a particle made up of three quarks, one of each color (a red quark, a blue quark, and a green quark). The former type of particle – consisting of a quark and antiquark – is called a meson, and the latter – consisting of three quarks – is called a baryon. (Of course, anything you can do with quarks you can also do with antiquarks, so there are also antibaryons consisting of three antiquarks).
Any flavor of quark comes in all three colors, so we can make mesons and baryons out of any combination of flavors. Most of these combinations end up resulting in particles with very short lifetimes, but two particular combinations can yield long-lived particles: uud (that is, two up quarks and a down quark) and udd (one up quark and two down quarks). The former constitutes the proton, the latter the neutron.
The proton has a charge of +1e (the sum of +2/3e from each up quark and -1/3e from the down quark). The spins of the three constituent quarks can add up in two possible ways – without getting into the somewhat counterintuitive rules for addition of angular momentum in quantum physics, I’ll just state that either the three quarks can all be aligned, giving a total spin of 3/2, or two can be aligned and one anti-aligned, giving a total spin of 1/2. The latter turns out to be a lower energy, and thus more stable, state, so it is specifically the spin-1/2 combination of uud quarks that is the proton (the spin-3/2 uud baryon is called a Delta baryon). Having spin 1/2, the proton is a fermion. In fact, all baryons end up being fermions, with a spin of either 1/2 or 3/2, while mesons end up having a spin of either 0 or 1, making them bosons.
The proton has a mass of about 938.3 MeV (if you look back at what I told you about the masses of the up and down quarks, you might notice something peculiar here, but I’ll let you puzzle that out for now and I’ll come back to it shortly). This makes it more than 1800 times as massive as the electron, but it is the lightest of all baryons. So it should not be too surprising that in the Standard Model, the proton is stable. Like an electron, a proton will never spontaneously decay into other particles6.
The neutron is the baryon with quark content udd and spin 1/2. Its electric charge is 0 (the +2/3e from the up quark cancelling out with the -1/3e from each of the down quarks). Its mass is about 939.6 MeV, just a little bit heavier than a proton. Unlike the proton, the neutron is not stable. A free neutron has an average lifetime of about 882 seconds – a little less than 15 minutes – decaying into a proton, an electron, and an antineutrino. This might surprise you; after all, neutrons are one of the building blocks of matter. If half of all neutrons decay within 15 minutes of being created, why has my body not disintegrated (I mean, more than it already has); why hasn’t the whole earth decayed away into just protons and electrons, for that matter?
The trick here is that I said a free neutron has an average lifetime of 882 seconds. Remember that when it decays, the neutron essentially turns into a proton and emits an electron and an antineutrino. If a neutron is by itself, moving freely through space, there’s nothing to prevent it from doing this. But bound within a nucleus, the protons and neutrons can only occupy discrete energy levels, just like the discrete energy levels of an electron that’s part of an atom. And because protons and neutrons are fermions, they obey the Pauli exclusion principle – no two particles can occupy the same state. If a neutron decays and produces a proton, then, that proton can’t occupy one of the energy states already occupied by another proton in the nucleus. But those other protons will typically already be filling up all the low energy states, which means that the neutron can only decay if it has enough energy to put the resulting proton in one of the unoccupied energy levels. In most nuclei, this is not possible, which means that the neutrons in those nuclei are stable. If, on the other hand, a nucleus contains the right combination of neutrons and protons so that a proton energy state is available for a neutron to decay into, then that type of nucleus is unstable. This decay of a neutron, called beta decay, is one of the main types of radioactive decay that certain elements and isotopes undergo.
All right, let’s come back to the topic of the mass of the proton and neutron. Did you notice the puzzle here? I told you the mass of the proton is about 938.3 MeV. But the mass of an up quark is only 2.2 MeV, and the mass of a down quark is 4.7 MeV. If we add up the masses of the two up quarks and one down quark that make up the proton, we get just 9.1 MeV – less than one percent of the actual mass of a proton. Similarly, if we add up the quark masses for a neutron, we get 10.6 MeV, much less than the neutron’s actual mass of 939.6 MeV. So where does that extra mass come from? Some of this is the kinetic energy of the quarks. Think about this for a moment: if we imagine a stationary proton and we “zoom in”, so to speak, to look at the quarks, they won’t be stationary; they’ll be revolving about, like electrons in an atom, and will thus have some kinetic energy. Now imagine we “zoom out” and think of the proton as a stationary particle, and therefore one with no kinetic energy – if we don’t count the kinetic energy of its quarks as part of the mass of the proton, we will have undercounted the amount of energy in the system. In other words, if we’re looking at the proton from the outside, the kinetic energy of its constituent quarks looks like part of the mass of the proton.
But this still doesn’t add up to enough mass. The rest of the mass of the proton and neutron comes from what we call the QCD binding energy. The usual way to explain this is to say that this is the amount of energy that would be required to pull the quarks apart, the energy needed to counteract the force of the strong interaction holding them together. And this is true, as far as it goes, but it’s never struck me as particularly enlightening (after all, if we’re not pulling a proton apart, why should the amount of energy this hypothetical process would require have any bearing on the proton’s actual mass?). In fact, this binding energy is stored in the gluon field binding the quarks together, and can be thought of as the energy carried by the gluons being exchanged between them.
But it’s more complicated than that, and this is the bit where I tell you that the simple picture of a proton as consisting of three quarks is kind of a lie. Because, you see, the strong force is strong. Quarks and gluons don’t just sit there being quarks and gluons; they’re constantly doing stuff. Quarks can spontaneously emit a gluon, changing color in the process; or they can absorb a gluon and similarly change color. And gluons couple to themselves; a gluon can emit or absorb another gluon. A gluon can also convert into a quark/antiquark pair; and likewise, a quark/antiquark pair can annihilate into a gluon. And because the strong force is strong, they do this pretty much all the time. The result is that if you could somehow take a snapshot of a proton, you wouldn’t see this:
You’d see something like this:
There are lots of quarks and antiquarks (denoted with a bar above the letter) of all three colors flying around, constantly exchanging gluons, being produced by gluons, and annihilating with each other into gluons. When we say that a proton consists of two up quarks and one down quark, one of each color, what we mean is that if you were to count the quarks in that image above, pairing up each quark with an antiquark of the same flavor and color, you’d end up with two up quarks and a down quark left over at the end, one red, one green, and one blue. We call these three leftovers the “valence quarks”, and the others the “sea quarks”. And to be clear, it’s not as though there are three valence quarks that stand aloof from all the pair production and annihilation going on among the sea quarks; it’s just that at any one time, there are two extra up quarks and one extra down quark. And so, you can think of the extra “binding energy” in the proton’s mass (and, of course, everything I’m saying here applies to the neutron too) as being the energy of that writhing, tumultuous sea of extra quarks and gluons.
But again, if we zoom out a bit, and squint a little, the proton really does look like it’s made out of three quarks, since all the charges and colors of the sea quarks cancel out with each other. For almost all the purposes of most kinds of particle physics, we can pretty much pretend that the proton and neutron consist of three quarks each.
The Residual Strong Force
There’s one more topic I want to touch on before finishing up for today. We’ve talked about how the quarks within a proton or neutron are bound together by the strong force, and we know that electrons are bound to the nucleus of an atom by electromagnetism. What, then, binds an atomic nucleus together? A nucleus consists of protons and neutrons, which are electrically positive and neutral, respectively. The protons, then, should repel each other electrically, so there must be some other force attracting them together – but what force is it?. I remember being very confused about this when I was younger, and the popular physics books I read didn’t seem to give a straight answer.
The answer is that it is the strong force that holds the protons and neutrons together in the nucleus – fundamentally, the same strong force that holds the quarks together in the protons and neutrons. Because of color confinement, any given proton or neutron is color neutral, so, say, two protons won’t exert a direct attraction on each other through the strong force. But the quarks within a proton are not all in the same place. At any one moment, one of the three valence quarks in proton A will be closer to proton B than the other two, and vice versa. This means that from the point of view of a quark in proton B, the three color charges of proton A will not have exactly the same strength, and will not cancel out exactly. So, on average, there will be some leftover, un-cancelled-out, strong force felt between two protons (or between a proton and a neutron, or two neutrons). This is called the “residual strong force”. It is transient, and obviously not as strong as the force between quarks of different colors, but since the strong force is so strong to begin with, even this residual force is enough to overcome the electrical repulsion between protons, once those protons are close enough together. Note that unlike the direct strong force between quarks, this residual strong force does decrease with distance – the farther away you get from a proton, the less it matters that one of its quarks is a tiny bit closer to you than another. If you remember high school chemistry, you might note that this residual strong force is the same basic idea as the “London forces” or “van der Waal forces” between non-polar molecules.
But this is particle physics; we’re supposed to be describing forces in terms of particles being exchanged, right? Indeed, the residual strong force is, fundamentally, a matter of particles being absorbed and emitted. Just as the attraction between quarks comes down to the emission and absorption of gluons, the attraction between protons and neutrons comes down to the emission and absorption of another kind of composite particle, the pion.
I mentioned earlier that there are two ways of making color-neutral composite particles. You can have three quarks, one of each color, which makes a baryon, like the proton or neutron. Or you can have one quark and one antiquark of the same (opposite) color charge, which makes a meson. With the up quark and down quark that we’ve introduced so far, we have four possible combinations. An up quark and an antidown quark make up a , a pion with a charge of +1e. A down and an antiup, similarly, make a , with a charge of -1e. And we can make a neutral either with an up and antiup or a down and an antidown. The charged pions have masses of about 139.6 MeV, the neutral pion about 135 MeV – so, something like one seventh the mass of the proton and neutron. While the proton is stable, and the neutron has a half-life of nearly 15 minutes, the charged pions have half-lives of just 26 nanoseconds (still quite long in the world of particle physics!), and the neutral pion only 84 attoseconds – that is, 8.4*10^-17 seconds. The neutral pion most commonly decays to two photons, the charged pions to some particles we’ll introduce in the next article, the muon and its corresponding neutrino.
But for our purposes here, note that there are allowed processes involving the strong force by which a proton or neutron can emit a pion. Like so:
Here we represent the proton with its three valence quarks drawn together. In reality, of course, there would be all kinds of gluons popping in and out of those quarks, and a host of other “sea quarks”, but as I mentioned, we’re OK just considering the valence quarks for most purposes. So here, we start with a proton, consisting of a blue up quark, a green up quark, and a red down quark. The quarks exchange some gluons, which changes their colors (remember, color charge must be conserved at every vertex), and we end up with two particles coming out of the proton. Remember that when a fermion’s arrow points against the direction of time, that represents the corresponding antiparticle. Thus, what we have here is the emission of a blue down quark and a blue antidown, which together make up a 7.
Thus, a diagram like the following is the sort of process that constitutes the attraction between a proton and neutron in a nucleus.
We can hide away some of that detail and draw that diagram like this:
The shape of this diagram should look familiar from earlier in this article, or from the previous part; it’s much the same as any number of other particle interactions, like this interaction between a positron and an electron:
Only here, in place of the electron and positron, we have two protons, and in place of the photon, we have a pion. I think it’s kind of neat that even though protons and pions are composite particles, quite different from the elementary electrons and photons, we end up with this effective interaction that looks the same as any “fundamental” Feynman diagram, with two fermions exchanging a (virtual) boson.
All right, that’s it for today. Again, this series has just kept getting longer and longer as I’ve gone on, but I think it’s nice to dig into some of this stuff instead of just giving a whirlwind tour. Next time, we’ll meet the rest of the quarks and introduce the weak force, my personal favorite if only because it’s the one I study. Depending on how long that ends up being, we may or may not also get to the rest of the lepton family next time.