While it’s nice to know about electrons, up quarks, and down quarks, there are a lot of weird numbers to remember about them. Imagine how scientists felt, then, when they found out that there are more than a hundred more particles to learn the numbers for! It’s too complicated to memorize all that stuff, and it doesn’t explain anything. What we need are easy-to-remember patterns. That’s what The Standard Model gives us.
Elementary Fermions
We’ll start with the patterns for elementary fermions. Elementary fermions are the particles that are good for making stuff. We’ll worry about the other particles, the elementary bosons, later.
The standard model says that we can describe fermions using a mathematical idea called U(1)×SU(2)×SU(3). The “U(1)” part tells us that every fermion has a hypercharge, the “SU(2)” part tells us that every fermion has an isospin, and the “SU(3)” part tells us that every fermion has a color. So now you know why we were talking about hypercharge, isospin, and color. But what’s more interesting is that U(1)×SU(2)×SU(3) is a subgroup of SU(5),[1] which is a fancy math way of saying that you can pick a fermion and know nearly everything about it by answering five yes/no questions. Here are the five questions:
It the fermion isospin up? (Worth +1 hypercharge and +1/2 isospin, which means +1 charge.)
It the fermion isospin down? (Worth +1 hypercharge and -1/2 isospin, which means no change in charge.)
It the fermion red? (Worth -2/3 hypercharge, which means -1/3 charge.)
It the fermion green? (Worth -2/3 hypercharge, which means -1/3 charge.)
It the fermion blue? (Worth -2/3 hypercharge, which means -1/3 charge.)
This is kind of like making a character in a video game; you answer the questions and see what it does to the particle’s stats. No matter how you answer, you will always get the stats for a real fermion.
For example, let’s say I design a particle that is isospin up but not down and has only the color red. My answers would be “yes”, “no”, “yes”, “no”, and “no”, or YNYNN when abbreviated. Then the particle’s hypercharge will be 1 - 2/3 = +1/3, its isospin will be +1/2, and its charge will be 1 - 1/3 = 2/3. That sounds exactly like a left-handed red up quark.
In fact, the answers to the five questions not only tell you stats, but also tell you other things:
A fermion is right-handed if the number of “yes” answers is odd. It is left-handed if the number of “yes” answers is even.
A fermion is matter if the number of “yes” answers to color questions is odd. It is antimatter if the number of “yes” answers to color questions is even.
A fermion is a lepton if the color questions all have the same answer. It is a quark if the color questions have different answers.
A lepton is a charged lepton if the “isospin up” question has a different answer than the color questions. It is a neutrino if the “isospin up” question and the color questions all have the same answers.
A lepton is white if it is matter and black if it is antimatter.
A quark is red, green, or blue if that is the only color with a “yes” answer. A quark is antired, antigreen, or antiblue if the opposite is the only color with a “no” answer.
The one thing these questions can’t easily tell you is how heavy the particle is. But you can sort-of tell by answering a sixth question:
Is the fermion first-generation (light and unlikely to fall apart), second generation (heavy and quick to fall apart), or third generation (extremely heavy and extremely quick to fall apart)?
Again, you can make any choice you want here and still be talking about a real particle.
Elementary Bosons (Force Carriers)
Now imagine an experiment: We smash together a left-handed red down quark (NYYNN, isospin=-1/2) and a left-handed electron neutrino (YNYYY, isospin=+1/2). Because they are both have nonzero isospin, the weak force can affect them. One way that could happen is that they switch isospin answers (the first two yes/no answers) with each other. That means that the quark changes to YNYNN, a left-handed red up quark, and the neutrino changes to NYYYY, a left-handed electron. But other outcomes never happen. Why?
One important rule is that when two particles affect each other using some force, the changes to one particle have to be balanced out by changes to the other. If one particle loses something, the other has to gain it. In The Standard Model, a something that can be lost or gained because of a force is called a force carrier or an elementary boson.
In the example, the quark lost its isospin downness (worth +1 hypercharge and -1/2 isospin) and gained isospin upness (worth +1 hypercharge and +1/2 isospin), so the neutrino had to gain isospin downness and lose isospin upness. Or, said another way, the quark gave away 1 isospin downness and -1 isospin upness to the neutrino through the weak force. That transfer, 1 isospin downness and -1 isospin upness together, is called the W⁻ boson, which is a force carrier for the weak force. And we can compute its stats by knowing what its changes are worth: (+1 hypercharge and -1/2 isospin) - (+1 hypercharge and +1/2 isospin) = (0 hypercharge and -1 isospin).
The give and take doesn’t have to be giving and taking question answers though. For instance, the electromagnetic force’s boson is a photon. When particles exchange photons, they transfer momentum and energy, not anything to do with their types.
In some cases, force carriers can also exist on their own, without obviously being part of a trade. For example, sometimes an electron in an atom loses momentum and energy by shooting a photon off into empty space. We call photons like that light.
Inside The Standard Model, these are the fundamental force carriers:
The B boson is the force carrier for hypercharge.
The W⁻, W⁰, and W⁺ bosons are the force carriers for isospin.
Eight gluons are force carriers for color. (There are different sets of eight gluons that you can pick to describe the effects of the strong force. Scientists don’t agree on which set of eight is the best one.)
The Higgs boson is unlike all the other force carriers. It follows unusual rules, and it makes other particles follow unusual rules. The only way to overcome those effects is with an insane amount of energy.
However, you won’t hear many people talking about the B boson or the W⁰ boson. The reason is that the Higgs boson messes up how they work, so we don’t see them on their own. Instead, we usually see them in special combinations:
The Z boson is the combination of a W⁰ boson minus half of a B boson, and
The photon is the combination of a W⁰ boson plus half of a B boson.
So the weak force’s force carriers are usually listed as the W⁻, Z, and W⁺ bosons, while the electromagnetic force’s force carrier is the photon. (Remember how the B boson goes with hypercharge, and the W⁰ boson goes with isospin? Since the photon is half of a B boson plus a W⁰ boson means, that’s where we get the Gell-Mann–Nishijima formula from, the rule that electric charge is half a particle’s hypercharge plus its isospin.)
For a while, scientists thought that SU(5) would be enough all by itself to describe fermions. Unfortunately, when they tried that, their computations said that protons can fall apart, which nobody has ever seen happen, so the scientists knew they were still missing something. They have ideas, but the search for the right something continues even today. ↩︎
Bonus Appendix: Catalog of Elementary Fermions in The Standard Model
Here is a list of the 32 elementary fermions in the Standard Model’s first generation. The letters at the beginning tell you the answers to the five questions in order, and they are followed by one of the particle’s names and its stats.
Grade 0 (zero “yes” answers):
NNNNN: left-handed electron antineutrino; hypercharge=0, isospin=0, color=black
YYYYY: right-handed electron neutrino; hypercharge=0, isospin=0, color=white
The 32 fermions in the second generation follow the same pattern, but replace the word “electron” with “muon”, the word “up” with “charm”, and the word “down” with “strange”. For the 32 fermions in the third generation, replace the word “electron” with “tau”, the word “up” with “top”, and the word “down” with “bottom”.
Patterns
While it’s nice to know about electrons, up quarks, and down quarks, there are a lot of weird numbers to remember about them. Imagine how scientists felt, then, when they found out that there are more than a hundred more particles to learn the numbers for! It’s too complicated to memorize all that stuff, and it doesn’t explain anything. What we need are easy-to-remember patterns. That’s what The Standard Model gives us.
Elementary Fermions
We’ll start with the patterns for elementary fermions. Elementary fermions are the particles that are good for making stuff. We’ll worry about the other particles, the elementary bosons, later.
The standard model says that we can describe fermions using a mathematical idea called U(1)×SU(2)×SU(3). The “U(1)” part tells us that every fermion has a hypercharge, the “SU(2)” part tells us that every fermion has an isospin, and the “SU(3)” part tells us that every fermion has a color. So now you know why we were talking about hypercharge, isospin, and color. But what’s more interesting is that U(1)×SU(2)×SU(3) is a subgroup of SU(5),[1] which is a fancy math way of saying that you can pick a fermion and know nearly everything about it by answering five yes/no questions. Here are the five questions:
This is kind of like making a character in a video game; you answer the questions and see what it does to the particle’s stats. No matter how you answer, you will always get the stats for a real fermion.
For example, let’s say I design a particle that is isospin up but not down and has only the color red. My answers would be “yes”, “no”, “yes”, “no”, and “no”, or YNYNN when abbreviated. Then the particle’s hypercharge will be 1 - 2/3 = +1/3, its isospin will be +1/2, and its charge will be 1 - 1/3 = 2/3. That sounds exactly like a left-handed red up quark.
In fact, the answers to the five questions not only tell you stats, but also tell you other things:
The one thing these questions can’t easily tell you is how heavy the particle is. But you can sort-of tell by answering a sixth question:
Again, you can make any choice you want here and still be talking about a real particle.
Elementary Bosons (Force Carriers)
Now imagine an experiment: We smash together a left-handed red down quark (NYYNN, isospin=-1/2) and a left-handed electron neutrino (YNYYY, isospin=+1/2). Because they are both have nonzero isospin, the weak force can affect them. One way that could happen is that they switch isospin answers (the first two yes/no answers) with each other. That means that the quark changes to YNYNN, a left-handed red up quark, and the neutrino changes to NYYYY, a left-handed electron. But other outcomes never happen. Why?
One important rule is that when two particles affect each other using some force, the changes to one particle have to be balanced out by changes to the other. If one particle loses something, the other has to gain it. In The Standard Model, a something that can be lost or gained because of a force is called a force carrier or an elementary boson.
In the example, the quark lost its isospin downness (worth +1 hypercharge and -1/2 isospin) and gained isospin upness (worth +1 hypercharge and +1/2 isospin), so the neutrino had to gain isospin downness and lose isospin upness. Or, said another way, the quark gave away 1 isospin downness and -1 isospin upness to the neutrino through the weak force. That transfer, 1 isospin downness and -1 isospin upness together, is called the W⁻ boson, which is a force carrier for the weak force. And we can compute its stats by knowing what its changes are worth: (+1 hypercharge and -1/2 isospin) - (+1 hypercharge and +1/2 isospin) = (0 hypercharge and -1 isospin).
The give and take doesn’t have to be giving and taking question answers though. For instance, the electromagnetic force’s boson is a photon. When particles exchange photons, they transfer momentum and energy, not anything to do with their types.
In some cases, force carriers can also exist on their own, without obviously being part of a trade. For example, sometimes an electron in an atom loses momentum and energy by shooting a photon off into empty space. We call photons like that light.
Inside The Standard Model, these are the fundamental force carriers:
However, you won’t hear many people talking about the B boson or the W⁰ boson. The reason is that the Higgs boson messes up how they work, so we don’t see them on their own. Instead, we usually see them in special combinations:
So the weak force’s force carriers are usually listed as the W⁻, Z, and W⁺ bosons, while the electromagnetic force’s force carrier is the photon. (Remember how the B boson goes with hypercharge, and the W⁰ boson goes with isospin? Since the photon is half of a B boson plus a W⁰ boson means, that’s where we get the Gell-Mann–Nishijima formula from, the rule that electric charge is half a particle’s hypercharge plus its isospin.)
For a while, scientists thought that SU(5) would be enough all by itself to describe fermions. Unfortunately, when they tried that, their computations said that protons can fall apart, which nobody has ever seen happen, so the scientists knew they were still missing something. They have ideas, but the search for the right something continues even today. ↩︎
Bonus Appendix: Catalog of Elementary Fermions in The Standard Model
Here is a list of the 32 elementary fermions in the Standard Model’s first generation. The letters at the beginning tell you the answers to the five questions in order, and they are followed by one of the particle’s names and its stats.
The 32 fermions in the second generation follow the same pattern, but replace the word “electron” with “muon”, the word “up” with “charm”, and the word “down” with “strange”. For the 32 fermions in the third generation, replace the word “electron” with “tau”, the word “up” with “top”, and the word “down” with “bottom”.