A post for general readers:
Within the Standard Model, the quarks (and anti-quarks) are my favorite particles, because they are so interesting and so diverse. Physicists often say, in their whimsical jargon, that quarks come in various “flavors” and “colors”. But don’t take these words seriously! They’re just labels; neither has anything to do with taste or vision. We might just as well have said the quarks come in “gerflacks” and “sharjees”; or better, we might have said “types” and “versions”.
Today I’ll show you how one can easily see that each of the six flavors of quark comes in three colors (i.e., each gerflack/type of quark comes in three sharjees/versions.) All we’ll need to do is examine a simple property of the W boson, one of the other particles in the Standard Model.
[Another way to say this is that the Standard Model is often described as having a kind of symmetry named “SU(3)xSU(2)xU(1)”; today we’ll put the “3” in SU(3). ]
Gerflacks and Sharjees of Quarks
We know there are six types/gerflacks/flavors of quarks because each type of quark has its own unique mass and lifetime, a fact that’s relatively easy to confirm experimentally. Quarks 1 and 2 are called down and up, quarks 3 and 4 are called strange and charm, and quarks 5 and 6 are called bottom and top; again, the whimsical names don’t have any meaning, and we often just label them d, u, s, c, b, t.
But to understand why each type of quark comes in three versions/sharjees/colors is more subtle, because two quarks of the same “flavor” which differ only by their “color” appear the same in experiments (despite our intuition for what the word “color” usually means.)
What, in fact, is a “color”? Each color/sharjee/version is a kind of strong nuclear charge, analogous to electric charge, which we encounter in daily life through static electricity and other phenomena. Electric charge determines which objects attract and repel each other via electrical forces. Electrons have electric charge, and so do quarks; that’s why electrical forces affect them. But quarks, unlike electrons, have strong nuclear charge too, and those charges determine how quarks attract or repel one another via the the strong nuclear force.
And here’s the interesting point: whereas there is only one version of electric charge (electrons and protons and atomic nuclei have different amounts of it, but it is different amounts of the same thing), there are three different versions/sharjees/colors of strong nuclear charge. They are often called “red”, “green” and “blue”, or “redness”, “greeness” and “blueness”. (Remember, these are just names for sharjees — for versions of strong nuclear charge. In no sense do they represent actual colors that your eyes would see, any more than the six types/flavors of quarks would taste differently.)
“Color”? Which One?
The particles of the Standard Model which have strong nuclear charge are the quarks, their anti-particles (anti-quarks), and the gluons (associated to the strong nuclear force as photons are associated with electric and magnetic forces.) What strong nuclear charges do they have?
Before answering that, let me remind you about electric charges. Every type of particle in nature has a fixed electric charge. Ordinarily, atoms have electric charge 0 (i.e. they are electrically neutral), but within an atom,
- electrons have electric charge -1,
- protons have electric charge +1,
- neutrons, as their name suggests, are neutral — electric charge 0,
Also, photons, the particles of light that are associated with the electric field and electric forces, are electrically neutral too.
[In first-year university physics, we usually teach that electrons have electric charge “-e“, but professionals, for reasons I won’t address now, prefer to say the charge is “-1” and associate the “e” part of the charge to the electromagnetic force itself.]
In an analogous way,
- A quark has one color: a +1 for one (and only one) of the three sharjees
- An anti-quark has one anti-color: a -1 for one (and only one) of the three sharjees
- A gluon has one color and one anti-color: +1 for one sharjee, and -1 for one sharjee
Notice that while photons have no electric charge, gluons have strong nuclear charge. This has enormous importance. It makes it impossible to observe a particle’s color, because as the particle interacts via the strong nuclear force, its color changes. Metaphorically, a quark is bit like a light bulb that is always on but that flickers rapidly and unpredictably between red, green and blue. Contrast this with the electric charge of electrons, which never changes.
Worse, a quark is always confined within a proton or a neutron or some other hadron, combinations of particles whose total color is zero. We can never isolate a quark and try to examine it carefully; they are stuck inside colorless objects. By contrast, although atoms have zero electric charge, we can separate an electron from an atom and study it in isolation.
Since we never really observe a particle with a definite “color”, how can we possibly count how many colors there are? Fortunately, processes involving other forces, such as the weak nuclear force, don’t care what color a quark has, and so they can count for us.
The Decays of the W Boson
The particles associated with the weak nuclear force are the Z boson and the two W bosons (a W-plus with positive electric charge, and its anti-particle, a W-minus with negative electric charge.) The W bosons have a large mass, over 80 times the mass of a proton. They also have a very short lifetime, decaying in about a trillionth of a trillionth of a second.
Let’s put their decays to good use. Below in Figure 1 are shown the experimentally-observed probabilities for the various decays of the W-minus boson (W–) to an electron or one of its cousins (the muon and the tau) and a corresponding anti-neutrino, or to quark/antiquark pairs. [For W+ bosons, the probabilities are the same, except with each particle replaced by its anti-particle.] A striking pattern appears; of the W’s decays, 11% or about 1/9 are to an electron, and similarly for the muon and the tau, while 33% or about 1/3 — which is 3/9 — go to each quark/anti-quark pair — except the bottom/top pair, where we get zero.
The zero for the last column is easy to understand in terms of a basic rule that applies to all decays: the rule of decreasing rest mass.
- The rest mass of a decaying particle must exceed the total rest mass of the particles emerging from the decay.
Since a top quark has greater mass than does a W boson, decays of a W to a top quark or anti-quark (plus anything else) are forbidden by this rule.
Once we account for this, it’s natural to interpret the experimental results as in Figure 2, where I’ve depicted the three versions/sharjees/colors of the quarks with visual colors. Because the W is color-less, if it decays to a red quark, the accompanying anti-quark must be anti-red (at least at the moment of their creation.) So if there are three colors of down quarks, then there are three ways that a W can decay to a down quark and an up anti-quark, one for each color. That means that in addition to the 3 pairs of electron-like particles and anti-neutrinos, there are really 6 quark/anti-quark pairs corresponding to two flavor possibilities with three colors each. That gives a total of nine pairs, each of which has probability 1/9 = 11%.
Notice that this only works with three colors/sharjees/versions. If we have N quark colors, then N<3 gives too large a probability for decays to electron + anti-neutrino, while N>3 gives one that’s too small. More precisely,
- the probability for W– to decay to electron plus anti-neutrino or any other similar pair = 1 / (3+2N)
- the probability for W- to decay to all colors of a particular quark/anti-quark pair = N / (3+2N)
With the precise measurements available today, it’s clear that only N=3 will do!
A few final comments
This argument has a loophole, for I quietly assumed that the weak nuclear force has the same strength for quarks and electrons. That’s not a foregone conclusion! One could try instead to explain Figure 1 by suggesting that there’s only one color, but the weak nuclear force is stronger for quarks, making W decays to quarks more likely. But such a hypothesis would be inconsistent with other experiments. For instance, the tau (the heaviest cousin of the electron) and the charm quark have very similar masses, and decay in similar ways. Because of this,
- if my original assumption is correct, their lifetimes should be similar, while
- if instead the weak nuclear force is stronger for quarks, then the charm quark should decay faster than the tau and so its lifetime should be markedly shorter.
Experimentally the tau and charm have approximately the same lifetimes, so the assumption is supported by the data. By itself, this piece of evidence doesn’t close the case, but it’s just one of many; decays of neutrons, scattering of neutrinos from atoms, etc. all support the idea that the weak nuclear force is “universal” — has the same strength for all quarks, neutrinos and electron-like particles. Also persuasive, although it requires expertise beyond today’s post, is that there’s no simple math that can make the weak nuclear force stronger for quarks; it leads to inconsistent equations.
The W boson is not the only particle that counts the number of colors. Decays of other particles, such as the Z boson, the Higgs boson, the tau, and the charm and bottom quarks, do so too. But each of these is a bit more complicated than the W, with new subtleties. I’ll return to some of these in later posts.
Finally, decays aren’t the only processes that can tell us the number of colors. In fact, the rate at which collisions of electrons and positrons produce hadrons can tell us both the number of colors per quark type and the electric charges of the different types of quarks. My next post in this series will explain how that works.