Particle Physics

The Standard Model More Deeply: Lessons on the Strong Nuclear Force from Quark Electric Charges

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For readers who want to go a bit deeper into details (though I suggest you read last week’s posts for general readers first [post 1, post 2]):

Last week, using just addition and subtraction of fractions, we saw that the ratio of production rates

  • R = Rate (e+ e— ⟶ quark anti-quark) / Rate (e+ e— ⟶ muon anti-muon)

(where e— stands for “electron” and e+ for “positron”) can be used to verify the electric charges of the quarks of nature. [In this post I’ll usually drop the word “electric” from “electric charge”.] Specifically, the ratio R, at different energies, is both sensitive to and consistent with the Standard Model of particle physics, not only confirming the quarks’ charges but also the fact that they come in three “colors”. (About colors, you can read recent posts here, here and here.)

To keep the previous posts short, I didn’t give evidence that the data agrees only with the Standard Model; I’ll start today by doing that. But I did point out that the data doesn’t quite match the simple prediction. You can see that in the figure below, repeated from last time; it shows the data (black dots) lies close to the predictions (the solid lines) but generally lies a few percent above them. Why is this? The answer: we neglected a small but noticeable effect from the strong nuclear force. Not only does accounting for this effect fix the problem, it allows us to get a rough measure of the strength of the strong nuclear force. From these considerations we can learn several immensely important facts about nature, as we’ll see today and in the next post.

Figure 1: Data (black dots) showing R as a function of the collision energy 2Ee. Horizontal colored lines show the three predictions for R in the regions where the data is simple and 3, 4 or 5 of the quarks are produced. The minor jumpiness in the data is due to measurement imperfections.

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Celebrating the Standard Model: Checking The Electric Charges of Quarks

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A post for general readers who’ve heard of quarks; if you haven’t, you might find this article useful:

Yesterday I showed you that the usual argument that determines the electric charges of the various types of quarks uses circular reasoning and has a big loophole in it. (The up quark, for example, has charge 2/3, but the usual argument would actually allow it to have any charge!) But today I’m going to show you how this loophole can easily be closed — and we’ll need only addition, subtraction and fractions to close it.

Throughout this post I’ll shorten “electric charge” to just “charge”.

A Different Way to Check Quark Charges

Our approach will be to study the process in which an electron and a positron (the electron’s anti-particle) collide, disappear (“annihilate”), and are converted into one or another type of quark and the corresponding anti-quark; see Figure 1. The rate for this process to occur, and the rate of a similar one in which a muon and anti-muon are produced, are all we will need to know.

In an electron-positron collision, many things may happen. Among the possibilities, the electron and positron may be converted into two new particles. The new particles may have much more mass (specifically, rest mass) than the electron and positron do, if the collision is energetic enough. This is why physicists can use collisions of particles with small mass to discover unknown particles with large mass.

Figure 1: (Top) an electron and positron, each carrying energy Ee, collide head-on. (Bottom) from the collision with total energy 2Ee , a quark and anti-quark may emerge, as long as Ee is bigger than the quark’s rest mass M times c2.

In particular, for any quark of mass M, it is possible for an electron-positron collision to produce that quark and a corresponding anti-quark as long as the electron’s energy Ee is greater than the quark’s mass-energy Mc2. As Ee is gradually increased from low values, more and more types of quark/anti-quark pairs can be produced.

This turns out to be a particularly interesting observation in the range where 1 GeV < Ee < 10 GeV, i.e. when the total collision energy (2 Ee) is between 2 and 20 GeV. If Ee is any lower, the effects of the strong nuclear force make the production of quarks extremely complicated (as we’ll see in another post). But when the collision energy is above 2 GeV, things start to settle down, and become both simple and interesting.

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Celebrating the Standard Model: The Electric Charges of Quarks

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A post for general readers who’ve heard of quarks; if you haven’t, try reading here:

The universe has six types of quarks, some of which are found in protons and neutrons, and thus throughout all ordinary material. For no good reasons, we call them up, down, strange, charm, bottom and top. Today and tomorrow I want to show you how we know their electric charges, even though we can’t measure them directly. The only math we’ll need is addition, subtraction, and fractions.

This also intersects with my most recent post in this series on the Standard Model, which explained how we know that each type of quark comes in three “colors”, or versions — each one a type of strong nuclear charge akin to electric charge.

Today we’ll review the usual lore that you can find in any book or on any website, but we’ll see that there’s a big loophole in the lore that we need to close. Tomorrow we’ll use a clever method to close that loophole and verify the lore is really true.

The Lore for Protons and Neutrons

Physicists usually define electric charge so that

  • the proton has electric charge +1
  • the electron has charge -1,
  • the neutron has charge 0 (i.e. electrically neutral, hence its name).

[Throughout the remainder of this post, I’ll abbreviate “electric charge” as simply “charge“.]

As for the six types of quarks, the lore is that their charges are [using notation that “Qu” means “electric charge of the u quark“]:

  • Up, Charm, Top (u,c,t): Qu = Qc = Qt = 2/3
  • Down, Strange, Bottom (d,s,b): Qd = Qs = Qb = -1/3

But how do we know this?

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The Standard Model More Deeply: Gluons and the Math of Quark “Color”

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For readers who want to dig deeper; this is the second post of two, so you should read the previous one if you haven’t already. (Readers who would rather avoid the math may prefer this post.)

In a recent post I described, for the general reader and without using anything more than elementary fractions, how we know that each type of quark comes in three “colors” — a name which refers not to something that you can see by eye, but rather to the three “versions” of strong nuclear charge. In the post previous to today’s, I went into more detail about how the math of “color” works; you’ll need to read that post first, and since I will sometimes refer to its figures, you may want to keep in handy in another tab.

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The Standard Model More Deeply: The Simplified Math of Quark “Color”

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For non-expert readers who want to dig a bit deeper. This is the first post of two, the second of which will appear in a day or two:

In my last post I described, for the general reader and without using anything more than elementary fractions, how we know that each type of quark comes in three “colors” — a name which refers not to something that you can see by eye, but rather to the three “versions” of strong nuclear charge. Strong nuclear charge is important because it determines the behavior of the strong nuclear force between objects, just as electric charge determines the electric forces between objects. For instance, elementary particles with no strong nuclear charge, such as electrons, W bosons and the like, aren’t affected by the strong nuclear force, just as electrically neutral elementary particles, such as neutrinos, are immune to the electric force.

But a big difference is that there’s only one form or “version” of electric charge: in the language of professional physicists, protons have +1 unit of this charge, electrons have -1 unit of it, a nucleus of helium has +2 units of it, etc. By contrast, the strong nuclear charge comes in three versions, which are sometimes referred to as “redness”, “blueness” and “greenness” (because of a vague but highly imprecise analogue with the inner workings of the human eye). These versions of the charge combine in novel ways we don’t see in the electric context, and this plays a major role in the protons and neutrons found in every atom. It’s the math that lies behind this that I want to explain today; we’ll only need a little bit of trigonometry and complex numbers, though we’ll also need some careful reasoning.

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Celebrating the Standard Model: How We Know Quarks Come in Three “Colors”

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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.)

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The Standard Model More Deeply: The Nature of Neutrinos

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Earlier this week I explained how neutrinos can get their mass within the Standard Model of particle physics, either by engaging with the Higgs field once, the way the other particles do, or by engaging with it twice. In the first case, the neutrinos would be “Dirac fermions”, just like electrons and quarks. In the second, they’d be “Majorana fermions”. Decades ago, in the original Standard Model, neutrinos were thought not to have any mass at all, and were “Weyl fermions.” Although I explained in my last post what these three types of fermions are, today I want go a little deeper, and provide you with a diagrammatic way of understanding the differences among them, as well as a more complete view of the workings of the “see-saw mechanism”, which may well be the cause of the neutrinos’ exceptionally small masses.

[N.B. On this website, mass means “rest mass” except when otherwise indicated.]

The Three Types of Fermions

What’s a fermion? All particles in our world are either fermions or bosons. Bosons are highly social and are happy to all do the same thing, as when huge numbers of photons are all locked in synch to make a laser. Fermions are loners; they refuse to do the same thing, and the “Pauli exclusion principle” that plays a huge role in atomic physics, creating the famous shell structure of atoms, arises from the fact that electrons are fermions. The Standard Model fermions and their masses are shown below.

Figure 1: The masses of the known elementary particles, showing how neutrino masses are much smaller and much more uncertain than those of all the other particles with mass. The horizontal grey bar shows the maximum masses from cosmic measurements; the vertical grey bars give an idea of where the masses might lie based on current knowledge, indicating the still very substantial uncertainty.

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Celebrating the Standard Model: Why Are Neutrino Masses So Small?

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For the general reader interested in particle physics or astronomy:

Most of the Standard Model’s particles have a mass [a rest mass, to be precise], excepting only the photon (the particle of light) and the gluon (found in protons and neutrons.) For reasons not understood at all, these masses stretch out over a range of a trillion or more.

If it weren’t for the three types of neutrinos, the range would be a mere 400,000, from the top quark’s mass (172 GeV/c2) to the electron’s (0.000511 GeV/c2), still puzzling large. But neutrinos make the puzzle extreme! The universe’s properties strongly suggest that the largest mass among the neutrinos can’t be more than 0.0000000001 GeV/c2 , while other experiments tell us it can’t be too much less. The masses of the other two may be similar, or possibly much smaller.

Figure 1: The masses of the known elementary particles, showing how neutrino masses are much smaller and much more uncertain than those of all the other particles with mass. The horizontal grey bar shows the maximum masses from cosmic measurements; the vertical grey bars give an idea of where the masses might lie based on current knowledge, indicating the still very substantial uncertainty.

This striking situation is illustrated in Figure 1, in which

  • I’ve used a “logarithmic plot”, which compresses the vertical scale; if I used a regular “linear” plot, you’d see only the heaviest few masses, with the rest crushed to the bottom;
  • For later use, I’ve divided the particles into two classes: “fermions” and “bosons”.
  • Also, though some of these particles have separate anti-particles, I haven’t shown them; it wouldn’t add anything, since the anti-particle of any particle type has exactly the same mass.

As you can see, the neutrinos are way down at the bottom, far from everyone else? What’s up with that? The answer isn’t known; it’s part of ongoing research. But today I’ll tell you why

  • once upon a time it was thought that the Standard Model solved this puzzle;
  • today we know of two simple solutions to it, but don’t know which one is right;
  • each of these requires a minor modification of the Standard Model: in one case a new type of particle, in another case a new phenomenon.

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