Quarks, Annihilation, and Transmutation

Here are two questions about particle physics that I’m sure will drive the physicists nuts, and a third that seems more like chemistry. I do appreciate your bearing with me.

  1. Quarks and Color Charge: So, apparently each of the quarks in a proton or whatever has a different color charge, one of red, green, or blue. My question is, is there any way to tell if a quark has a particular color? Apparently, the colors of quarks are in flux and being traded and so on,* but is it possible to say with some degree of certainty that any particular quark at any particular moment is blue? I guess I’m analogizing color charge to electrical charge, and while positive and negative charges are more or less the same, we can still tell which is which. I’m wondering if we can do something similar with color charge? Also, does the color charge have a magnitude?

  2. Annihilation: How do particles “know” that they’re supposed to annihilate? Apparently, if you bring a positron and an electron together, they’ll turn into photons, but what I don’t get is that if the particles don’t actually take up any space, then how do they collide? What does it mean for them to collide? And what causes the annihilation? Do the two particles have to annihilate, or can they just bounce off each other? What happens if an electron hits an antiproton?

  3. Transmutation: How do you change lead into gold? The Wikipedia article on transmutation gives the equations for changing gold into lead, but that is obviously not very interesting. Are the equations the same, but read from end to beginning, or is it totally different, at least in practice?

  • (Side question: How often does this happen? Once a second? Once a nanosecond? Totally at random?)

The short answer, is no, we cannot tell which is red, green, blue, etc. Your analogy to electrical charge is not terrible, but breaks down for a couple of reasons related to exactly how the strong force works. The main problem with the strong force is a property called asymptotic freedom, which very roughly means that it behaves oppositely to how the electromagnetic force works in that the strength of the interaction decreases as distances get smaller.

What this means is that if you take two colored particles and move them apart, the force will get so strong that additional colored particles will be made out of the vacuum to negate the imbalanced charge. The result is that it is impossible to have free particles that are not color neutral.

That’s fine, you say - I’m talking about quarks in a proton, not free quarks. But now you’re in even more trouble. The contents of the proton are unfortunately not simply three quarks, in the sense that if you hit a proton with something, you will not hit an up quark 2/3 of the time and a down quark 1/3 of the time. There’s a whole bunch of other stuff in there as well.

Even worse, if you accept my definition of the contents of a proton based on what you hit when you shoot things at it, the contents of the proton change with the energy of the particle you shoot at it! The buzzword here, if you’d like to do more reading, is Parton Distribution Functions. So not only can you not really talk about the colors of the quarks that make up the proton, you can’t even talk about what types of quarks they are, or even if they’re quarks at all! At the LHC, which is where I work, we shoot protons at protons and a large fraction of the time, we don’t even hit quarks - we hit gluons instead.

The basic rule of quantum field theory (which is the math underlying particle physics) is that if it can happen, it does. When you describe an interaction, you talk about these things called vertices, which are basically a description of an interaction between (typically) three things. For example, an electron emitting a photon is described by an electron coming in and a photon and electron going out.

You’re allowed to move particles from incoming to outgoing if you flip them from particle to antiparticle. So the electron in to photon + electron out becomes electron and positron in and photon out, or electron/positron annihilation. The why is basically that because electrons and photons interact and there’s this rule (buzzword here is CPT invariance) that says you can move incoming to outgoing with a particle->antiparticle shift.

From an experimentalist (which is what I am) point of view, you ask some good questions when you ask what it means for things to collide and whether they have to annihilate or can they just bounce off each other.

Electrons and positrons can interact in basically two ways: they can annihilate and produce a photon, or one of them can emit a photon which can interact with the other one. A very common outcome of the production of the photon from annihilation is the immediate production of an electron-positron pair from the photon. That is, you get back what you started with! Due to some rules of quantum mechanics, when you get back what you started with, we can’t actually tell on a collision by collision basis whether it was because of annihilation or because they shot a photon at each other.

What determines whether or not we call it a collision is typically whether or not the resulting particles go into our detector or continue down the beampipe, which in turn depends on how much energy is transferred between the two particles. So from a very practical point of view, everything is interacting with everything else, and they only collide when they interact strongly enough to get kicked into our detector.

Nice post Krinthis.

This interests me, becsasuse I was always under the (not massively well-informed) impression that there had been scattering experiments in which quarks had been observed in protons as scattering centres. The other stuff I assume is gluons?:confused:


Sorry if I was a bit unclear. You’re absolutely correct that many scattering experiments have seen quarks in protons. My point was that its not as simple as 2/3 of the time you hit an up quark and 1/3 of the time you hit a down quark. As you say, quite a bit of the proton is made of gluons, and depending on what energy you’re at, heavier quarks (like charm, strange, and bottom) and even anti-quarks.

If you throw a probe (say, an electron) at a proton at sufficiently low energy, you see only a proton. It appears as if it has no substructure. But, we know that saying the proton is fundamental is just a low-energy approximation.

If you increase the energy a bit, you can see evidence of three distinct quarks. But, this too is just a low-energy approximation, and not a terribly good one. The interior of a proton is really a quantum chromodynamical soup. The three quarks you think of (up + up + down) are called the “valence” quarks, and they lead to the proton’s macroscopic quantum numbers. But, they live in a soup of quark-antiquark pairs (“sea” quarks) and gluons. The likelihood of interacting with a sea quark or a gluon increases with energy.

Nevertheless, it is still useful and correct to talk about three quarks in baryons versus the two (quark-antiquark pair) in mesons. For instance, you can predict that the pion-proton scattering rate at high energy will be about two-thirds the proton-proton scattering ratae, simply because there are two-thirds as many valence (non-virtual) quarks in the pion than in the proton.

A few other points to expand on Krinthis’s post…

In a sense, yes, but it isn’t usually discussed. You can just think of it as one unit of colorness in each of three color directions, but with an unusual arithmetic (such that 1R+1G+1B=0).

How does Halley’s comet “collide” with the sun every 75 years without touching it? The answer: the force is long range. In the case of fundamental particle interactions, “long range” is relative, but they are still action-at-a-distance forces. What’s more, the forces here can not only alter the momentum and energy of the participating particles but also their very species.

Even though particles don’t “touch” in the sense you mean, a spatial visualization of particle collision is fruitful, and it is why the term “cross section” is prevalent in particle physics. When you calculate an interaction probability, you often cast it in terms of a “cross section” – the effective cross sectional area of the particles when considering a particular type of interaction. For strong interactions (say, proton-proton), you might have cross sections of 10[sup]-25[/sup] cm[sup]2[/sup]. For weak interactions (neutrino-proton), you might have cross sections of 10[sup]-36[/sup] cm[sup]2[/sup].

Yes, they can just bounce off. In the case of electron-position collision, you can get simple “billiard ball” scattering (a la Halley’s comet), but there is a chance for annihilation to real photons. (Krinthis’s statement about the resulting (single) photon turning right back into something else is for virtual photon production, where there never was an actual photon in the first place. But, real annihilation to real photons (plural – can’t go to only one) happens regularly.)