## Protons and Charm Quarks: A Lesson From Virtual Particles

There’s been a lot of chatter lately about a claim that charm quarks are found in protons. While the evidence for this claim of “intrinsic charm” (a name that goes back decades) is by no means entirely convincing yet, it might in fact be true… sort of. But the whole idea sounds very confusing. A charm quark has a larger mass than a proton: about 1.2 GeV/c2 vs. 0.938 GeV/c2. On the face of it, suggesting there are charm quarks in protons sounds as crazy as suggesting that a football could have a lead brick inside it without you noticing any difference.

What’s really going on? It’s a long story, and subtle even for experts, so it’s not surprising that most articles about it for lay readers haven’t been entirely clear. At some point I’ll write a comprehensive explanation, but that will require a longer post (or series of posts), and I don’t want to launch into that until my conceptual understanding of important details is complete.

But in the meantime, here’s a related question: how can a particle with zero mass (zero rest mass, to be precise) spend part of its time as a combination of objects that have positive mass? For instance, a photon [a particle of light, including both visible and invisible forms of light] has zero rest mass. [Note, however, that it has non-zero gravitational mass]. Meanwhile electrons and positrons [the anti-particles of electrons] both have positive rest mass. So what do people mean when they say “A photon can be an electron-positron pair part of the time”? This statement comes with a fancy “Feynman diagram”, in which the photon is shown as the wavy line, time is running left to right, and the loop represents an electron and a positron created from the photon.

## Celebrating the Standard Model: Checking The Electric Charges of Quarks

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.

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.