Even as a student I had trouble with the Dirac equation and its implication that an infinitely small thing could also be spinning around its axis. It just bothered me somehow. My classmates would quote Lewis Carroll at me, saying that I should be able to believe at least one impossible thing before breakfast. The White Queen, after all, could believe six, and she wasn’t even a physicist. Still, I felt more like Alice and regarded the whole thing as absurd.
Yet it is so. Not only is Dirac’s equation mathematically sound, there are a dozen different particles that move in accordance with it as verified by very many very precise experiments. The electron is one. If it has any size to it at all, it must be less than 0.0000000000000000008 inches across, more or less. The top quark is another such particle. And of course it might be either spinning in one direction or spinning in the other direction.
“Correlation” just means that two things tend to happen together, for example, wet driveways and rainfall. We often think that correlation implies causation – that the driveway is wet because there is rainfall. That is not necessarily true. Things can tend to happen together without one causing the other. Washing your car can cause there to be water all over your driveway, and of course we have all suspected that it will cause rainfall as well.
Most of the top quarks produced in the Tevatron (and the LHC) are produced as quark–antiquark pairs. Both move according to the Dirac equation, and both spin one way or the other.
So, to measure spin correlations in top pair production is to ask, “If one of the tops is spinning in this direction, is the other likely to be spinning the same way? Or is it likely to be spinning the opposite way? Or do you not have a good chance of knowing?” The reason we want to know is to learn about the details of top pair production. If the top pair was produced by colliding quarks within the beam protons, knowing the spin of one top tells us that the other spin will almost surely be the same. If, however, colliding gluons made the tops, their spins would tend to be opposite each other about two-thirds of the time.
Recently, DZero measured the correlation of spins in top pairs produced at the Tevatron using its full data set. The result matches the prediction of the Standard Model very well. The measured correlation also tells us the fraction of top pairs produced by colliding gluons, and this result is also in agreement with the theoretical predictions.
But this business of zero-sized particles spinning around their axes still doesn’t seem quite right to me.