It’s a busy time in the physics/life/web world: Fermilab may have broken the Standard Model (but probably not), Physics Stack Exchange is holding moderator elections, and most importantly, Mythbusters is back on with a new season. But I kind of have to ignore all that since I’m preparing for my comprehensive exam next week.

For those not familiar with it, the comprehensive exam at Penn State basically marks the transition from being primarily a student to being primarily a researcher. Accordingly, I’m starting to get questions about what my research is about — not that people didn’t ask before, but it’s reaching the point where “some high-energy stuff” ceases to be an adequate answer. So I’ve been thinking about how to concisely explain what I’m trying to do with my time. The more I think about this, the more I think it’s a good exercise for anyone in physics to go through; after all, if you can’t summarize what you’re doing at some level to a non-specialist, do you really understand it?

At a high level, the project I’m on right now deals with the rapidity evolution of the saturation momentum for parton distribution functions. But let me break that down. In QCD, the quantum theory that describes the internal structure of hadrons (like the proton), one of the mathematical objects we work with is a parton distribution function (PDF, no relation to the file type). Essentially, when you shoot a “probe” (particle) at a hadron, a PDF tells you the probability that your probe will interact with one of the constituents of the hadron. Since, in quantum physics, the content of a particle can be influenced by the way you detect it, the PDF depends on both the square of the probe momentum, \(Q^2\), and a variable \(x\) which is related to the momentum of the constituent particle.

The main reason these PDFs are theoretically useful is that once we measure them for certain values of \(x\) and \(Q^2\), we can predict them at other values of \(x\) and \(Q^2\), for other collisions that perhaps haven’t been or can’t be carried out. The equations that allow us to make these predictions are called the DGLAP equation and the BFKL equation. Specifically, the DGLAP equation tells you how the PDF changes as you increase the probe momentum \(Q^2\), and the BFKL equation tells you how the PDF changes as you decrease the momentum variable \(x\).

But there is a problem. The BFKL equation normally predicts that as you decrease \(x\), the PDF gets larger and larger, which corresponds to there being more and more constituent particles in the hadron with that particular value of \(x\). Eventually you reach a point at which the number of particles you would expect to find, based on the value of the PDF, simply can’t fit — mathematically, the equation starts producing nonsensical results. This point is called the saturation scale, and its exact value depends somewhat on the value of \(x\). In order to work around the runaway growth in the PDF, we need to know how the saturation scale depends on \(x\).

Now, as it turns out, nobody knows how to write down the BFKL equation exactly; the best we can do is approximate it, either by a perturbation series, or by making an “educated guess” at the true form of the equation. Naturally, the way in which the saturation scale depends on \(x\) changes, depending on which BFKL approximation you use. This is where my research project comes in. We’re trying to calculate the dependence of the saturation scale on \(x\) using a better BFKL approximation than anyone else has so far.

Anyway, the point is that despite having a bunch of great things I could be writing about here, I’ll be conspicuously absent from this site for the next couple weeks. At least now you know what I’m doing, and I’m sure it’s a better excuse than just being lazy like I usually am :-)