Fine Structure

Parton Distribution Functions

With the abundance of talk recently about the LHC coming online and all the work the Tevatron is doing to reach the very limits of it's power, I figured it's only a matter of time before someone mentions a topic that is just on the edge of my knowledge and inspires more research into how these machines work. David from Shores of the Dirac Sea posted about luminosity and barns recently, something I've covered very briefly before, and he made a comment which strayed from how I understood protons. He was discussing the fact that scientists use only a small fraction of the events (collisions) produced when 600 million protons finally cross paths. Specifically, he said:

"Most of the times, the quarks and gluon bits scatter at relatively low energies, and only very seldom do the individual pieces of each proton carry enough stuff in them to make a really big collision."

This was curious, I always thought protons were all the same - or at least had the same amount of stuff in them. Three quarks make up most of the particles we're familiar with and the particular arrangement of quarks defines what particle they represent. So this begged the question...

What makes certain protons different enough that some of them make interesting events and but most don't?

So I left David a comment to that effect. Shortly afterwards he came back with an answer and one of the best analogies in particle physics I've ever heard. David suggested that yes, all protons contain two up quarks and a down quark. The distinguishing factor is how all the quarks and gluons that make up a proton hold some fraction of the total proton momentum, just like the total momentum of you driving in your car is made up by momentum of yourself and the momentum of your car. Inside of a proton, this division of momentum is defined by the parton distribution function. More on that in a minute. David continued by giving an analogy for particle collider events:

"To give you a picture: think of a proton as a big bag of jello with very few ball bearings. If the jello scatters it is not interesting, but if the bearings find each other, then it is. This happens randomly."

And this, dear readers, is a brilliant example of a physics analogy. Too often these analogies are created with really obvious defects that break down in the similarities between what you're trying to explain and what's familiar to the student, not to mention occasions when the analogy completely fails to hit common ground. This one actually deserves to be carried out in an "experiment" (Lime Jello Collider, anyone?).

So, moving past our jellocelerator, we're still left with this mysterious parton distribution function which tells us about momentum within the proton. Thinking classically (which we should really stop doing), we would think that half the momentum would be held in the down quark, the other half divided equally between two up quarks and gluons holding none. Unfortunately, things moving at close to the speed of light behave curiously so we have some more investigation to do before answering the qustion...

What is a parton distribution function?

From what I gather, parton distribution functions represent the probability of finding a particular part of a proton (or other hadron) with a particular chunk of the original momentum. At first glace, you may think "distribution" relates to where the quark is likely to be found inside a proton (similar to electron densities) but this would be false! "Distribution" refers to how the total momentum is split up between each of the components and these distribution functions define those numbers, based on the components and the total energy. Actual location (or density probability) doesn't seem to play much of a role here which seems to be related to David's "This happens randomly" remark. Curiously, parton distribution functions are purely experimentally defined and there's currently no way to theoretically predict them. There are plenty of sites listing huge tables of these probability functions, so I imagine if you want to observe what happens when up quarks collide at high energies you'd look up the highest probability for high-energy up quarks in these tables, find the correlating momentum for a particular hadron and set your particle accelerator to spin those hadrons to reach that momentum level before eventually colliding them. Naturally, you'd collide a lot of these hadrons in the hope of seeing your collision at a certain rate.

Okay, I think we still have some questions but we'll leave it here for now. I'm starting a new page listing open physics questions that I still have after a post like this and I'd like to welcome anyone with an answer to leave it in the comments or contact me if you'd like to guest post about it. As always, the comments are open for clarifications, corrections and other related questions that you're curious about.

Questions we didn't answer: