
Yes, those are real units.
A barn is a unit of area and can be converted to things like square meters, acres, etc. It equals 10^-24 square centimeters, or about the size of a uranium nucleus. In particle physics, we use barns to measure cross-sections, or how likely two objects are to interact. Think of throwing two balls at each other; the larger the balls are (the greater their cross-sectional areas), the easier it should be to get them to hit. Hence the name, which harkens back to ideas such as "hitting the broad size of a barn." Of course, we're smashing together quantum mechanical objects that don't exactly have a size, and the fact that this quantity has units of area after the unit massaging we did seems suspect . . . but it makes sense and we're running with it.
A barn is actually a huge cross-section for a fundamental particle, and most of the processes we work with are in the microbarn to femtobarn range. Most of the stuff that science articles in the newspaper are in the hundreds of picobarns to femtobarns range. Of course, since our theories can predict these cross-sections, we have a good idea of how likely a particular process is to happen. The formula goes like this:
Number of events you see = cross-section (likelihood event will happen) x luminosity (how much opportunity the event had to happen)
Since the number of events has to be a number, luminosity is typically reported in inverse barns to make the math of the above formula easy. And while luminosity is technically how much chance a particle interaction had of happening and therefore depends on the energy of the accelerator and the number of particles involved and many other things, for a currently running accelerator more luminosity means simply more data. More data of course means you've allowed more physics processes to happen and have a greater chance of seeing rare stuff. More data = good.
The LHC has been running well lately, and so has been taking lots of data. As in, in all of the 2010 running (April - October) the multi-purpose experiments collected about 40 inverse picobarns of data. The LHC can easily deliver that much data in twelve hours now, and recently the accelerator has been pushing towards higher and higher luminosity collisions. We have over 2 inverse femtobarns per experiment recorded so far this year along. For comparison, the Tevatron currently uses about eight inverse femtobarns in its analyses, and those experiments have been running for over ten years. That is a lot of data.

I still occasionally find time to bake, though.
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