Understanding luminosity through 'barn', a unit that helps physicists count particle events
What on earth is a "femtobarn," and what does it have to do with the amount of data an accelerator produces?
At dinner one night in December 1942, physicists M. G. Holloway and C. P. Parker were lamenting the lack of a catchy unit name for discussing the size of an atomic nucleus of uranium. They considered naming a unit of this area "the Oppenheimer" or "the Bethe," after physicists leading a project involving uranium cross sections.
Since Holloway and Parker were on the campus of Purdue University in Indiana, the barn, a dominant feature of Midwestern U.S. farmlands, naturally came to mind.
"Barn" is easier to say than "Oppenheimer" and does not, like "Bethe," sound like the second letter of the Greek alphabet. In June 1943, the barn began appearing in internal technical reports at the secret laboratory at Los Alamos.
The cross-sectional area of a uranium nucleus is about 10 -24 square centimeters, small on the human scale, but large compared with other atomic nuclei. "Femto" means a factor of 10-15: a thousandth of a millionth of a millionth. A femtobarn, then, is 10-39 square centimeters an incomprehensibly small unit of area.
Imagine you throw enough tomatoes at a barn to get an average of two tomato hits per square foot. If the barn door is 10 feet by 15 feet, then the cross section for tomato-barn door interactions is 150 square feet, and the number of tomatoes that splat on the door is given by:
150 square feet x 2 tomatoes per square foot = 300 tomato interactions.
In this case, what physicists call the integrated luminosity is 2 tomatoes per square foot (or, in physics jargon, 2 "inverse square feet").
So, to calculate how many B-meson pairs PEP-II had delivered by July 1, you multiply the cross-section for those events (1.1 million femtobarns) by the integrated luminosity (100 events per femtobarn), and you get 110,000,000 events.
Now, the only question left is why physicists make something so simple sound so complicated.