A Quantum Diaries Survivor

The Tevatron has been painstakingly producing proton-antiproton collisions for six years now, at an accelerating pace. The goal of 3 inverse femtobarns of collisions has now been crossed, as shown in the graph below (of which you can always find an up-to-date version in  http://www.fnal.gov/pub/now/tevlum.html ).

To understand what the heck is a integrated luminosity of  three inverse femtobarns, just think about shooting a lot of bullets with a short gun at a dime placed ten yards away. You do not expect to hit the dime, do you ? In fact, your bullets will cover a wide area around the dime rather randomly - say an area of about a square foot wide (if you are good). In order to hit the dime you will on average need to shoot a number of bullets equal to the ratio between the area covered by the dime (about a sixth of a square inch, or one cm^2) and one square foot - or about a thousand of them.

Let us put this in a tidier form: if we shot 1000 bullets per square foot, that is exactly the same concept physicists talk about when discussing the amount of collisions they managed to make: an “integrated luminosity”  L = 1000/sq ft, or about 1/cm^2 since a square foot is about 1000 cm^2. Since the dime has a cross section S of one cm^2, you expect to have made N=  SL = 1 cm^2 x 1/cm^2 = 1 hit on average!

Now, physicists use the same line of reasoning to estimate the chance of producing a rare process when colliding particles.  Rare processes have a very small cross section, and so to produce them we need to shoot many bullets! The dreaded “inverse femtobarn” is nothing but a measure of the number of bullets we shot per unit area. A femtobarn is the impossibly small area of 10^-39 cm^2: the area of a square whose side is a few billionths of a billionth of a meter. So three inverse femtobarns means having “illuminated” with three protons every such square of the incoming antiproton.

With three inverse femtobarns, one can produce really rare processes. The total cross section of a proton-antiproton collision is about S = 10^-25 cm^2, so with L=3/fb = 3/(10^-39 cm^2) we have actually produced N = SL = 3 x 10^14 collisions (or three hundred thousand billions)! Now, a really rare process such as Higgs boson production has a cross section of a few hundred femtobarns: with 3 inverse femtobarns of data we expect to have produced several hundreds of them!

The problem, then, is finding these few hundred Higgs bosons in the three hundred thousand billions… Hehm. It is much harder than finding the dime once it was hit by your bullet!

Not to worry. CDF and D0 are up to the task. And the Tevatron is expected to more than double the total amount of collisions it produced this far by the end of 2009… More dimes to find, more chances to get rich.